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Argilla Warehouse 16

Science Fair Project Encyclopedia The chloride ion is formed when the element chlorine picks up one electron to form the anion (negatively charged ion) Cl−. The salts of hydrochloric acid HCl contain chloride ions and are also called chlorides. An example is table salt, which is sodium chloride with the chemical formula NaCl. In water, it dissolves into Na+ and Cl− ions. The word chloride can also refer to a chemical compound in which one or more chlorine atoms are covalently bonded in the molecule. This means that chlorides can be either inorganic or organic compounds. The simplest example of an inorganic covalently bonded chloride is hydrogen chloride, HCl. A simple example of an organic covalently bonded chloride is chloromethane (CH3Cl), often called methyl chloride. Other examples of inorganic covalently bonded chlorides which are used as reactants are: - phosphorus trichloride, phosphorus pentachloride, and thionyl chloride - all three are reactive chlorinating reagents which have been used in a laboratory. - Disulfur dichloride (SCl2) - used for vulcanization of rubber. Chloride ions have important physiological roles. For instance, in the central nervous system the inhibitory action of glycine and some of the action of GABA relies on the entry of Cl− into specific neurons. The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details

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Evidence from caves in Siberia indicates that a global temperature increase of 1.5° Celsius may cause substantial thawing of a large tract of permanently frozen soil in Siberia. The thawing of this soil, known as permafrost, could have serious consequences for further changes in the climate. Permafrost regions cover 24 percent of the land surface in the northern hemisphere, and they hold twice as much carbon as is currently present in the atmosphere. As the permafrost thaws, it turns from a carbon sink (meaning it accumulates and stores carbon) into a carbon source, releasing substantial amounts of carbon dioxide and methane into the atmosphere. Both of these gasses enhance the greenhouse effect. By looking at how permafrost has responded to climate change in the past, we can gain a better understanding of climate change today. A team of international researchers looked at speleothems, such as stalagmites, stalactites, and flowstones. These are mineral deposits that are formed when water from snow or rain seeps into the caves. When conditions are too cold or too dry, speleothem growth ceases, since no water flows through the caves. As a result, speleothems provide a detailed history of periods when liquid water was available as well as an assessment of the relationship between global temperature and permafrost extent. Using radioactive dating and data on growth from six Siberian caves, the researchers tracked the history of permafrost in Siberia for the past 450,000 years. The caves were located at varying latitudes, ranging from a boundary of continuous permafrost at 60 degrees North to the permafrost-free Gobi Desert. In the northernmost cave, Lenskaya Ledyanaya, no speleothem growth has occurred since a particularly warm period around 400,000 years ago—the growth at that time suggests water was flowing in the area due to a melt in the permafrost. The extensive thawing at that time allows for an assessment of the warming required globally to cause a similar change in the permafrost boundary. Global temperatures at that time were only 1.5°C warmer than today, suggesting that we could be approaching a critical point at which the coldest permafrost regions would begin to thaw. Not only will increasing global temperatures cause substantial thawing of permafrost, but it may also create wetter conditions in the Gobi Dessert, based on data from the southern-most cave obtained for the same time period. This suggests a dramatically changed environment in continental Asia. Aside from changes in temperature and precipitation, thawing permafrost enables coastal erosion and the liquefaction of ground that was previously frozen. This poses a risk to the infrastructure of Siberia, including major oil and gas facilities.

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Far north within the Arctic Circle off the northern coast of Norway lies a small chain of islands known as Svalbard. These craggy islands have been scoured into shape by ice and sea. The effect of glacial activity can be seen in this image of the northern tip of the island of Spitsbergen. Here, glaciers have carved out a fjord, a U-shaped valley that has been flooded with sea water. Called Bockfjorden, the fjord is located at almost 80 degrees north, and it is still being affected by glaciers. The effect is most obvious in this image in the tan layer of silty freshwater that floats atop the denser blue water of the Arctic Ocean. The fresh water melts off land-bound glaciers and flows over the sandstone, collecting fine red-toned silt. In this image, the tan-colored fresh water flows northward up the fjord and is being pushed to the east side of the fjord by the rotation of the Earth. Glaciers here and elsewhere on Spitsbergen are cold bottom glaciers, which means that they are frozen to the ground rather than floating on top of a thin layer of melt water. The glaciers are also land glaciers since their terminus (end) lies on land, rather than floating on the water (a tidewater glacier). Land glaciers grow and retreat slowly, balancing fresh snow with the melting and draining of old ice. Their rate of growth or retreat can be affected by global warming. In most cases, including the glaciers around Bockfjorden, global warming has caused glaciers to retreat from increased melting. On the eastern side of Svalbard, however, glaciers are growing from enhanced snowfall. The reason for this pattern remains only one of many intriguing unanswered questions of Arctic science in the islands. The Advanced Spaceborne Thermal Emission and Reflection Radiometer, (ASTER) on NASA's Terra satellite captured this false-color image on June 26, 2001.

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5th Grade Oral Language Resources Students will:• Learn about the concept of whales. • Access prior knowledge and build background about whales. • Explore and apply the concept of whales. Students will:• Demonstrate an understanding of the concept of whales. • Orally use words that describe different types of whales and where they live. • Extend oral vocabulary by speaking about terms that describe whales and whale body parts. • Use key concept words [inlet, humpback, ocean, fins, underwater; submerge, ascend, Baleen, mammal]. Explain• Use the slideshow to review the key concept words. • Explain that students are going to learn about: • Where whales live. • Parts of a whale's body. Model• After the host introduces the slideshow, point to the photo on screen. Ask students: What kind of animal do you see in this picture? (whale). What do you know about these animals? (answers will vary). • Ask students: What are the dangers facing whales? (too much hunting, polluted environment). • Say: In this activity, we're going to learn about whales. How can we protect whales? (not pollute the environment, join groups that are concerned with their safety). Guided Practice• Guide students through the next two slides, showing them examples of whales and the way whales live. Always have the students describe how people are different from whales. Apply• Play the games that follow. Have them discuss with their partner the different topics that appear during the Talk About It feature. • After the first game, ask students to talk about what they think a whale's living environment is like. After the second game, have them discuss what they would like and dislike about having the body of a whale. Close• Ask students: How do you move in the water? • Summarize for students that since whales are mammals, they have to come above water to breathe. Encourage them to think about how they breathe underwater.

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A tsunami is a series of waves most commonly caused by violent movement of the sea floor. In some ways, it resembles the ripples radiating outward from the spot where stone has been thrown into the water, but a tsunami can occur on an enormous scale. Tsunamis are generated by any large, impulsive displacement of the sea bed level. The movement at the sea floor leading to tsunami can be produced by earthquakes, landslides and volcanic eruptions. Most tsunamis, including almost all of those traveling across entire ocean basins with destructive force, are caused by submarine faulting associated with large earthquakes. These are produced when a block of the ocean floor is thrust upward, or suddenly drops, or when an inclined area of the seafloor is thrust upward or suddenly thrust sideways. In any event, a huge mass of water is displaced, producing tsunami. Such fault movements are accompanied by earthquakes, which are sometimes referred to as “tsunamigenic earthquakes”. Most tsunamigenic earthquakes take place at the great ocean trenches, where the tectonic plates that make up the earth’s surface collide and are forced under each other. When the plates move gradually or in small thrust, only small earthquakes are produced; however, periodically in certain areas, the plates catch. The overall motion of the plates does not stop; only the motion beneath the trench becomes hung up. Such areas where the plates are hung up are known as “seismic gaps” for their lack of earthquakes. The forces in these gaps continue to build until finally they overcome the strength of the rocks holding back the plate motion. The built-up tension (or comprehension) is released in one large earthquake, instead of many smaller quakes, and these often generate large deadly tsunamis. If the sea floor movement is horizontal, a tsunami is not generated. Earthquakes of magnitude larger than M 6.5 are critical for tsunami generation. Tsunamis produced by landslides: Probably the second most common cause of tsunami is landslide. A tsunami may be generated by a landslide starting out above the sea level and then plunging into the sea, or by a landslide entirely occurring underwater. Landslides occur when slopes or deposits of sediment become too steep and the material falls under the pull of gravity. Once unstable conditions are present, slope failure can be caused by storms, earthquakes, rain, or merely continued deposit of material on the slope. Certain environments are particularly susceptible to the production of landslide-generated earthquakes. River deltas and steep underwater slopes above sub-marine canyons, for instance, are likely sites for landslide-generated earthquakes. Tsunami produced by Volcanoes: The violent geologic activity associated with volcanic eruptions can also generate devastating tsunamis. Although volcanic tsunamis are much less frequent, they are often highly destructive. These may be due to submarine explosions, pyroclastic flows and collapse of volcanic caldera. (1) Submarine volcanic explosions occur when cool seawater encounters hot volcanic magma. It often reacts violently, producing stream explosions. Underwater eruptions at depths of less than 1500 feet are capable of disturbing the water all the way to the surface and producing tsunamis. (2) Pyroclastic flows are incandescent, ground-hugging clouds, driven by gravity and fluidized by hot gases. These flows can move rapidly off an island and into the ocean, their impact displacing sea water and producing a tsunami. (3) The collapse of a volcanic caldera can generate tsunami. This may happen when the magma beneath a volcano is withdrawn back deeper into the earth, and the sudden subsidence of the volcanic edifice displaces water and produces tsunami waves. The large masses of rock that accumulate on the sides of the volcanoes may suddenly slide down slope into the sea, causing tsunamis. Such landslides may be triggered by earthquakes or simple gravitational collapse. A catastrophic volcanic eruption and its ensuing tsunami waves may actually be behind the legend of the lost island civilization of Atlantis. The largest volcanic tsunami in historical times and the most famous historically documented volcanic eruption took lace in the East Indies-the eruption of Krakatau in 1883. Tsunami waves : A tsunami has a much smaller amplitude (wave height) offshore, and a very long wavelength (often hundreds of kilometers long), which is why they generally pass unnoticed at sea, forming only a passing "hump" in the ocean. Tsunamis have been historically referred to tidal waves because as they approach land, they take on the characteristics of a violent onrushing tide rather than the sort of cresting waves that are formed by wind action upon the ocean (with which people are more familiar). Since they are not actually related to tides the term is considered misleading and its usage is discouraged by oceanographers. These waves are different from other wind-generated ocean waves, which rarely extend below a dept of 500 feet even in large storms. Tsunami waves, on the contrary, involvement of water all the way to the sea floor, and as a result their speed is controlled by the depth of the sea. Tsunami waves may travel as fast as 500 miles per hour or more in deep waters of an ocean basin. Yet these fast waves may be only a foot of two high in deep water. These waves have greater wavelengths having long 100 miles between crests. With a height of 2 to 3 feet spread over 100 miles, the slope of even the most powerful tsunamis would be impossible to see from a ship or airplane. A tsunami may consist of 10 or more waves forming a ‘tsunami wave train’. The individual waves follow one behind the other anywhere from 5 to 90 minutes apart. As the waves near shore, they travel progressively more slowly, but the energy lost from decreasing velocity is transformed into increased wavelength. A tsunami wave that was 2 feet high at sea may become a 30-feet giant at the shoreline. Tsunami velocity is dependent on the depth of water through which it travels (velocity equals the square root of water depth h times the gravitational acceleration g, that is (V=√gh). The tsunami will travel approximately at a velocity of 700 kmph in 4000 m depth of sea water. In 10 m, of water depth the velocity drops to about 35 kmph. Even on shore tsunami speed is 35 to 40 km/h, hence much faster than a person can run.It is commonly believed that the water recedes before the first wave of a tsunami crashes ashore. In fact, the first sign of a tsunami is just as likely to be a rise in the water level. Whether the water rises or falls depends on what part of the tsunami wave train first reaches the coast. A wave crest will cause a rise in the water level and a wave trough causes a water recession. Seiche (pronounced as ‘saysh’) is another wave phenomenon that may be produced when a tsunami strikes. The water in any basin will tend to slosh back and forth in a certain period of time determined by the physical size and shape of the basin. This sloshing is known as the seiche. The greater the length of the body, the longer the period of oscillation. The depth of the body also controls the period of oscillations, with greater water depths producing shorter periods. A tsunami wave may set off seiche and if the following tsunami wave arrives with the next natural oscillation of the seiche, water may even reach greater heights than it would have from the tsunami waves alone. Much of the great height of tsunami waves in bays may be explained by this constructive combination of a seiche wave and a tsunami wave arriving simultaneously. Once the water in the bay is set in motion, the resonance may further increase the size of the waves. The dying of the oscillations, or damping, occurs slowly as gravity gradually flattens the surface of the water and as friction turns the back and forth sloshing motion into turbulence. Bodies of water with steep, rocky sides are often the most seiche-prone, but any bay or harbour that is connected to offshore waters can be perturbed to form seiche, as can shelf waters that are directly exposed to the open sea. The presence of a well developed fringing or barrier of coral reef off a shoreline also appears to have a strong effect on tsunami waves. A reef may serve to absorb a significant amount of the wave energy, reducing the height and intensity of the wave impact on the shoreline itself. The popular image of a tsunami wave approaching shore is that of a nearly vertical wall of water, similar to the front of a breaking wave in the surf. Actually, most tsunamis probably don’t form such wave fronts; the water surface instead is very close to the horizontal, and the surface itself moves up and down. However, under certain circumstances an arriving tsunami wave can develop an abrupt steep front that will move inland at high speeds. This phenomenon is known as a bore. In general, the way a bore is created is related to the velocity of the shallow water waves. As waves move into progressively shallower water, the wave in front will be traveling more slowly than the wave behind it .This phenomenon causes the waves to begin “catching up” with each other, decreasing their distance apart i.e. shrinking the wavelength. If the wavelength decreases, but the height does not, then waves must become steeper. Furthermore, because the crest of each wave is in deeper water than the adjacent trough, the crest begins to overtake the trough in front and the wave gets steeper yet. Ultimately the crest may begin to break into the trough and a bore formed. A tsunami can cause a bore to move up a river that does not normally have one. Bores are particularly common late in the tsunami sequence, when return flow from one wave slows the next incoming wave. Though some tsunami waves do, in deed, form bores, and the impact of a moving wall of water is certainly impressive, more often the waves arrive like a very rapidly rising tide that just keeps coming and coming. The normal wind waves and swells may actually ride on top of the tsunami, causing yet more turbulence and bringing the water level to even greater heights.

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Learn something new every day More Info... by email A predicate is part of a sentence or clause in English and is one of two primary components that serves to effectively complete the sentence. Sentences consist of two main components: subjects and predicates. Subjects are the primary “thing” in a sentence which the rest of the words then describe through either a direct description or by indicating what type of action that subject is performing. The predicate is this secondary aspect of the sentence and usually consists of a verb or adjective, though complicated sentences may have multiple verbs and a number of descriptions affecting the subject. It can be easiest to understand predicates by first understanding subjects and how sentences are constructed. A sentence just about always has a subject, though it can be implied in some way and not necessarily directly stated. In a simple sentence like “The cat slept,” the subject is “the cat,” which is a noun phrase consisting of the direct article “the” and the noun “cat.” Subjects can be longer and more complicated, but they are usually fairly simple in nature. The predicate of a sentence is then basically the rest of the sentence, though this is not always the case for longer and more complicated sentences. In “The cat slept,” the predicate is quite simple and merely consists of the word “slept.” This is simple because “slept” is an intransitive verb, which means that it requires no further description or objects to make it complete. The sentence could be expanded as “The cat slept on the bed,” but this is not necessary and merely adds a descriptive component to the predicate through the prepositional phrase “on the bed.” In a somewhat more complicated sentence, such as “The man gave the ball to his son,” the subject of the sentence is still quite simple: “The man.” The predicate in this sentence, however, has become substantially more complicated and consists of the rest of the sentence: “gave the ball to his son.” This has been made more complicated because the verb “gave” is transitive, specifically ditransitive, which indicates both a direct object and an indirect object. The act of “giving” requires that there is a direct object, which is the item given, and an indirect object, which is who or what it is given to. In this instance, the predicate consists of the verb “gave” and the direct object “the ball” with a connecting preposition “to” and the indirect object “his son.” Predicates can become even more complicated as an idea expands, such as a sentence like “The rock rolled off the table, landed on top of a skateboard, and proceeded to roll down the hill until it was stopped by a wall.” In this sentence, the subject is only “The rock,” which means that the rest of the sentence is the predicate.

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Prefixes, Suffixes, Inflectional Endings, and Root Words Spelling Words Correctly Using Prefixes This strategy will focus on the prefix "re-" to help predict the meaning of words. The same strategy can be used to introduce other common prefixes such as "dis-", "in-" and "im-". Prefixes and Suffixes Students will create two Mini Books. One will incorporate prefixes and the other will focus on suffixes. Each book will include the meanings, sample words, and two well- written sentences for each suffix or prefix. Also supports Tech COS 12 Making Singular Nouns Plural This lesson involves the use of the Structural Analysis element of the Inflectional Ending "-s" to make singular nouns plural. Vocabulary Root Word Drawing A Lesson Plans Page lesson plan, lesson idea, thematic unit, or activity in Language Arts and Art called Vocabulary Root Word Drawing. Forming Possessives Showing possession in English is a relatively easy matter (believe it or not). By adding an apostrophe and an s we can manage to transform most singular nouns into their possessive form: Word Confusion: Students choose the correct word to complete the sentence in this online game. Inflected Endings: Some languages, such as Chinese, Hmong, and Vietnamese do not use inflected endings to form verb tenses. Students may need help understanding that adding -ed to a verb indicates that the action happened in the past. Spelling changes in inflected verbs may be difficult for ELLs to master. Prefixes and Suffixes: Some English prefixes and suffixes have equivalent forms in the Romance languages. For example, the prefix dis- in English (disapprove) corresponds to the Spanish des- (desaprobar), the French des- (desapprouver), and the Haitian Creole dis- or dez- (dezaprouve). Students who are literate in a Romance language may be able to transfer their understanding of prefixes and suffixes much easier than those from non-Romance languages. E/B, D, E: Help ELLs classify English words into meaningful categories. Use word walls, graphic organizers, and concept maps to group related words, record them in meaningful ways, and create visual references that can be used in future lessons. Teachers can help students group and relate words in different ways. For example, place a large picture of a tree on the wall. Place prefix and suffix cards on the different branches (i.e. prefixes: pre-, re- un-; suffixes: -ful, -less) and root words on the roots (write, view, paint). This visual representation can help students conceptualize that prefixes and suffixes are added on to root words. E/B, D, E: The teacher creates a display of words containing Greek and Latin roots and adds to it during the school year. ELLs can refer to the display to help in understanding new words. (Example of display: the tree display above, or a poster with three columns - Root, Meaning, and Word, i.e. aqua, water, aquarium) E/B: Read one's own writing or simple narrative text and begin to produce phonemes appropriately. E/B: Recognize and produce English phonemes students already know, and possibly use them in simple phrases or sentences. E/B: Recognize sounds in spoken words with accompanying illustrations E/B: Use cues for sounding out unfamiliar words with accompanying illustrations E/B: Blend sounds together to make words, shown visually D: Remove or add sounds to existing words to make new words, shown visually (i.e. "Cover up the t in cart. What do you have now?") D: Use letter-sound relationships and word roots to produce and understand multi-syllabic words; E: Use letter-sound relationships and word roots to produce and understand new word families. D, E: Recognize and use prefixes and suffixes to find meanings of unknown words. E: Segment illustrated sentences into words and phrases. E: Identify and analyze sentence and context clues to find meanings of unknown words. E/B, D, E: When sharing new vocabulary words, make sure to write each word divided into syllables (i.e. dic-tion-ar-y). When introducing each word, sound it out, pausing between each syllable, and then blend the syllables together. Have students repeat after you. Ask students how many syllables the word has. Tell students: Pay attention to the syllables in a word. This will help you spell the word, and it will help you pronounce it, too. E/B, D, E: Before teaching the phonics skills, introduce the target words orally to students by using them in activities such as chants and riddle games, or asking and answering questions that use the words. Some of the above ELL suggestions came from the following resources: WIDA Consortium's English Language Proficiency Standards and Resource Guide, PreK - Grade 12 Scott Foresman Reading Street ELL and Transition Handbook Grades 3-6 A Guide to the Standard Course of Study for Limited English Proficient Students / Grades K-5 (Public Schools of N.C.)

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Say it with FEELING!! Rationale: “Fluency means reading faster, smoother, more expressively, or more quietly with the goal of reading silently. Fluent reading approaches the speed of speech.” (Murray) At this development stage, fluency is a major goal of the student and the teacher. This lesson is aimed to teach and emphasize one aspect of fluency: expression. Reading with expression brings a story, and its characters, to life, making reading more enjoyable for everyone. The teacher will read a story, showing great expression, to model for children. Materials: Copy of Tiki Tiki Tembo, various classroom library books, notebook paper, pencils 1. Review with students the difference that punctuation makes make at the end of a sentence. Read the following sentences twice through. The first time, pay NO ATTENTION to the punctuation marks at the end of the sentence. The second time, use the correct inflection in your voice, depending on the punctuation mark at the end of the sentence. “JIMMY WENT RUNNING., JIMMY WENT RUNNING?, JIMMY WENT RUNNING!. CAN ANYONE TELL ME THE DIFFERENCES IN THOSE SENTENCES?” Hopefully children will answer that the first was a statement, the second was a question, and the third was an exclamation. 2. “WHAT A WONDERFUL DAY WE HAVE!!!” After you have excited the kids with that exclamation, the teacher says ‘“NOW THAT WAS LOUD AND FULL OF EXCITEMENT WASN’T IT? THAT WAS HAPPY EXPRESSION. WHEN WE TALK OR READ WITH EXPRESSION, WE CHANGE THE TONE OF OUR VOICE (HAPPY TO SAD), THE VLOUME OF OUR VOICE (LOUD TO SOFT), AND USE OUR FACES TO SHOW THE FEELING OF THE BOOK. DIFFERENT FEELINGS HAVE DIFFERENT SOUNDS AND FACIL LOOKS.” 3. “CAN SOMEONE TELL ME WHY WE SHOULD USE EXPRESSION WHEN WE READ? Students will offer their own explanations. “GREAT! WE USE EXPRESSION TO MAKE THE STORY MORE INTERESTING AND FUN TO READ!!!” 4. “WHAT WOULD MY VOICE SOUND LIKE IF I WERE SCARED?” Children raise their hands and answer, using facial expressions and vocal tones. “WHAT ABOUT IF I WERE ANGRY? WOULD I YELL OR WHISPER?” Children will answer correctly to the question. 5. Now, gather the children around your reading center and read ‘“Tiki Tiki Tembo’”. Make sure to OVEREXAGGERATE your expressions. (vocal tone, facial expressions, and volume) When done reading, ask children what emotions you were trying to convey at different parts of the story. Have a mini group discussion. 6. Pair children up and have them select a book from the classroom library to read. Set a timer for 5-8 minutes and let each child read to their partner. “REMEMEBER TO READ TO YOUR READING BUDDY WITH LOTS OF EXPRESSION! MAKE YOUR READING BUDDY FEEL LIKE THEY ARE IN THE STORY.” Teacher circulates with rubric and evaluates each child as they read. Now have the kids switch roles. Reading buddy becomes reader and reader becomes reading buddy. 7. After the children are done with the reading, have each child individually write three sentences about their book that end with various punctuation marks. “OKAY CLASS, NOW THAT WE HAVE LEARNED TO READ WITH EXPRESSION, I WANT US TO WRITE WITH EXPRESSION. TAKE OUT PAPER AND A PENCIL. WRITE THREE SENTENCES ABOUT THE STORY YOU JUST READ. ONE SHOULD BE A STATEMENT AND END WITH A PERIOD. ONE SHOULD BE A QUESTION AND END WITH A QUESTION MARK. ONE SHOULD BE AN EXCLAMATION AND END WITH AN EXCLAMATION POINT.” Have each child come to your desk or reading table and have them read, with expression, their original sentences. This will assess their grasp of punctuation and also the concept of expression: how to write it and convey it to the reader. You also have the checklist rubric that you evaluated their oral reading on. www.auburn.edu/rdggenie The Reading Genie Website Click here to return to Openings

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What is the media? What does it do? Students examine the types and roles of the media by taking on the role of newsmaker and agenda setter. Students will be able to: ANTICIPATE by asking students if they’ve ever seen a television newscast. Ask students to recall any details they remember (graphics, music, story topics). Ask students who they think makes decisions about what stories television newscasts discuss. DISTRIBUTE the Reading pages to each student. READ the two reading pages with the class, pausing to discuss as necessary. CHECK for understanding by doing the T/F Active Participation activity. Have students respond “True” or “False” as a chorus or use thumbs up/thumbs down. DISTRIBUTE scissors, glue, and the Agenda Cutout Activity pages. Students can complete this activity individually or in pairs. READ the directions for the cutout activity. ALLOW students to complete the cutout activity. REVIEW the answers to the cutout activity. DISTRIBUTE one worksheet to each student and review the directions for the activities. ALLOW students to complete the worksheet. DISTRIBUTE one Extension Activity to each student and review the directions. ALLOW students to complete the extension activity. CLOSE by asking students to silently recall as many roles of the media as they can. Call on students until all roles have been named.

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You must be familiar with slope-intercept form (y = mx + b), and understand which numbers in the equation are m and b, and how to graph them. Mark b on the graph, then graph the slope (m) from that point. Inequalities are very similar, with only a few differences: - It's not a line of solutions as in a linear equation; it is a solid or dashed boundary line that shows on which side all the solutions are. - Shade above or below the boundary line, showing on which side all the solutions are. - Change the direction of the inequality (>, <) if you divide by a negative number. ►Check your work by using (0,0) as a test point. This will help you know if your answer is correct, and if you forgot to change the direction of the inequality. These videos cover the same topic, but go about solving in slightly different ways. I watched all of them, and gleaned a little more from each one. (1) from YourTeacher.com - graphing using a table (2) boundary line (3) graphing using slope-intercept form, y = mx + b (4) graphing using slope-intercept form. He is fast, so pause and read the text on the board. (5) graphing using slope-intercept form

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Delegates (C# Programming Guide) A delegate is a type that defines a method signature. When you instantiate a delegate, you can associate its instance with any method with a compatible signature. You can invoke (or call) the method through the delegate instance. Delegates are used to pass methods as arguments to other methods. Event handlers are nothing more than methods that are invoked through delegates. You create a custom method, and a class such as a windows control can call your method when a certain event occurs. The following example shows a delegate declaration: Any method from any accessible class or struct that matches the delegate's signature, which consists of the return type and parameters, can be assigned to the delegate. The method can be either static or an instance method. This makes it possible to programmatically change method calls, and also plug new code into existing classes. As long as you know the signature of the delegate, you can assign your own method. In the context of method overloading, the signature of a method does not include the return value. But in the context of delegates, the signature does include the return value. In other words, a method must have the same return value as the delegate. This ability to refer to a method as a parameter makes delegates ideal for defining callback methods. For example, a reference to a method that compares two objects could be passed as an argument to a sort algorithm. Because the comparison code is in a separate procedure, the sort algorithm can be written in a more general way. Delegates have the following properties: Delegates are like C++ function pointers but are type safe. Delegates allow methods to be passed as parameters. Delegates can be used to define callback methods. Delegates can be chained together; for example, multiple methods can be called on a single event. Methods do not have to match the delegate signature exactly. For more information, see Using Variance in Delegates (C# and Visual Basic). C# version 2.0 introduced the concept of Anonymous Methods, which allow code blocks to be passed as parameters in place of a separately defined method. C# 3.0 introduced lambda expressions as a more concise way of writing inline code blocks. Both anonymous methods and lambda expressions (in certain contexts) are compiled to delegate types. Together, these features are now known as anonymous functions. For more information about lambda expressions, see Anonymous Functions (C# Programming Guide). For more information, see the C# Language Specification. The language specification is the definitive source for C# syntax and usage.

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The people in south Asia had no warning of the next disaster rushing toward them the morning of December 26, 2004. One of the strongest earthquakes in the past 100 years had just destroyed villages on the island of Sumatra in the Indian Ocean, leaving many people injured. But the worst was yet to come—and very soon. For the earthquake had occurred beneath the ocean, thrusting the ocean floor upward nearly 60 feet. The sudden release of energy into the ocean created a tsunami (pronounced su-NAM-ee) event—a series of huge waves. The waves rushed outward from the center of the earthquake, traveling around 400 miles per hour. Anything in the path of these giant surges of water, such as islands or coastlines, would soon be under water. The people had already felt the earthquake, so why didn't they know the water was coming? As the ocean floor rises near a landmass, it pushes the wave higher. But much depends on how sharply the ocean bottom changes and from which direction the wave approaches. Energy from earthquakes travels through the Earth very quickly, so scientists thousands of miles away knew there had been a severe earthquake in the Indian Ocean. Why didn't they know it would create a tsunami? Why didn't they warn people close to the coastlines to get to higher ground as quickly as possible? In Sumatra, near the center of the earthquake, people would not have had time to get out of the way even if they had been warned. But the tsunami took over two hours to reach the island of Sri Lanka 1000 miles away, and still it killed 30,000 people! It is important, though, to understand just how the tsunami will behave when it gets near the coastline. As the ocean floor rises near a landmass, it pushes the wave higher. But much depends on how sharply the ocean bottom changes and from which direction the wave approaches. Scientists would like to know more about how actual waves react. MISR has nine cameras all pointed at different angles. So the exact same spot is photographed from nine different angles as the satellite passes overhead. The image at the top of this page was taken with the camera that points forward at 46°. The image caught the sunlight reflecting off the pattern of ripples as the waves bent around the southern tip of the island. These ripples are not seen in satellite images looking straight down at the surface. Scientists do not yet understand what causes this pattern of ripples. They will use computers to help them find out how the depth of the ocean floor affects the wave patterns on the surface of the ocean. Images such as this one from MISR will help. Images such as these from MISR will help scientists understand how tsunamis interact with islands and coastlines. This information will help in developing the computer programs, called models, that will help predict where, when, and how severely a tsunami will hit. That way, scientists and government officials can warn people in time to save many lives.

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Simple Equations Introduction to basic algebraic equations of the form Ax=B ⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles. - Let's say we have the equation seven times x is equal to fourteen. - Now before even trying to solve this equation, - what I want to do is think a little bit about what this actually means. - Seven x equals fourteen, - this is the exact same thing as saying seven times x, let me write it this way, seven times x, x in orange again. Seven times x is equal to fourteen. - Now you might be able to do this in your head. - You could literally go through the 7 times table. - You say well 7 times 1 is equal to 7, so that won't work. - 7 times 2 is equal to 14, so 2 works here. - So you would immediately be able to solve it. - You would immediately, just by trying different numbers - out, say hey, that's going to be a 2. - But what we're going to do in this video is to think about - how to solve this systematically. - Because what we're going to find is as these equations get - more and more complicated, you're not going to be able to - just think about it and do it in your head. - So it's really important that one, you understand how to - manipulate these equations, but even more important to - understand what they actually represent. - This literally just says 7 times x is equal to 14. - In algebra we don't write the times there. - When you write two numbers next to each other or a number next - to a variable like this, it just means that you - are multiplying. - It's just a shorthand, a shorthand notation. - And in general we don't use the multiplication sign because - it's confusing, because x is the most common variable - used in algebra. - And if I were to write 7 times x is equal to 14, if I write my - times sign or my x a little bit strange, it might look - like xx or times times. - So in general when you're dealing with equations, - especially when one of the variables is an x, you - wouldn't use the traditional multiplication sign. - You might use something like this -- you might use dot to - represent multiplication. - So you might have 7 times x is equal to 14. - But this is still a little unusual. - If you have something multiplying by a variable - you'll just write 7x. - That literally means 7 times x. - Now, to understand how you can manipulate this equation to - solve it, let's visualize this. - So 7 times x, what is that? - That's the same thing -- so I'm just going to re-write this - equation, but I'm going to re-write it in visual form. - So 7 times x. - So that literally means x added to itself 7 times. - That's the definition of multiplication. - So it's literally x plus x plus x plus x plus x -- let's see, - that's 5 x's -- plus x plus x. - So that right there is literally 7 x's. - This is 7x right there. - Let me re-write it down. - This right here is 7x. - Now this equation tells us that 7x is equal to 14. - So just saying that this is equal to 14. - Let me draw 14 objects here. - So let's say I have 1, 2, 3, 4, 5, 6, 7, 8, - 9, 10, 11, 12, 13, 14. - So literally we're saying 7x is equal to 14 things. - These are equivalent statements. - Now the reason why I drew it out this way is so that - you really understand what we're going to do when we - divide both sides by 7. - So let me erase this right here. - So the standard step whenever -- I didn't want to do that, - let me do this, let me draw that last circle. - So in general, whenever you simplify an equation down to a - -- a coefficient is just the number multiplying - the variable. - So some number multiplying the variable or we could call that - the coefficient times a variable equal to - something else. - What you want to do is just divide both sides by 7 in - this case, or divide both sides by the coefficient. - So if you divide both sides by 7, what do you get? - 7 times something divided by 7 is just going to be - that original something. - 7's cancel out and 14 divided by 7 is 2. - So your solution is going to be x is equal to 2. - But just to make it very tangible in your head, what's - going on here is when we're dividing both sides of the - equation by 7, we're literally dividing both sides by 7. - This is an equation. - It's saying that this is equal to that. - Anything I do to the left hand side I have to do to the right. - If they start off being equal, I can't just do an operation - to one side and have it still be equal. - They were the same thing. - So if I divide the left hand side by 7, so let me divide - it into seven groups. - So there are seven x's here, so that's one, two, three, - four, five, six, seven. - So it's one, two, three, four, five, six, seven groups. - Now if I divide that into seven groups, I'll also want - to divide the right hand side into seven groups. - One, two, three, four, five, six, seven. - So if this whole thing is equal to this whole thing, then each - of these little chunks that we broke into, these seven chunks, - are going to be equivalent. - So this chunk you could say is equal to that chunk. - This chunk is equal to this chunk -- they're - all equivalent chunks. - There are seven chunks here, seven chunks here. - So each x must be equal to two of these objects. - So we get x is equal to, in this case -- in this case - we had the objects drawn out where there's two of - them. x is equal to 2. - Now, let's just do a couple more examples here just so it - really gets in your mind that we're dealing with an equation, - and any operation that you do on one side of the equation - you should do to the other. - So let me scroll down a little bit. - So let's say I have I say I have 3x is equal to 15. - Now once again, you might be able to do is in your head. - You're saying this is saying 3 times some - number is equal to 15. - You could go through your 3 times tables and figure it out. - But if you just wanted to do this systematically, and it - is good to understand it systematically, say OK, this - thing on the left is equal to this thing on the right. - What do I have to do to this thing on the left - to have just an x there? - Well to have just an x there, I want to divide it by 3. - And my whole motivation for doing that is that 3 times - something divided by 3, the 3's will cancel out and I'm just - going to be left with an x. - Now, 3x was equal to 15. - If I'm dividing the left side by 3, in order for the equality - to still hold, I also have to divide the right side by 3. - Now what does that give us? - Well the left hand side, we're just going to be left with - an x, so it's just going to be an x. - And then the right hand side, what is 15 divided by 3? - Well it is just 5. - Now you could also done this equation in a slightly - different way, although they are really equivalent. - If I start with 3x is equal to 15, you might say hey, Sal, - instead of dividing by 3, I could also get rid of this 3, I - could just be left with an x if I multiply both sides of - this equation by 1/3. - So if I multiply both sides of this equation by 1/3 - that should also work. - You say look, 1/3 of 3 is 1. - When you just multiply this part right here, 1/3 times - 3, that is just 1, 1x. - 1x is equal to 15 times 1/3 third is equal to 5. - And 1 times x is the same thing as just x, so this is the same - thing as x is equal to 5. - And these are actually equivalent ways of doing it. - If you divide both sides by 3, that is equivalent to - multiplying both sides of the equation by 1/3. - Now let's do one more and I'm going to make it a little - bit more complicated. - And I'm going to change the variable a little bit. - So let's say I have 2y plus 4y is equal to 18. - Now all of a sudden it's a little harder to - do it in your head. - We're saying 2 times something plus 4 times that same - something is going to be equal to 18. - So it's harder to think about what number that is. - You could try them. - Say if y was 1, it'd be 2 times 1 plus 4 times 1, - well that doesn't work. - But let's think about how to do it systematically. - You could keep guessing and you might eventually get - the answer, but how do you do this systematically. - Let's visualize it. - So if I have two y's, what does that mean? - It literally means I have two y's added to each other. - So it's literally y plus y. - And then to that I'm adding four y's. - To that I'm adding four y's, which are literally four - y's added to each other. - So it's y plus y plus y plus y. - And that has got to be equal to 18. - So that is equal to 18. - Now, how many y's do I have here on the left hand side? - How many y's do I have? - I have one, two, three, four, five, six y's. - So you could simplify this as 6y is equal to 18. - And if you think about it it makes complete sense. - So this thing right here, the 2y plus the 4y is 6y. - So 2y plus 4y is 6y, which makes sense. - If I have 2 apples plus 4 apples, I'm going - to have 6 apples. - If I have 2 y's plus 4 y's I'm going to have 6 y's. - Now that's going to be equal to 18. - And now, hopefully, we understand how to do this. - If I have 6 times something is equal to 18, if I divide both - sides of this equation by 6, I'll solve for the something. - So divide the left hand side by 6, and divide the - right hand side by 6. - And we are left with y is equal to 3. - And you could try it out. - That's what's cool about an equation. - You can always check to see if you got the right answer. - Let's see if that works. - 2 times 3 plus 4 times 3 is equal to what? - 2 times 3, this right here is 6. - And then 4 times 3 is 12. - 6 plus 12 is, indeed, equal to 18. Be specific, and indicate a time in the video: At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger? Have something that's not a question about this content? This discussion area is not meant for answering homework questions. Share a tip When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831... Have something that's not a tip or feedback about this content? This discussion area is not meant for answering homework questions. Discuss the site For general discussions about Khan Academy, visit our Reddit discussion page. Flag inappropriate posts Here are posts to avoid making. 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Plot Cartesian Coordinate Points on a Cartesian Graph When math folks talk about using a graph, they’re usually referring to a Cartesian graph (also called the Cartesian coordinate system). The below figure shows an example of a Cartesian graph. A Cartesian graph is really just two number lines that cross at 0. These number lines are called the horizontal axis (also called the x-axis) and the vertical axis (also called the y-axis). The place where these two axes (plural of axis) cross is called the origin. Plotting a point (finding and marking its location) on a graph isn’t much harder than finding a point on a number line, because a graph is just two number lines put together. Every point on a Cartesian graph is represented by two numbers in parentheses, separated by a comma, called a set of coordinates. To plot any point, start at the origin, where the two axes cross. The first number tells you how far to go to the right (if positive) or left (if negative) along the horizontal axis. The second number tells you how far to go up (if positive) or down (if negative) along the vertical axis. For example, here are the coordinates of four points called A, B, C, and D: A = (2, 3) B = (–4, 1) C = (0, –5) D = (6, 0) The above figure depicts a graph with these four points plotted. Start at the origin, (0, 0). To plot point A, count 2 spaces to the right and 3 spaces up. To plot point B, count 4 spaces to the left (the negative direction) and then 1 space up. To plot point C, count 0 spaces left or right and then count 5 spaces down (the negative direction). And to plot point D, count 6 spaces to the right and then 0 spaces up or down.

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Lesson Plans for Secondary School Educators Unit Nine: "The Quest Is Achieved" Content Focus: The Lord of the Rings, Book Six Thematic Focus: What Makes a Hero? As befits its vast scope and extraordinary ambition, The Lord of the Rings boasts three major heroes Frodo, Aragorn, and Sam plus many secondary characters whose deeds are manifestly noble and courageous. In Unit Nine students consider the meaning of heroism and look back on the other thematic threads that make the novel a unified whole. By the end of Unit Nine, the student should be able to: Contrast Aragorn's obvious valor with Frodo's concealed heroism. Give some possible reasons Tolkien regarded Sam as the "chief hero" of The Lord of the Rings. Account for the "joy-in-sorrow atmosphere" of Tolkien's epic fantasy. Indicate which of Tolkien's characters might be considered archetypes. Trace the development of the novel's themes, including corruption, free will, destiny, despair, and heroism, from Book One through Book Six. Unit Nine Content Comments for Teachers These lesson plans were written by James Morrow and Kathryn Morrow in consultation with Amy Allison, Gregory Miller, Sarah Rito, and Jason Zanitsch. Lesson Plans Homepage

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The OSI (Open Systems Interconnection) model was created by the ISO to help standardize communication between computer systems. It divides communications into seven different layers, which each include multiple hardware standards, protocols, or other types of services. The seven layers of the OSI model include: - The Physical layer - The Data Link layer - The Network layer - The Transport layer - The Session layer - The Presentation layer - The Application layer When one computer system communicates with another, whether it is over a local network or the Internet, data travels through these seven layers. It begins with the physical layer of the transmitting system and travels through the other layers to the application layer. Once the data reaches the application layer, it is processed by the receiving system. In some cases, the data will move through the layers in reverse to the physical layer of the receiving computer. The best way to explain how the OSI model works is to use a real life example. In the following illustration, a computer is using a wireless connection to access a secure website. The communications stack begins with the (1) physical layer. This may be the computer's Wi-Fi card, which transmits data using the IEEE 802.11n standard. Next, the (2) data link layer might involve connecting to a router via DHCP. This would provide the system with an IP address, which is part of the (3) network layer. Once the computer has an IP address, it can connect to the Internet via the TCP protocol, which is the (4) transport layer. The system may then establish a NetBIOS session, which creates the (5) session layer. If a secure connection is established, the (6) presentation layer may involve an SSL connection. Finally, the (7) application layer consists of the HTTP connection to the website. The OSI model provides a helpful overview of the way computer systems communicate with each other. Software developers often use this model when writing software that requires networking or Internet support. Instead of recreating the communications stack from scratch, software developers only need to include functions for the specific OSI layer(s) their programs use.

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On this day in 1784, at the Maryland State House in Annapolis, the Continental Congress ratifies the Treaty of Paris. The document, negotiated in part by future President John Adams, contained terms for ending the Revolutionary War and established the United States as a sovereign nation. The treaty outlined America's fishing rights off the coast of Canada, defined territorial boundaries in North America formerly held by the British and forced an end to reprisals against British loyalists. Two other future presidents, Thomas Jefferson and James Monroe, were among the delegates who ratified the document on January 14, 1874. Thomas Jefferson had planned to travel to Paris to join Adams, John Jay and Benjamin Franklin for the beginning of talks with the British in 1782. However, after a delay in his travel plans, Jefferson received word that a cessation of hostilities had been announced by King George III the previous December. Jefferson arrived in Paris in late February after the treaty had already been negotiated by Adams, Franklin and Jay. Adams' experience and skill in diplomacy prompted Congress to authorize him to act as the United States' representative in negotiating treaty terms with the British. Following his role in ending the Revolutionary War and his participation in drafting the Declaration of Independence, Adams succeeded George Washington as the second president of the United States in 1797.

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The process that breaks up and carries away the rocks and soils that make up the Earth’s surface is called erosion. It is caused by flowing water, waves, glaciers, and the wind, and it constantly changes the shape of the landscape. Erosion happens more quickly on bare rock, which is unprotected by soil. It often begins with weathering, where rocks are weakened by the weather’s elements, such as sunshine, frost, and rain. Rocks can be eroded by physical weathering through heat, cold and frost, and CHEMICAL WEATHERING. Erosion may lead to the MASS MOVEMENT of rock and soil. Waves erode the base of cliffs, undermining them and making them collapse. This can create coastal features such as the Twelve Apostles in Victoria, Australia. The stacks (rock towers) are left when headlands are worn away from both sides until they crumble. The broken rocks form shingle and sand beaches. Erosion happens faster when shingle is thrown against the cliffs by the waves. Mountain ranges contain deep valleys that have been carved out by glaciers. A glacier is like a slow-moving river of ice that flows downhill, carried forwards by its huge weight. The rocks dragged along underneath it gouge deep into the ground, creating U-shaped valleys with steep sides and flat bottoms. Sand blown by strong winds has sculpted the slender sandstone pillars of Bryce Canyon, Utah, USA. Their rugged outlines are caused by the softer layers of rock are being eroded more quickly than the harder layers. Wind erosion is common in deserts, where sand is blown about because there are few plants to hold the soil in place and there is no rain to bind the soil particles together. Some rocks are broken down by chemical action, in a process called chemical weathering. The minerals they contain are changed chemically by the effects of sunlight, air, and especially water. The rocks are weakened and wear away more easily. Limestone, for example, is dissolved by rainwater, because the water contains carbon dioxide from the atmosphere, making it slightly acidic. Erosion normally breaks down the landscape a tiny piece at a time, but sometimes rocks and soil move downhill in large volumes. These movements, which include landslides, mudflows, and rock falls, are called mass movements. They happen when rock, debris, or soil on a slope becomes unstable and can no longer resist the downward force of gravity. Soil creep is the extremely slow movement of soil down a steep hillside. It is caused by soil expanding and contracting, when it goes from wet to dry or frozen to unfrozen. The top layers of the soil move faster than the layers underneath. The movement is far too slow to see, but bent trees, leaning fence posts and telegraph poles, and small terraces in fields are all evidence of soil creep. Soil may also build up against a wall or at the bottom of the hillside. A slump is a mass movement that happens when a large section of soil or soft rock breaks away from a slope and slides downwards. Short cliffs called scarps are left at the top of the slope. Slumps often happen where the base of a slope is eroded by a river or by waves, or when soil or soft rock becomes waterlogged. A lahar is a mudflow of water mixed with volcanic ash. This forms when ash mixes with melting ice during an eruption, or with torrential rain. The mud flows down river valleys and sets hard when it comes to a stop. Lahars can cause destruction on a massive scale. Debris is made up of broken rock, sometimes mixed with soil. These pieces of debris may collect on a slope and begin to roll or slide downwards. Debris slides often happen where people have cleared hillsides of trees and other vegetation, which causes the soil and rock to be eroded quickly.

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Removal Act of 1830 On May 26, 1830, the Indian Removal Act of 1830 was passed by the Twenty-First Congress of the United states of America. After four months of strong debate, Andrew Jackson signed the bill into law. Land greed was a big reason for the federal government's position on Indian removal. This desire for Indian lands was also abetted by the Indian hating mentallity that was peculiar to some American frontiersman. This period of forcible removal first started with the Cherokee Indians in the state of Georgia. In 1802, the Georgia legislature signed a compact giving the federal government all of her claims to western lands in exchange for the government's pledge to extigiush all Indian titles to land within the state. But by the mid-1820's Georgians began to doubt that the government would withhold its part of the bargain. The Cherokee Indian tribes had a substantial part of land in Georgia that they had had for many generations though. They were worried about losing their land so they forced the issue by adopting a written constitution. This document proclaimed that the Cherokee nation had complete jurisdiction over its own territory. But by now Indian removal had become entwined with the state of Georgia's rights and the Cherokee tribes had to make their claims in court. When the Cherokee nation sought aid from newly elected president Andrew Jackson, he informed them that he would not interfere with the lawful prerogatives of the state of Georgia. Jackson saw the solution of the problem with the removal of the Cherokee tribes to lands west. This would keep contact between Indians and colonists rare. He suggested that laws be past so that the Indians would have to move west of the Mississippi river. Similar incidents happened between the other "civilized" tribes and white men. The Seminole tribe had land disputes with the state of Florida. The Creek Indians fought many battles against the federal army so they could keep their land in the states of Alabama and Georgia. The Chickisaw and Choctaw had disputes with the state of Mississippi. To ensure peace the government forced these five tribes called the Five Civilized Tribes to move out of their lands that they had lived on for generations and to move to land given to them in parts of Oklahoma. Andrew Jackson was quoted as saying that this was a way of protecting them and allowing them time to adjust to the white culture. This land in Oklahoma was thinly settled and was thought to have little value. Within 10 years of the Indian Removal Act, more than 70,000 Indians had moved across the Mississippi. Many Indians died on this journey. "The Trails of Tears" The term "Trails of Tears" was given to the period of ten years in which over 70,000 Indians had to give up their homes and move to certain areas assigned to tribes in Oklahoma. The tribes were given a right to all of Oklahoma except the Panhandle. The government promised this land to them "as long as grass shall grow and rivers run." Unfortunately, the land that they were given only lasted till about 1906 and then they were forced to move to other reservations. The Trails of Tears were several trails that the Five civilized Tribes traveled on their way to their new lands. Many Indians died because of famine or disease. Sometimes a person would die because of the harsh living conditions. The tribes had to walk all day long and get very little rest. All this was in order to free more land for white settlers. The period of forcible removal started when Andrew Jackson became Presidentin 1829. At that time there was reported to be sightings of gold in the Cherokee territory in Georgia which caused prospectors to rush in, tearing down fences and destroying crops. In Mississippi, the state laws were extended over Choctaw and Chickisaw lands, and in 1930 the Indians were made citizens which made it illegal to hold any tribal office. Also in Georgia, the Cherokee tribes were forbade to hold any type of tribal legislature except to ratify land cessions, and the citzens of Georgia were invited to rob and plunder the tribes in their are by making it illegal for an Indian to bring suit against a When President Jackson began to negotiate with the Indians, he gave them a guarantee of perpetual autonomy in the West as the strongest incentive to emigration. The Five tribes gave all of their Eastern lands to the United States and agreed to migrate beyond the Mississippi by the end of the 1830's. The Federal agents accomplished this by bribery, trickery,and intimidation. All of the treaties signed by the Indians as the agreed to the terms of the removal contained guarantees that the Indians, territory should be perpetual and that no government other than their own should be erected over them without their consent. The land retained by the five civilized tribes was known as the Indian Territory. The 19,525,966 acres were divded among the the five tribes. The Choctaws received 6,953,048 acres in the southeast part of Oklahoma; the Chickisaw recieved over 4,707,903 acres west of the Choctaws reservation; the Cherokees received 4,420,068 acres in the northeast; the received 3,079,095 acres southwest of the Cherokees; and the Seminoles purchased 365,852 acres which they purchased from their kin, the Creeks. The Chickisaw and the Choctaw owned their lands jointly because they were so closely related but the tribes still exercised jurisdiction over its own territory though. Besides the land that the tribes obtained, they also received a large sum of money fom the sale of its Eastern territories. This money was a considerable part of the revenue for the tribes and was used by their legislatures for the support of schools and their governments. The Cherokee nation held $2,716,979.98 in the United States trust; the Choctaw nation had $975,258.91; the Chickisaw held __BODY__,206,695.66;the Creek had $2,275,168.00; and the Seminole had $2,070,000.00 by the end of 1894. After the end of the Trails of Tears, the conversion tof all tribes to Christianity had been efected rapidly. The Seminoles and Creeks were conservative to their customs but other tribes were receptive to any custom considered supperior to their own. The tribes found Christian teachings fitted to their own. Mainly the modernization change began at the end of the removal. Andrew Jackson Gave a speech on the Indian removal in the year of 1830. He said, "It gives me great pleasure to announce to Congress that the benevolent policy of the government, steady pursued for nearly thirty years, in relation with the removal of the indians beyond the white settlements is approaching to a happy "The consequences of a speedy will be important to the United States, to individual states, and to the Indians themselves. It puts an end to all possible danger of a collision betweewn the authorities of the general and state governments, and of the account the Indians. It will place a dense population in large tracts of country now occupied by a few savaged hunters. By opening the whole territory between Tenesee on the north and Louisiana on the south to the settlement of the whites it will incalcuably strengthen the Southwestern frontier and render the adjacent states strong enough to repel future invasion without remote aid." "It will seperate the indians from immediate contact with settlements of whites; enable them to pusue happiness in their own way and under their own rude institutions; will retard the progress of decay, which is lessening their numbers, and perhaps cause them gradually, under the protection of the government and through the influences of good counsels, to cast off their savage habits and become an interesting, civilized, and christian community." For two decades Fort Gibson was the base of operations for the American army as they tried to keep the peace. During the 1810's to 1830's, John C. Calhoun, James Monroe's secretary of war, tried to relocate several Eastern tribes beyond the area of the white settlements. Fort Gibson was brought up because it served as barracks for the army. The relocation area for the Eastern tribes was part of other tribes land. The other tribes wanted toprotect it so they fought for it. The soldiers from Fort Gibson began to make boundaries, construct roads, and escort delegates to the region. The soldiers also started to implement the removal process in other ways to. The soldiers of Fort Gibson were fiercly hated by the Indian tribes of that region. Yet during the many years of the indian removal, there was never a alsh between the soldiers or the tribes. An Indian was never killed by the Army. The soldiers at Fort Gibson served as a cultural buffer between the whites and the indians. The Fort was established in the 1820's by General Matthew Arbuckle. He served and commanded it through most of it's two decades during the Indian removal. He wrote his last report from it on June 21, 1841. THE CHEROKEE INDIANS The Cherokee Indians live in many parts of the United states, but more than 100,000 live in parts of Oklahoma. Many Cherokee have moved elsewhere. In the 1800's, the Cherokee Nation was one of the strongest Indian tribes in the United States. They were part of the Five Civilized Tribes. The Cherokee Nation began to adopt the economic and political stucture of the white settlers in the early 1800's. They owned large plantations and some even kept slaves. The Cherokee Nation was a form of republican government. A Cherokee Indian named Sequoya introduced a system of writing for the Cherokee language in 1821 also. White settlers began to protest the Cherokee's right to own land in the early 1800'. They demanded that the Cherokee Nation be moved west of the Mississippi to make room for white settlers. Some members of the Cherokee Nation signed treaties with the government in 1835 agreeing to move to designated areas in Oklahoma. Most of the tribe did not want to be relocated so they opposed the treaty. But most of the Cherokees, led by Chief John Ross, were forced to move to the Indian Territory in the winter of 1838-1839. More than 17,000 Cherokees marched from their homes to Oklahoma. This march was called the Trail of Tears. Many Indians died on this journey. Even though most of the Cherokee nation been forced to move, more than a 1,000 Cherokee escaped and remained in the Great Smoky Mountains, which is in parts of Tenessee and North Carolina. These tribes became known as the Eastern Band of Cherokee. The Cherokee who went west reformed the political system that they had before. The Cherokee Nation set up schools and churches. But all this progress was stopped in the late 1800's. Congress voted to abolish the Cherokee Nation to open yet more land for settlement by whites. Today most of the Cherokee remain in northeastern Oklahoma, where they have reestablished their form of government. The Chickisaw Indians were a tribe that lived in the southern United States. Their land included western Tenessee and Kentucky, northwestern Alabama, and northern Mississippi before the Indian removal. They were relocated to Oklahoma by the government in the 1830's. The Chickisaws lived in several small vilages with one- room log cabins. The people supported meach other by trading with other tribes, fishing, farming, and hunting. Each village was headed by a chief. The Chickisaw Indians were known as fierce warriors. They fought for Great Britain when they fought France and Spain for control of the southern United States. They also helped them fight against the colonists in the Revolutionary War (1775-1783). And During the Civil War, the tribe fought for the Confederacy (1861-1865). The tribe was relocated to the Indian Territory in 1837 by the National Government. They also took part in the Trail of Tears. In 1907, the Chickisaw Indian territory became part of the new state of Oklahoma. About 5,300 Chickisaw descendants live in Oklahoma. They have a Democratic government in which they elect their leaders for the welfare of the tribe. The Choctaw tribe originates from Alabama and Mississippi. They believed in the primitive ways and hunted and farmed to support themselves. They raised corn and other crops to trade with other Indians. They celebrate their crops with their chief religious ceremony which is a harvest celebration called the Green Corn Dance. One of their legends states that the Choctaw Indian tribe was created at a sacred mount called Nanih Waiya, near Noxapater, Mississippi. After the Indian Removal Act was passed, the Choctaw Indians were forced to move west in order to make room for more white settlers. They were forced to sighn the Treaty of Dancing Rabbit Creek after fierce fighting with the United States army. This treaty exchanched the Indians land for the assigned Indian Territory in what is now Oklahoma. In the early 1830's, over 14,000 Choctaws moved to the Indian Territory in several groups. Although many groups of Indians were gone, over 5,000 Choctaws remained in The Choctaws who moved to the Indian Territory established their own way of life. They modernized themselves by establishing schools and an electoral form of government. In the Civil War, the Choctaw Indians fought on the side of the Confederacy and when the south was defeated, they were forced to give up much of their land. Their tribal governments were dissolved by 1907, when Oklahoma became a state. It stayed that way unttil 1970 when they were recognized by congress and allowed to elect their own chief. Today, many Choctaw are farmers. About 11,000 still live in Oklahoma and nearly 4,000 still live in Mississippi as a seperate tribe. The Creek Indians a part of a 19 tribal group that once resided in much of what is now Alabama and Georgia. Today, many of the 20,000 Creek Indians live in Oklahoma. The Muskogee and the Alabama are the largest Creek tribes. Most of them live north of the other Creek tribes. They are called the Upper Creeks. The lower Creek tribes belong to either Yuchi or Hitichi tribes. In the 1800's, the Creeks fought wars with people trying to settle on their lands. They fought in the first and second Creek Wars. They were great warriors who attacked with the element of surprise. After the Battle of Horseshoe Bend, the Creeks were forced to sign a Treaty that made them give up their land. In the 1830's, they were forced to move to the Indian Territory in what is know Oklahoma. Very few Indians were left behind and they ones who did leave had to leave their belongings behind. The Creeks recieved very little payment for their lands. The Creeks were forced to live in poverty for many years. Many Creeks are still very poor today. Some struggled with crops and became fairly prosperous. Much of the land given to them was not of much value. Also in 1890, a series of laws broke up many tribal landholdings of the Creeks and they were sold to individual Indians. After this, many Creeks were forced back into poverty. The Seminole Indians are a tribe the used to reside in Florida in the early 1800's. The Seminole originally belonged to the Creek tribe. They broke apart from them and moved out of Alabama and Georgia and moved into Florida in the 1700's They became known as Seminoles because the name means runaways. The Seminoles opposed the United States when they came for the Seminole's land. The United acquired Florida in 1819, and began urging them to sell their land to the government and to move to the Indian Territory along with the other southeasten tribes. In 1832, some of the Seminole leaders signed a treaty and promised to relocate. The Seminole tribe split at this time. After the Indians that agreed to move had gone the other part of the tribe fought to keep their lands. They fled into the Florida swamps. They started the Second Seminole war (1835). This was fought over the remaining land that the Seminole had fled to. It lasted for seven years. 1,500 American men died and the cost to the United States was $20 million. The Seminole were led by Osceola until he was tricked by General Thomas Jessup. Osceola was seized and imprisoned by Jessup during peace talks under a flag of truce. Osceola died in 1838 when he still in prison. After the war, many Seminoles moved west but still asmall group stayed hidden in the Florida swamps.

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In the 1950s a mountain range was discovered beneath the ice in Antarctica. The mountains were named the Gamburtsevs. Recently, scientists used ice-penetrating radar and a network of seismometers (size-ma-me-ters) to determine the size and shape of the range. Scientists have learned that the mountains are similar in size and shape to the Alps, with sharp peaks and deep valleys. Previously, secular scientists assumed the Gamburtsevs would be mostly flat. They believed that Antarctica’s ice sheet formed slowly, over millions of years. The steep and jagged mountain peaks would be worn down as the glaciers continually scraped across the mountaintops. Finding such high, jagged peaks under the ice shows that the ice formed quickly. This fits with the creationist model of a catastrophic Ice Age. (An ice age is defined as a time of extensive glacial activity during which a large part of the land is covered by ice.) Most creationists agree that there was one major Ice Age following the Flood. It occurred largely because volcanic ash in the air blocked the sun’s rays, making the summers much cooler. This combined with warm oceans to bring about lots of precipitation, which fell over the high areas and formed ice sheets. Secular scientists have a hard time coming to agreement about ice ages. They have proposed that there were anywhere from four to thirty different times when glaciers covered much of the land. A catastrophic Ice Age would explain why the huge Antarctic mountains were not worn away but were instead covered rapidly. This is another example of how true science confirms what the Bible has already told us!

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Hearing When we hear, we are processing sound waves that are made up of compressions of air or water. We hear vibrations in the air as they strike a part of the ear called the eardrum and make it vibrate. These vibrations are sent through other parts of the ear and finally sent as action potentials to the brain. Sound waves have both amplitude and frequency. Amplitude is a sound’s intensity, and loudness is the perception of that intensity. Frequency of a sound is the number of compressions per second. Pitch is closely related to frequency. Hearing – Outer Ear The part of the hearing system that we see on the outside of the head is called the pinna (the ear). It is designed to capture sound. When a sound reaches the ear, it passes through the tube called the external auditory canal until it reaches the tympanic membrane or eardrum. Hearing – Middle Ear The eardrum vibrates at the same frequency as the sound waves that hit it. Attached to the eardrum are three very small bones (the smallest bones in the body!) that also vibrate to the frequency of the sound. These bones are known as the hammer, anvil, and stirrup because of their shapes. Together, they are known as the ossicles. The three bones are attached to the oval window. The oval window is the beginning of the inner ear. Hearing – Inner Ear The inner ear has the cochlea, a snail-shaped fluid-filled structure. Vibrations from sound in the fluid in the cochlea displace hair cells that are the neuron receptors for sound at the bottom of the cochlea in the basilar membrane. The tectorial membrane covers the hair cells and protects them. The hair cells send signals to the auditory nerve, which sends a signal about sound to the temporal lobe of the brain. Visualization of the Ear Theories about Hearing There are three theories about hearing. The first theory is known as the frequency theory. This theory says that the basilar membrane that holds the hair cells vibrates at the same frequency as sound. This causes the auditory nerve axons to produce action potentials at the same frequency. However, the maximum firing rate of a neuron is short of the highest frequencies we can hear. Theories about Hearing The second theory is known as the place theory. This theory suggests that the basilar membrane is similar to the strings of a piano and that each area along the membrane is tuned to a specific frequency and vibrates to that frequency. The nervous system would have to decide among the frequencies based on which neurons are active. However, the problem with this theory is that some parts of the basilar membrane are bound together too tightly for any part to vibrate like a piano string. Theories about Hearing The final theory is known as the volley principle. This theory suggests we use methods that combine aspects of the frequency theory and the place theory. The basilar membrane is stiff at its base where the stirrup connects with the cochlea and floppy at the other end of the cochlea. Hair cells along the basilar membrane would act differently depending on their location. When we hear sounds at a very high frequency, we use something like the place theory. When we hear lower pitched sounds, we use something like the frequency theory. So combining parts of the first two theories explains how we hear better than using either one of the first two theories separately. Hearing and the Brain Information about hearing, just like information about vision, is first routed through the thalamus and other brain areas below the cortex before reaching the primary auditory cortex, located in the temporal lobe of the cerebral cortex. Different areas of the auditory cortex, just like is true in the visual cortex, process information in different ways, including about the location of a sound and the motion of sound. And just like vision, hearing requires a certain amount of experience with sounds for our hearing to be fully developed. Areas of the brain associated with vision and hearing

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Reading to Learn: Comprehension Strategies Rationale: In order to gain insight while reading one must be able to comprehend. However, students often fail to comprehend (and remember) what they have read. Because of this, teachers have been given comprehension strategies that can be taught to children in order to give them a helping hand. One such strategy is called story-grammar. The following activity will show children how to use the story-grammar strategy to help them comprehend what they are reading. Materials: You will need two copies of ten different conventional stories (The Orphan Kittens by Margaret Wise Brown, Oliver Finds a Home by Justin Korman, Bambi by Felix Salten, Paul Revere by Irwin Shapiro, etc.) that the children will find interesting, Charlotte's Web by E.B. White (with highlighted passages for modeling), a question-answer sheet, and a pencil. Procedure: 1. Explain to the boy's and girl's that today they will be learning a strategy that will show them how to go about comprehending what they read. 2. Have each child come up and choose a book from your selection (There should be two children throughout the room with the same book). Next pass out two question-answer sheets to each child. Tell the children to put the book and one of the question-answer sheets under their desk to be used at a later date. 3. Explain to the children that you want them to listen to you read Charlotte's Web. Tell them that after you read for a few minutes, you will stop, think about the first question on the sheet, and then answer it. Explain that you want them to answer the same question at their desk. You will do this throughout the reading of the book. 4. Now begin reading. After reading a few paragraphs (Read only the highlighted passages for modeling) ask the children to answer the first question: Who are the main characters? Give them two or three minutes to answer, and then read on. After you have read a few more passages, ask them to answer the second question: Where and when did the story take place? Continue this until you have read the entire story and the children have answered the other three questions consisting of What did the main characters do?, How did the story end?, and How did the main character feel? Be sure to let the children know there is no right or wrong answer for the question How did the main character feel? because itís is an open-ended question (Depends on readers interpretation of the story). Now have a class discussion about their answers. 5. The second part of the lesson requires the children to read silently (which is very good for a lot of reading skills such as fluency and comprehension) at their desk for ten minutes. (Model reading silent by telling the students to read by thinking the words in their head without saying them out loud). Ask the children to take out the book that they choose earlier along with the second question-answer sheet. Explain to them how you will set a timer for ten minutes, during which time they are to be reading the book they choose. When the ten minutes are up, ask the children to answer the first question on the sheet in front of them. Give them ample time to reflect on what they have read and then set the timer again. Do this throughout the entire book. (You may want to choose shorter stories or treat this as a daily but weekly, meaning they work on the same books all week, assignment). 7. When the children have finished the book and answered all the questions, have them pair up with the other person in the room who read the same book. Explain how you want them to discuss their answers with each other. If there is a disagreement among them, tell them to talk it over to see why. This will help them see how someone else came to their conclusions. Don't forget to read silently along with the children. (You may want to have one of your students read the same book that you are reading and then discuss it with them. If you do this, write your answers in their language). (This will keep them from feeling over-powered). 8. For a review you can ask the children what five questions they should ask themselves, while reading, to help them comprehend what they have read. References: Pressley, M., Johnson, C. J., Symons, S., McGoldrick, J. A., & Kurity, J. A. (1989). "Strategies That Improve Childrenís Memory and Comprehension of Text. The Elementary School Journal, (1990, Pp. 3-32). Click here to return to Elucidations

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Conjunction Activities for Children This game is great for teaching proper usage of conjunctions. Simply click on the above highlighted link and it will take you to an online crossword puzzle that your students can use. Or, if you would like to make this an in-the-class activity, simply print it off and make copies for everyone. This could be used as a introductory or culminating activity for a conjunction unit. Use this activity as a timed exercise in which you provide the students with fifty simple sentences. The students must then link the sentences together to further comprehend the purpose of conjunctions. In this particular activity students will create compound sentences with the use of conjunctions. The purpose of this assignment is to show the importance of conjunctions and the role that they play in everyday grammar and written form. The objective will be to get students to write two paragraphs using a variety of simple and compound sentences. This is a great way to get your students to visualize the function that conjunctions perform! Try it out, and let us know if it helped! This activity will allow students to create their own sentences using the conjunction "But". Students will divide into teams and then create sentences starting with "Yes, but...."

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The first spacecraft to globally map the Moon left lunar orbit on May 3, 1994. Clementine, a joint Department of Defense-NASA mission, had systematically mapped the Moon’s surface over 71 days, collecting almost 2 million images. For the first time, scientists could put results of the Apollo lunar sample studies into a regional, and ultimately, a global context. Clementine collected special data products, including broadband thermal, high resolution and star tracker images for a variety of special studies. But in addition to this new knowledge of lunar processes and history, the mission led a wave of renewed interest in the processes and history of the Moon, which in turn, spurred a commitment to return there with both machines and people. We peeked into the Moon’s cold, dark areas near the poles and stood on the edge of a revolution in lunar science. Prior to Clementine, good topographic maps only existed for areas under the ground tracks of the orbital Apollo spacecraft. From Clementine’s laser ranging data, we obtained our first global topographic map of the Moon. It revealed the vast extent and superb preservation state of the South Pole-Aitken (SPA) basin and confirmed many large-scale features mapped or inferred from only a few clues provided by isolated landforms. Correlated with gravity information derived from radio tracking, we produced a map of crustal thickness, thereby showing that the crust thins under the floors of the largest impact basins. Two cameras (with eleven filters) covered the spectral range of 415 to 1900 nm, where absorption bands of the major lunar rock-forming minerals (plagioclase, pyroxene and olivine) are found. Varying proportions of these minerals make up the suite of lunar rocks. Global color maps made from these spectral images show the distribution of rock types on the Moon. The uppermost lunar crust is a mixed zone, where composition varies widely with location. Below this zone is a layer of nearly pure anorthosite, a rock type made up solely of plagioclase feldspar (formed during the global melting event that created the crust). Craters and large basins act as natural “drill holes” in the crust, exposing deeper levels of the Moon. The deepest parts of the interior (and possibly the upper mantle) are exposed at the surface within the floor of the enormous SPA basin on the far side of the Moon. Clementine showed us the nature and extent of the poles of the Moon, including peaks of near permanent sun-illumination and crater interiors in permanent darkness. From his first look at the poles, Gene Shoemaker (Leader of the Clementine Science Team) got an inkling that something interesting was going on there. Gene was convinced that water ice might be present, an idea about which I had always been skeptical. At that time, no trace of hydration had ever been found in lunar minerals and the prevailing wisdom was that the Moon is now and always had been bone dry. With Gene arguing to keep an open mind and Stu Nozette (Deputy Program Manager) devising a bistatic radio frequency (RF) experiment to use the spacecraft transmitter to “peek” into the dark areas of the poles, we moved ahead on planning the observations. To my astonishment (and delight), a pass over the south pole of the Moon showed evidence for enhanced circular polarization ratio (CPR) – a possible indicator of the presence of ice. A control orbit over a nearby sunlit area showed no such evidence. However, CPR is not a unique determinant for ice, as rocky, rough surfaces and ice deposits both show high CPR. It took a couple of years to reduce and fully understand the data, but the bistatic experiment was successful. In part, our ice interpretation was supported by the discovery of water ice at the poles of Mercury (a planet very similar to the Moon). We published our results in Science magazine in December 1996, setting off a media frenzy and a decade of scientific argument and counter-argument about the interpretation of radar data for the lunar poles (an argument that continues to this day, despite subsequent confirmation of lunar polar water from several other techniques). Along with Clementine’s success came a growing interest in lunar resources and a new appreciation for the complexity of the Moon. This interest led to the selection of Lunar Prospector (LP) as the first PI-led mission of NASA’s new, low-cost Discovery series of planetary probes. LP flew to the Moon in 1998 and carried instruments complementary to the data produced by Clementine, including a gamma-ray spectrometer to map global elemental composition, magnetic and gravity measurements, and a neutron spectrometer to map the distribution of hydrogen. LP found enhanced concentrations of hydrogen at both poles, again suggesting that water ice was probably present. The debate on the abundance and physical nature of the water ice continued, with estimates ranging from a simple enrichment of solar wind implanted hydrogen in polar soils, to substantial quantities of water ice trapped in the dark, cold regions of the poles. Buttressed by this new information, the Moon became an attractive destination for robotic and human missions. With direct evidence for significant amounts of hydrogen (regardless of form) on the surface, there now was a known resource that would support long-term human presence. This hydrogen discovery was complemented by the identification in Clementine images of several areas near the pole that remain sunlit for substantial fractions of the year – not quite the “peaks of eternal light” first proposed by French astronomer Camille Flammarion in 1879 but something very close to it. The availability of material and energy resources – the two biggest necessities for permanent human presence on the Moon – was confirmed in one fell swoop. Combined, the results of Clementine and LP finally gave scientists the Lunar Polar Orbiter mission we had long sought. These two missions certified the possibility of using lunar resources to provision ourselves in space, permanently establishing the Moon as a valuable, enabling asset for human spaceflight. Remaining was to verify and extend the radar results from Clementine and map the ice deposits of the poles. The Clementine bistatic experiment led to the development of an RF transponder called Mini-SGLS (Space Ground Link System), which flew on the Air Force mission MightySat II in 2000. This experiment miniaturized the RF systems necessary for a low mass, low power imaging radar. With the 2008 inclusion of our Mini-SAR on India’s Chandryaan-1 lunar orbiter, we finally got the chance to build and fly such a system. Chandrayaan-1 not only mapped the high CPR material at both poles, it also carried a spectrometer (the Moon Mineralogy Mapper, or M3) that discovered large amounts of adsorbed surface water (H2O) and hydroxyl (OH) at high latitudes. Coupled with the measurement of exospheric water above the south pole by its Moon Impact Probe, Chandrayaan-1 significantly advanced our understanding of polar water, revealing it to be abundant and present in more varied forms on the Moon than had previously been imagined. The ever increasing weight of evidence for the presence of significant amounts of water at the lunar poles led to the LCROSS experiment being “piggybacked” on NASA’s 2008 Lunar Reconnaissance Orbiter (LRO) mission. LCROSS was a relatively inexpensive add-on, designed to observe the collision of the LRO launch vehicle’s Centaur upper stage with the lunar surface, looking for water in the ejecta plume of that impact. Water in both vapor and solid form was observed, suggesting the presence of water ice in the floor of the crater Cabaeus (at concentration levels between 5 and 10 weight percent). LRO orbits the Moon and collects data to this day. Although much remains unknown about lunar polar water, we now know for certain that it exists; such knowledge has completely revised our thinking about the future use and habitation of the Moon. The Clementine programmatic template has influenced spaceflight for the last 20 years. The Europeans flew SMART-1 to the Moon in 2002, largely as a technology demonstration mission with goals very similar to those of Clementine. NASA directed the Applied Physics Laboratory (APL) to fly Near-Earth Asteroid Rendezvous (NEAR) to the asteroid Eros in 1995 as a Discovery mission, attaining the asteroid exploration opportunity missed when control of the Clementine spacecraft was lost after leaving the Moon. India’s Chandrayaan-1 was of a size and payload scope similar to Clementine. The selection of LCROSS as a low-cost, fast-tracked, limited objectives mission further extended use of the Clementine paradigm. The “Faster-Better-Cheaper” mission model, once panned by some in the spaceflight community, is now recognized as a preferred mode of operations, absent the emotional baggage of that name. A limited objectives mission that flies is more desirable than a gold-plated one that sits forever on the drawing board. While some missions do require significant levels of fiscal and technical resources to attain their objectives, an important lesson of Clementine is that for most scientific and exploration goals, “better” is the enemy of “good enough.” Space missions require smart, lean management; they should not be charge codes for feeding the beast of organizational overhead. Clementine was lean and fast; perhaps we would have made fewer mistakes had the pace been a bit slower, but overall the mission gave us a vast, high-quality dataset, still extensively used to this day. The Naval Research Laboratory transferred the Clementine engineering model to the Smithsonian in 2002. The spacecraft hangs today in the Air and Space Museum, just above the Apollo Lunar Module. It is probably not too much of an exaggeration to say that Clementine changed the direction of the American space program. After the failure of SEI in 1990-1992, NASA was left with no long-term strategic direction. For the first time in its history, NASA had no follow-on program to Shuttle-Station, despite attempts by Dan Goldin and others to secure approval for a human mission to Mars (then and now, a bridge too far – both technically and financially). This programmatic stasis continued until 2003, when the tragic loss of Columbia led to a top-down review of U.S. space goals. Because Clementine had documented its strategic value, the Moon once again became an attractive destination for future robotic and human missions. The resulting Vision for Space Exploration (VSE) in 2004 made the Moon the centerpiece of a new American effort beyond low Earth orbit. While Mars was vaguely discussed as an eventual (not ultimate) objective, the activities to be done on the Moon were specified in detail in the VSE, particularly with regard to the use of its material and energy resources to build a sustainable program. Regrettably, various factors combined to subvert the Vision, thereby ending the strategic direction of America’s civil space program. Clementine was a watershed, the hinge point that forever changed the nature of space policy debates. A fundamentally different way forward is now possible in space – one of extensibility, sustainability and permanence. Once an outlandish idea from science fiction, we have found that lunar resources can be used to create new capabilities in space, a welcome genie that cannot be put back in the bottle. Americans need to ask why their national space program was diverted from such a sustainable path. We cannot afford to remain behind while others plan and fly missions to understand and exploit the Moon’s resources. Our path forward into the universe is clear. In order to remain a world leader in space utilization and development – and a participant in and beneficiary of a new cislunar economy – the United States must again direct her sights and energies toward the Moon. Note: Background history for the Clementine mission is described in a companion post at my Spudis Lunar Resources blog.

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The first African-American Member of Congress was elected nearly 100 years after the United States became a nation. Slavery had only been illegal for five years in the American South when Representative Joseph Rainey of South Carolina and Senator Hiram Revels of Mississippi were elected to office in 1870. In fact, the states they served had been represented by slave owners only 10 years earlier. The early African-American Members argued passionately for legislation promoting racial equality, but it would still be many years before they would be viewed as equals. On December 5, 1887, for the first time in almost two decades, Congress convened without an African-American Member. For nearly 30 years, no African Americans served in Congress. With his election to the U.S. House of Representatives from a Chicago district in 1928, Oscar De Priest of Illinois became the first African American to serve in Congress since George White of North Carolina left office in 1901. Use the interactive map to compile information on the representation of Black Americans in Congress, such as the number of Members who served from a particular state or region and when they served.

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As discussed in the previous part of Lesson 3, the slope of a position vs. time graph reveals pertinent information about an object's velocity. For example, a small slope means a small velocity; a negative slope means a negative velocity; a constant slope (straight line) means a constant velocity; a changing slope (curved line) means a changing velocity. Thus the shape of the line on the graph (straight, curving, steeply sloped, mildly sloped, etc.) is descriptive of the object's motion. In this part of the lesson, we will examine how the actual slope value of any straight line on a graph is the velocity of the object. Consider a car moving with a constant velocity of +10 m/s for 5 seconds. The diagram below depicts such a motion. The position-time graph would look like the graph at the right. Note that during the first 5 seconds, the line on the graph slopes up 10 m for every 1 second along the horizontal (time) axis. That is, the slope of the line is +10 meter/1 second. In this case, the slope of the line (10 m/s) is obviously equal to the velocity of the car. We will examine a few other graphs to see if this a principle that is true of all position vs. time graphs. Now consider a car moving at a constant velocity of +5 m/s for 5 seconds, abruptly stopping, and then remaining at rest (v = 0 m/s) for 5 seconds. If the position-time data for such a car were graphed, then the resulting graph would look like the graph at the right. For the first five seconds the line on the graph slopes up 5 meters for every 1 second along the horizontal (time) axis. That is, the line on the position vs. time graph has a slope of +5 meters/1 second for the first five seconds. Thus, the slope of the line on the graph equals the velocity of the car. During the last 5 seconds (5 to 10 seconds), the line slopes up 0 meters. That is, the slope of the line is 0 m/s - the same as the velocity during this time interval. Both of these examples reveal an important principle. The principle is that the slope of the line on a position-time graph is equal to the velocity of the object. If the object is moving with a velocity of +4 m/s, then the slope of the line will be +4 m/s. If the object is moving with a velocity of -8 m/s, then the slope of the line will be -8 m/s. If the object has a velocity of 0 m/s, then the slope of the line will be 0 m/s. The widget below plots the position-time plot for an object moving with a constant velocity. Simply enter the velocity value, the intial position, and the time over which the motion occurs. The widget then plots the line with position on the vertical axis and time on the horizontal axis.

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In the last chapter, we graphed data. Now, we move to graphing equations with two variables. For simplicity, the discussion in this chapter is confined to linear equations, i.e. equations of degree 1 . Some of the general concepts carry over to more general equations, to be discussed later. The first section explains how to represent variables as ordered pairs. This is a convenient way of writing corresponding variable values. In this section, we will also learn how to graph ordered pair values (x, y) on an xy-graph. Graphing (x, y) values on a graph is similar to graphing x values on a number line, except that we are working in two dimensions instead of one. The second section provides an introduction to graphing equations. It explains how to make a data table of (x, y) values and how to make a graph from a data table. There are several methods of graphing equations. The next section introduces another method of graphing linear equations using the x-intercept and y-intercept. It is similar to creating a data table, but often quicker. The fourth section explains the concept of slope. Slope is a characteristic of a linear equation that will allow us to graph that linear equation, recognize its graph, and understand how it relates to other linear equations. The final section introduces a third method of graphing linear equations, which uses slope. It explains how to graph a linear equation given its slope and a single point, and it explains how to determine the slope of a line, given its equation. Graphing is an enormous topic in algebra I and algebra II. No matter what type of equations you study in future algebra, you will probably need to know how to graph them. Thus, it is important to understand the material in this introductory chapter. Each method of graphing learned here will become useful in later topics in algebra, pre- calculus, and even calculus. Graphing also has practical applications. Chemists and physicists use graphs to discover relationships between quantities. Graphs can be used to predict future values of important figures like population and the national debt. Graphs are used in almost every discipline, so it is important to develop an understanding of how to use them.

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The space near black holes is one of the most extreme environments in the Universe. The bodies' strong gravity and rotation combine to create rapidly spinning disks of matter that can emit huge amounts of light at very high energies. However, the exact mechanism by which this light is produced is uncertain, largely because high-resolution observations of black holes are hard to do. Despite their outsized influence, black holes are physically small: even a black hole a billion times the mass of the Sun occupies less volume than the Solar System. A new X-ray observation of the region surrounding the supermassive black hole in the Great Barred Spiral Galaxy may have answered one of the big questions. G. Risaliti and colleagues found the distinct signature of X-rays reflecting off gas orbiting the black hole at nearly the speed of light. The detailed information the astronomers gleaned allowed them to rule out some explanations for the bright X-ray emission, bringing us closer to an understanding of the extreme environment near these gravitational engines. Despite the stereotype of black holes "sucking" matter in, they attract it via gravity. That means stars, gas, and other things can fall into orbits around black holes, which may be stable for long periods of time. Gas often forms accretion disks and jets that release huge amounts of energy in the form of light. This energy can include X-ray emissions. So despite their name, black holes can be very luminous objects. Nearer the boundary of a rotating black hole—its event horizon—the strength of gravity is such that the space matter occupies can be also dragged around the black hole. This effect is called "frame dragging," and is predicted by Einstein's general theory of relativity. The region in which frame dragging becomes significant, however, is very close to the black hole's event horizon, which is relatively small, especially when imaged from Earth. As a result, astronomers could not be sure whether ordinary orbital effects or relativistic frame-dragging is more important for producing the intense X-ray emissions. Astronomers paid particularly close attention to the supermassive black hole at the center of the Great Barred Spiral Galaxy (also known by its catalog number NGC 1365) when a cloud of gas momentarily eclipsed it. That rare event allowed them to get a good size estimate for the accretion disk that surrounds the black hole. The current study followed up by monitoring fluctuations in the X-ray emissions, using the orbiting XMM-Newton and NuSTAR X-ray telescopes. In particular, the researchers looked at emission from neutral and partly ionized iron atoms in the gas. Prior observations showed that the emission lines were broadened, which can be caused by several different phenomena. Researchers considered two primary hypotheses: absorption by other gas along the line of sight between the black hole and us, or very fast motion of the gas itself. The new data strongly supported the latter option. In this scheme, the observed X-ray light reflected off the inner edge of the accretion disk, where the gas is moving at very close to the speed of light. According to the models, this scattering occured well within the frame-dragging region near the black hole. The inner edge of the accretion disk may be close to or at the minimum stable distance from the black hole. Closer than that distance, and matter can no longer orbit in a circular path—it will tend to spiral in. The authors argued that any explanation of the X-ray emission that fails to account for the general-relativistic effects just won't work. Previous observations estimated that the black hole in the Great Barred Spiral Galaxy is spinning nearly as fast as possible; whether other black holes will have similar properties remains an open question.

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These are not simply facts to be memorized. These are complex concepts that students need to develop through engagement with the natural world, through drawing on their previous experiences and existing knowledge, and through the use of models and representations as thinking tools. Students should practice using these ideas in cycles of building and testing models in a wide range of specific situations. At this grade band, students can begin to ask the questions: What is the nature of matter and the properties of matter on a very small scale? Is there some fundamental set of materials from which other materials are composed? How can the macroscopically observable properties of objects and materials be explained in terms of these assumptions? In addition, armed with new insight provided by their knowledge of the existence of atoms and molecules, they can conceptually distinguish between elements (substances composed of just one kind of atom) and compounds (substances composed of clusters of different atoms bonded together in molecules). They can also begin to imagine more possibilities that need to be considered in tracking the identity of materials over time, including the possibility of chemical change. Students have to be able to grasp the concept that if matter were repeatedly divided in half until it was too small to see, some matter would still exist—it wouldn’t cease to exist simply because it was no longer visible. Research has shown that as students move from thinking about matter in terms of commonsense perceptual properties (something one can see, feel, or touch) to defining it as something that takes up space and has weight, they are increasingly comfortable making these kinds of assumptions. This is one example of the ways in which the framework that students developed in the earlier primary and elementary grades prepares them for more advanced theorizing at the middle school level. Middle school science students must conjecture about and represent what matter is like at a level that they can't see, make inferences about what follows from different assumptions, and evaluate the conjecture based on how well it fits with a pattern of results. Research has shown that middle school students are able to discuss these issues with enthusiasm, especially when different models for puzzling phenomena are implemented on a computer and they must judge which models embody the facts. This approach led students who had relevant macroscopic understanding of matter to see the discretely spaced particle model as a better explanation than alternatives (e.g., continuous models and tightly packed particle models). Class discussions allowed students to establish more explicit rules for evaluating

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In late 1863, President Abraham Lincoln and the Congress began to consider the question of how the Union would be reunited if the North won the Civil War. In December President Lincoln proposed a reconstruction program that would allow Confederate states to establish new state governments after 10 percent of their male population took loyalty oaths and the states recognized the “permanent freedom of slaves.” Several congressional Republicans thought Lincoln’s 10 Percent Plan was too mild. A more stringent plan was proposed by Senator Benjamin F. Wade and Representative Henry Winter Davis in February 1864. The Wade-Davis Bill required that 50 percent of a state’s white males take a loyalty oath to be readmitted to the Union. In addition, states were required to give blacks the right to vote. Congress passed the Wade-Davis Bill, but President Lincoln chose not to sign it, killing the bill with a pocket veto. Lincoln continued to advocate tolerance and speed in plans for the reconstruction of the Union in opposition to the Congress. After Lincoln’s assassination in April 1865, however, the Congress had the upper hand in shaping Federal policy toward the defeated South and imposed the harsher reconstruction requirements first advocated in the Wade-Davis Bill.

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The Seasonal Merry-Go-RoundThe tilt of Earth's rotational axis and the Earth's orbit around the Sun work together to create the seasons. As the Earth travels around the Sun, it remains tipped over in the same direction, with its north pole pointed towards the star Polaris. This 23.5 degree tilt of the Earth's rotational axis to the Earth's orbital plane about the Sun (the ecliptic plane) causes Earth's two hemispheres to be exposed to different intensities of sunlight for different amounts of time throughout the year. The changing intensity and changing amount of sunlight to the different hemispheres has given rise to the seasons of summer, fall, winter and spring. In the Northern Hemisphere, the first day of summer, called the summer solstice, is around June 21st. The summer solstice marks the point at which the north pole of the Earth is tilted at its maximum towards the Sun. For any location in the northern hemisphere, the day of the summer solstice is the longest day of the year with the Sun reaching its greatest angular distance north (or its highest point in the sky for the year for that given location). During the time surrounding the summer solstice, the northern hemisphere is getting more direct sunlight for a longer amount of time, which heats that hemisphere efficiently causing warmer temperatures on average. Notice that when the northern hemisphere is tilted towards the Sun, the southern hemisphere is tilted away. This is why people in the North America, Europe, Asia, and other places north of the equator have the opposite season of people in South America, Australia, and other places south of the equator. So, while the summer solstice marks the beginning of summer for the northern hemisphere, it marks the beginning of winter for the southern hemisphere. The first day of winter for the northern hemisphere is called the winter solstice. This day, around December 21st each year, is when the north pole of the Earth is tilted at its maximum away from the Sun. The Sun’s rays are less intense at this time of year because they are spread over a greater surface area and must travel through more energy-absorbing atmosphere to reach the Earth. Also, the winter solstice is the shortest day of the year for those who live in the northern hemisphere. The decreased intensity of the sunlight received along with less daylight hours leads to the cooler temperatures often felt by those living in the northern hemisphere during winter months. Again, things are reversed for the southern hemisphere, where summer is being ushered in at the time of the winter solstice. Of course, between the season of summer and winter in the northern hemisphere comes the season of fall. The beginning of fall in the northern hemisphere is marked by the autumnal equinox (around September 23rd each year). And between the seasons of winter and summer in the northern hemisphere is spring. The beginning of spring in the northern hemisphere is marked by the vernal equinox (around March 21st each year). At the two equinoxes, neither the north pole nor the south pole is inclined toward the Sun. Equinox literally means "equal night". On the vernal (spring) and autumnal (fall) equinoxes, day and night are about the same length all over the world.

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If students are not familiar with or have not recently practiced plotting points on the first quadrant using ordered pairs, review that concept before continuing. Distribute the Coordinate Geometry sheet (M-5-3-3_Coordinate Geometry and KEY.docx) to each student. On a copy of the First Quadrant worksheet from Lesson 2 (M-5-3-2_First Quadrant and KEY.docx), have students plot the points in Figure 1 in order, connecting each point to the previous point and connecting the last point to the first to make a complete, closed shape. Ask students to come up with any words they can think of to describe Figure 1. They may only come up with “triangle.” “There are a lot of names we can call this figure. Shapes have many descriptions, just as you might. You are a person, a boy or girl, maybe a brother or sister, a student, maybe a baseball player, right- or left-handed, and so on. Just as there are many ways to describe you, there are many ways to describe shapes. So, this shape is a triangle since it has three sides, but we can also call it a polygon.” Depending on the class, you can break the word polygon down into two parts: poly- and -gon, and examine each part of the word, explaining that poly- means “many” and -gon means “angles,” and so the word polygon literally means “many angles.” This approach is useful when dealing with other terms like hexagon or octagon (and continues to be useful in higher mathematics when dealing with terms like polynomial). After explaining that a polygon is a figure that has many sides, tell students the sides must be straight lines and the figure must be closed. In other words, they have to connect the last point they plotted back to the first point with a straight line. “Next to the triangle you graphed, write the words polygon and triangle, and then graph Figure 2 on the same coordinate plane on which you graphed Figure 1.” After students have plotted Figure 2, ask them to describe it. Students may respond with rectangle and polygon (or incorrect answers). “What makes this shape a polygon?” (It has many sides, the sides are straight, and the figure is closed.) “What makes this shape a rectangle?” Here, students should focus on the four right angles in the figure. “How many sides does our rectangle have?” (Four) “Just like we have a general name for shapes with three sides—triangle—we also have a general name for shapes with four sides. We call them quadrilaterals.” Possibly write “quadrilaterals” on the board so students can see the term. Again, depending on the class, breaking down the word quadrilateral into parts might be helpful: quad- means “four” and -lateral means “sides.” If students are familiar with football, they may have heard of a lateral pass, which is a pass that goes sideways (as opposed to backward or forward). “So far, then, our shape has a few names. It is a polygon, it is a quadrilateral, and it is a rectangle. It actually has at least one more name. Look at the two long sides that go straight up and down. What word do we have for line segments that will never cross one another no matter how long they are?” (Parallel) “And what about the two short sides on the top and bottom of our rectangle?” (They are also parallel.) “Because our quadrilateral has two pairs of parallel sides, we call it a parallelogram.” Again, write this word on the board so students can see it written out, pointing out the word parallel inside the word parallelogram. Have students write all the terms associated with a parallelogram next to the rectangle. Have students graph Figure 3 on the same coordinate plane as Figures 1 and 2. Ask them to describe it. They should note that it’s a square, a polygon, a quadrilateral, and a parallelogram. If not, ask them if any of the previous terms that applied to rectangle also apply to it. Ask students to explain why the figure is a polygon, quadrilateral, and parallelogram. Lastly, ask them to explain how they know it’s a square. Here, students should focus on both the four right angles and the four sides of equal length. “Now, you said it’s a square because it has four sides of equal length and four right angles. Since it has four right angles, can we also call it a rectangle?” (Yes) “If I ask you to draw a square, can you ever draw one that doesn’t have four right angles?” (No) “So we know that every square is a rectangle.” Have students write down all the terms that apply to the square. Give each student a copy of Quadrilateral Venn diagram sheet (M-5-3-3_Quadrilateral Venn Diagram.docx). Describe how to interpret the diagram (i.e., all squares are rectangles, all rectangles are parallelograms, and all parallelograms are quadrilaterals). Make sure to emphasize that even though all squares are rectangles, for example, there are definitely rectangles (like the one they plotted) that are not squares. On the diagram, illustrate this by identifying the region that is inside the rectangle part of the figure but is outside the square part of the figure. “Write the words “Figure 2” and “Figure 3” on your diagram to show in which part of the diagram they belong.” (Figure 2 belongs in the rectangle portion but not the square portion, while Figure 3 belongs in the square portion.) “Where does Figure 1 go on the diagram?” (Students may respond with Outside the quadrilaterals or not on the diagram.) “We might need another diagram if we want to be able to organize all our polygons. This diagram just organizes quadrilaterals, which have how many sides?” (Four) Before plotting Figure 4, ask students what shape they think it’s going to be. If they aren’t sure (they may be trying to visualize it in their heads), ask them how many points they have to plot. They may at least guess it will have five sides even if they aren’t sure what the figure is called. After discussion, have students plot Figure 4 on the second coordinate plane. “Do any of the words we talked about with the figures on the first coordinate plane apply to this figure?” (Polygon) “We call a five-sided polygon a pentagon.” Again, explaining the meaning of the prefix penta- (five) may be helpful to students. They may also be familiar with the Pentagon in Washington, D.C. (This image: http://www.sciencephoto.com/image/357691/350wm/T8350265-Pentagon_building-SPL.jpg shows the Pentagon from overhead so students can clearly see that it has five sides.) Have students label their pentagon appropriately. Also, explain that whether a polygon is a pentagon is determined only by the number of sides it has. Even though the pentagon in Figure 5 isn’t exactly the same as the Pentagon, they both have five sides and so are both classified as pentagons. “How many sides will Figure 5 have, based on the number of points that need to be graphed?” (Six) Have students plot Figure 5. “What is our six-sided figure called?” Write the word hexagon on the board and explain that hex- means six, so the word literally means “six angles.” Have students label Figure 5 appropriately. Finally, have students plot Figure 6. “How many sides does it have?” (Eight) “What do we call an eight-sided polygon?” If students don’t know, guide them toward the realization that an octopus has eight arms and the prefix oct- means eight, and have them guess what we might call a polygon with eight angles. Have students label the octagon on their coordinate plane appropriately. The Coordinate Plane worksheet can be collected at the end of class and checked against the key to ensure understanding. (Students may use it for reference in Activity 3.) Have students work in pairs for Activity 3. Each student should draw a pattern or design on a coordinate plane that incorporates at least two different polygons, at least one of which should be a quadrilateral. Students should plot each part of their design and include coordinate instructions to provide to their partner. They should label each “set” of coordinates with the name or names of the appropriate polygon. (If they are drawing, for example, a square, they should label the set of coordinates describing the square with the terms square, rectangle, parallelogram, quadrilateral, and polygon.) Once students have listed the coordinates and double-checked their work, they should give their instructions to someone else. “Now, you have the instructions to make someone else’s design. Go ahead and start with the first point on the list and graph each set of points in order. Make sure that the shape you graph matches the name or names the instructions have listed. If you graph something and it’s not a square but the instructions say it is, for example, work with your partner to figure out if you made a mistake in graphing it, your partner made a mistake in writing down the coordinates, or if you both graphed it correctly and it just has the wrong description.” Once students are finished, they should compare their drawings and identify the source of any errors and correct them. This Activity can be repeated if students struggle with writing accurate instructions. Depending on time, to engage students further, they can color and decorate their designs. Use the following strategies to tailor the lesson to meet the needs of your students throughout the year. - Routine: As students explore other geometry topics throughout the year, they can graph the shapes on the coordinate plane, including regular polygons, rhombuses, and even circles (with a designated point as the center and a given radius). They can also explore polygons with more than eight sides, describing them through the use of coordinates. - Small Group: Using larger coordinate planes, students can work in groups to create elaborate designs, with each student responsible for creating the instructions (i.e., listing the coordinates) for part of the design. This activity can be done on large rolls of butcher paper (the coordinate plane can be drawn with a meterstick or yardstick) to create large murals. - Expansion: When working with parallelograms, students can be encouraged to make shapes with parallel sides that are not horizontal or vertical lines. They can explore the idea of slope in the context of “from this point I went to the right 5 units and up 2 units, so from this other point I have to do the same steps,” etc. Students can also be introduced to the distance formula and/or Pythagorean theorem when working on the coordinate plane. Students can also explore the idea of convex and concave polygons through graphing.

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Conditional statements make appearances everywhere. In mathematics or elsewhere, it doesn’t take long to run into something of the form “If P then Q.” Conditional statements are indeed important. What are also important are statements that are related to this conditional statement by changing the position of P, Q and the negation of a statement. Starting with an original statement, we end up with three new conditional statements that are named the converse, the contrapositive and the inverse. Before we define the converse, contrapositive and inverse of a conditional statement, we need to examine the topic of negation. Every statement in logic is either true or false. The negation of a statement simply involves the insertion of the word “not” at the proper part of statement. The addition of the word “not” is done so that it changes the truth status of the statement. It will help to look at an example. The statement “The right triangle is equilateral” has negation “The right triangle is not equilateral.” The negation of “10 is an even number” is the statement “10 is not an even number.” Of course, for this last example we could use the definition of an odd number and instead say that “10 is an odd number.” We note that the truth of a statement is the opposite of that of the negation. We will examine this idea in a more abstract setting. When the statement P is true, the statement “not P” is false. Similarly if P is true, its negation “not P” is true. Negations are commonly denoted with a tilde ~. So instead of writing “not P” we can write ~P. Converse, Contrapositive and Inverse Now we can define the converse, the contrapositive and the inverse for a conditional statement. We start with the conditional statement “If P then Q.” - The converse of the conditional statement is “If Q then P.” - The contrapositive of the conditional statement is “If not Q then notP.” - The inverse of the conditional statement is “If not P then notQ.” We will see how these statements work with an example. Suppose we start with the conditional statement “If it rained last night, then the sidewalk is wet.” - The converse of the conditional statement is “If the sidewalk is wet, then it rained last night.” - The contrapositive of the conditional statement is “If the sidewalk is not wet, then it did not rain last night.” - The inverse of the conditional statement is “If it did not rain last night, then the sidewalk is not wet.” We may wonder why it is important to form these other conditional statements from our initial one. A careful look at the above example reveals something. Suppose that the original statement “If it rained last night, then the sidewalk is wet” is true. Which of the other statements have to be true as well? - The converse “If the sidewalk is wet, then it rained last night” is not necessarily true. The sidewalk could be wet for other reasons. - The inverse “If it did not rain last night, then the sidewalk is not wet” is not necessarily true. Again, just because it did not rain does not mean that the sidewalk is not wet. - The contrapositive “If the sidewalk is not wet, then it did not rain last night” is a true statement. What we see from this example (and what can be proved mathematically) is that a conditional statement has the same truth value as its contrapositive. We say that these two statements are logically equivalent. We also see that a conditional statement is not logically equivalent to its converse and inverse. Since a conditional statement and its contrapositive are logically equivalent, we can use this to our advantage when we are proving mathematical theorems. Rather than prove the truth of a conditional statement directly, we can instead use the indirect proof strategy of proving the truth of that statement’s contrapositive. Contrapositive proofs work because if the contrapositive is true, due to logical equivalence, the original conditional statement is also true. It turns out that even though the converse and inverse are not logically equivalent to the original conditional statement, they are logically equivalent to one another. There is an easy explanation for this. We start with the conditional statement “If Q then P”. The contrapositive of this statement is “If not P then notQ.” Since the inverse is the contrapositive of the converse, the converse and inverse are logically equivalent.

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This is a free lesson from our course in Algebra I In this lesson you learn how to solve linearinequalities and also graph them. An inequality is an algebraic expression with one of these signs: <, >, <=, >=. For example 2x + 3y >= 5. A solution of an inequality is a number which when substituted for the variable makes the inequality a true statement. To graph solution set of linear inequality,for instance,they'd ask you to graph something like x > 2. How did you do it? You would draw your number line, find the "equals" part (in this case, x = 2), mark this point with the appropriate notation (an open dot or a parenthesis, indicating that the point x = 2 wasn't included in the solution), and then you'd shade everything to the right, because "greater than" meant "everything off to the right". The steps for graphing two-variable linear inequalities are very much the same. Winpossible's online math courses and tutorials have gained rapidly popularity since their launch in 2008. Over 100,000 students have benefited from Winpossible's courses... these courses in conjunction with free unlimited homework help serve as a very effective math-tutor for our students. All of the Winpossible math tutorials have been designed by top-notch instructors and offer a comprehensive and rigorous math review of that topic. We guarantee that any student who studies with Winpossible, will get a firm grasp of the associated problem-solving techniques. Each course has our instructors providing step-by-step solutions to a wide variety of problems, completely demystifying the Winpossible courses have been used by students for help with homework and by homeschoolers. Several teachers use Winpossible courses at schools as a supplement for in-class instruction. They also use our course structure to develop course worksheets.

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The Norwegian Fjords are steep, ice-carved valleys that stretch from the land out into the sea. Fjords are created not solely by glacier erosion, but also by the high-pressure melt water that flows beneath the ice. Fjord valleys can be carved hundreds to thousands of meters below sea level. The Hardangerfjorden shown in this image is about 179 km long, and reaches its maximum depth of more than 800 m about 100 km inland. In the above image, based on elevation data collected by the Shuttle Radar Topography Mission (SRTM), beige and yellow represent low elevations, while red, brown and white represent progressively higher elevations. Shades of blue represent water. The Hardangerfjord is left of center, and extends off the top of the image. Sorfjorden is towards the right edge of the image. The location of a fjord may be due to pre-glacial valleys, bedrock characteristics, or fractures in the Earth's crust. Fjords typically have U-shaped cross-sectional profiles, with the valley floor being flat or only slightly rounded. The fjord's longitudinal profile usually consists of a series of basins separated by rock barriers or moraine sills (glacial debris). Fjord entrances are usually quite shallow with shoals and small islands. Usually the deep basins are situated some distance inland from the mouth of the fjord. The shallow mouths are places where the glaciers that once filled the valley either began to float, or else had room to spread out. Inland, the glaciers were more confined, and so they carved more deeply into the Earth. About 10,000 years ago, at the end of the last major glaciation, the Scandinavian land mass began slowly rising up as warmer temperatures freed it from the enormous weight of glacial ice, a process called glacial rebound. However, the land's increased buoyancy did not keep pace with the rising sea level, and the lower parts of formerly glaciated valleys became flooded. The glacial rebound of the Scandinavian land mass is still occurring.

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- To comprehend and respond to books read aloud - To understand the concept of characters - To respond to questions - To use expressive language - To recall and retell parts of a selection - To build vocabulary Read Corduroy by Don Freeman, or another book with interesting characters. Tell children that people, animals, and talking toys in stories are called characters. Hold up a book you've read recently in class, and ask children to name some of its characters. - Read the new book. Then page back through it and ask children: Who are the characters in this book? Invite children to describe the characters. - Ask children: Which character do you like best? Why? What did that character do in the story? Help each child participate, even if it is to repeat another child's response. Help children order the sequence of events in the book. Ask: What happened first? Next? Last? - Proficient - Child listens attentively to the story and is able to name and make accurate observations about the characters. - In Process - Child listens fairly attentively to the story and shows understanding by actions, such as laughing or pointing, but needs prompting to name or describe characters. - Not Yet Ready - Child is distracted and does not yet show an understanding of the story characters. More on: Activities for Preschoolers Excerpted from School Readiness Activity Cards. The Preschool Activity Cards provide engaging and purposeful experiences that develop language, literacy, and math skills for preschool children.

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Solve equations that require two operations to isolate the variable. A list of student-submitted discussion questions for Two-Step Equations and Properties of Equality. To encourage students’ critical thinking about vocabulary concepts, to allow students to reflect on their knowledge of individual vocabulary words, and to increase vocabulary comprehension using the Vocabulary Self-Rate. Come up with questions about a topic and learn new vocabulary to determine answers using the table To activate prior knowledge, to generate questions about a given topic, and to organize knowledge using a KWL Chart. Develop understanding of concepts by studying them in a relational manner. Analyze and refine the concept by summarizing the main idea, creating visual aids, and generating questions and comments using a Four Square Concept Matrix. Students will apply their understanding of solving two-step equations to learn how to finance a car over a period of 60 months. Find out why 30 degrees in the United States does not feel the same as 30 degrees in Italy. This study guide looks at the properties of equality and solving linear equations in one variable. It also looks at the number of solutions to linear equations in one variable.

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Before defining the surface area, I want to start from the bottom of this concept. Kids start to learn about points in grade five or six. Points can be compared to real numbers. For example, the dot we use to mark the period (full stop ".") is a point. A point can be represented by a capital letter. Following are two points A and B in space: A . . B When we put trillions of points side by side we get a line segment. Hence points give birth to a line. Now if we join the above two points we get a line AB. Hence, a line segment can be represented using two capital letters. There are many examples of lines in daily life, such as a sewing thread, an electric wire can be compared to a line. As billions of points construct a line, similarly many lines on a piece of paper or on land can give rise to the concept of area. Lines has only one way to go at a time, which means a line can only be top to bottom (vertical) or left to right (horizontal) but it can't be both. Hence lines have only one dimension and we call it "the length". As we measure other quantities, similarly, we can define units to measure the length of a line. We can measure the length of lines in metres, centimeters, millimeters, inches, yards or even in miles or kilometers. Below are some examples of different lines: Look at above lines, line segments, right angles, rays and also a spider web containing a bunch of lines and curves. Hope it has cleared the idea of dimensions in kids' minds. If kids get the idea of dimensions, and know that lines are only one dimensional then they are ready to learn area and then surface area. Now, if we draw two parallel lines vertically and two horizontally and let them intersect we get a very simple geometric shape called a rectangle as shown below: So, four lines when cut each other in a specific order, they make a rectangle. Look at above rectangle, it can be measured two ways, left to right (horizontal line called length) and top to bottom (vertical line called breadth or width). Therefore a rectangle have two dimensions called length and breadth (width). A page of a note book or textbook is the simplest example of a rectangle. Below are some more example of two dimensional shapes: Hence the lines give birth to a shape. Remember we are talking about straight lines. A curve is also a line but not straight. Kids can draw more shapes using lines. Here I want to stop; when lines make a two dimensional shape, they occupy some space on the surface over where they have drawn. This space bounded between lines is called "the area" or "surface area" in case of solid three dimensional shapes.

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Learning About Simple Sentences This is an introductory lesson about simple sentences. • to introduce the concept of simple sentences; to review the sentence parts, subject and predicate; to reinforce the idea that sentences make a complete thought. You have learned that a sentence is a group of words that makes complete sense. All sentences must have two things: 1. A Subject: who or what does the action. 2. A Predicate: what the subject does. Subjects are nouns or pronouns. A sentence with one subject and one predicate is called a simple sentence. For example: ? Jimmy built his own rocket. ? We watched him. The predicate is the action word. Predicates are always verbs.

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Geometry for Elementary School/Pythagorean theorem In this chapter, we will discuss the Pythagorean theorem. It is used the find the side lengths of right triangles. It says: - In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse). This means that if is a right triangle, the length of the hypotenuse, c, squared eqauls the sum of a squared plus b squared. Or: Here's an example: In a right-angled triangle, a=5cm and b=12cm, so what is c? If c is not larger than a or b, your answer is incorrect. There may be a number of reasons that your answer is incorrect. The first is that you have calculated the sums wrong, the second is that the triangle you are trying to find the hypotenuse of is not a right angled triangle or the third is you have mixed up the measurements. There may be more finer points to having a wrong answer but the three stated are the most common

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Introduction to Rational Functions - Concept Once we have a thorough understanding of polynomials we can look at rational functions that are a quotient of two polynomials. These rational functions have certain behaviors, and students are often asked to find their limits, or to graph them. Their graphs can have different characteristics depending on whether the numerator function has degree less than, equal to, or greater than the denominator function. I want to talk about a very important class of functions called rational functions. A rational function is one that can be written f of x equals p of x over q of x where p of x and q of x are polynomials. Now, f of x is defined for any number of x unless q of x the denominator equals zero so the domain will be all real numbers except those that make the denominator zero. And the zeros of a rational function will be the zeros of the numerator just as long as they are not also zeros of the denominator, so let's practice using these definitions in an example. Each of these three is a rational function, polynomial divided by polynomial so p of x over q of x. Now, find the domain and zeros. The domain of this function is going to be all real numbers except where the denominator is zero, so where is the denominator zero? 2x-5=0 when 2x=5, so we divide by 2, x equals five halves so the domain is all real numbers except five halves, all real numbers except five halves, now what are the zeros? For the zeros we look to the numerator. When is the numerator equal to zero? 2x squared minus 5x minus 3. Now this looks like it's factorable so I'm going to try to factor it 2x, x. I need a 3 and a 1 now if I put -3 here and +1 here I'll get x-6x, -5x that works. That means that x equals negative one half and x=3 are both zeros of this function and because neither of those zeros is also a zero of the denominator, these are going to be zeros of my function so the zeros are negative one half, x=3. Okay let's take a look at this guy, what's the domain? Well first we have to figure out where the where the denominator equals zero, so x squared minus 4x equal 0, I can factor this it equal zero when x is 0 or 4, so the domain will be all real numbers except 0 or 4, all real numbers except 0 or 4, now for the zeros of the function the numbers that make this function 0 we look to the numerator, x squared minus 1 equals zero and that's really easy x squared equals 1, x equals plus or minus 1, so as long as plus or minus 1 are not also zeros of the denominator, these are zeros of my function so the zeros are plus and minus 1. Finally let's look look at this function, this denominator I can find the zeros by factoring, x cubed minus x squared minus 6x equals 0, so you get x times x squared minus x minus 6 and this can also be factored looks like it's going to be x and x. I need maybe a 2 and a 3 if I go -3+2 I get my minus 6 and I get -3x+2x negative x that works, so the zeros of the denominator are x=0, 3 or -2, so the domain will be all real numbers except those three. Domain all reals except 0, 3 or -2. And then what about the zeros of this function? Let's look at the numerator; x squared minus 4 equals zero means x squared equals 4 so x is plus or minus 2. Now here's a case where one of the zeros of the numerator is also a zero of the denominator now because 2 is a zero of both the numerator and denominator, the function is not going to be defined there so you can't say that the function's value is 0 there, its not a 0 the only 0 will be then be -2 again I'm sorry actually -2 is this is the it's where it's undefined so positive 2. Let me just clarify, the function is not defined at -2 so -2 can't be a zero so it has to be +2 only.

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Although the surface is cold, the base of an ice sheet is generally warmer due to geothermal heat. In places, melting occurs and the melt-water lubricates the ice sheet so that it flows more rapidly. This process produces fast-flowing channels in the ice sheet — these are ice streams. The present-day polar ice sheets are relatively young in geological terms. The Antarctic Ice Sheet first formed as a small ice cap (maybe several) in the early Oligocene, but retreating and advancing many times until the Pliocene, when it came to occupy almost all of Antarctica. The Greenland ice sheet did not develop at all until the late Pliocene, but apparently developed very rapidly with the first continental glaciation. This had the unusual effect of allowing fossils of plants that once grew on present-day Greenland to be much better preserved than with the slowly forming Antarctic ice sheet. The Antarctic ice sheet is the largest single mass of ice on Earth. It covers an area of almost 14 million km² and contains 30 million km³ of ice. Around 90% of the fresh water on the Earth's surface is held in the ice sheet, and, if melted, would cause sea levels to rise by 61.1 meters. The Antarctic ice sheet is divided by the Transantarctic Mountains into two unequal sections called the East Antarctic ice sheet (EAIS) and the smaller West Antarctic Ice Sheet (WAIS). The EAIS rests on a major land mass but the bed of the WAIS is, in places, more than 2,500 meters below sea level. It would be seabed if the ice sheet were not there. The WAIS is classified as a marine-based ice sheet, meaning that its bed lies below sea level and its edges flow into floating ice shelves. The WAIS is bounded by the Ross Ice Shelf, the Ronne Ice Shelf, and outlet glaciers that drain into the Amundsen Sea. The Greenland ice sheet occupies about 82% of the surface of Greenland, and if melted would cause sea levels to rise by 7.2 metres. Estimated changes in the mass of Greenland's ice sheet suggest it is melting at a rate of about 239 cubic kilometres (57.3 cubic miles) per year. These measurements came from NASA's Gravity Recovery and Climate Experiment (GRACE) satellite, launched in 2002, as reported by BBC News in August 2006 . The IPCC projects that ice mass loss from melting of the Greenland ice sheet will continue to outpace accumulation of snowfall. Accumulation of snowfall on the Antarctic ice sheet is projected to outpace losses from melting. However, loss of mass on the Antarctic sheet may continue, if there is sufficient loss to outlet glaciers. According to the IPCC, understanding of dynamic ice flow processes is "limited".

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Rationale: Children need alphabetic insight about letters and phonemes to help them with reading skills. Before children can understand that letters and phonemes match, they have to be able to hear phonemes in spoken words. This lesson will help children hear that p says /p/. They will learn to hear /p/ in spoken words. Materials: Primary paper, pencils, chart with Put the pretty pumpkin onto the perfect platform, cards with pictures on them (see = #6), classroom board for example in #3, pictures of a pirate, a pumpkin, a boat, a clown, and a princess. Procedures: 1. Introduce the lesson with an explanation of alphabetic code and phonemes. Explain that "today we will be learning about p and the sound it makes, /p/." Tell the students, "/p/ sounds kind of like popcorn when it is popping in the microwave. Let's see if you can make the /p/ sound like popping popcorn." Have the students pop up out of their seats when they say or hear /p/. 2. Next, say the tongue twister that has p's in it from the chart. Have the students pop up like popcorn when they hear the /p/ sound. Put the pretty pumpkin onto the perfect platform. Have the students repeat it after you. Then say it one more time. Next, say it again and stretch out the /p/ in each word. Model to the students and then have them do it themselves. Then have the students do it alone. 3. Explain to the students that now that they know what p sounds like they are going to learn what it looks like and how to write it. Pass out primary paper and model on the board how to write a p. Be sure to draw lines on the board like primary paper and walk them through the process. Have the students try it while still explaining. Have them write multiple upper and lowercase p's on their papers. 4. Tell the students, "Now I'm going to say a list of words and I want you to pop up like popcorn when you hear /p/." Say, princess, pineapple, motorcycle, popcorn, bird, pie, captain, pumpkin, pig, and owl. "Drag out the /p/ sound in the p words. 5. Show the students pictures of a pirate, a pumpkin, a boat, a clown, and a princess. Have them pop up like popcorn when they see a picture with the sound /p/ in it. 6. For an assessment, pass out cards with two pictures each on them, one with a /p/ sound and one without. Have each student circle which picture represents /p/. Murray, Bruce. "Example of Emergent Literacy Design: Sound the Foghorn". Harris, Katherine. "Penelope, The Precious Pig". http://www.auburn.edu/academic/education/reading_genie/voyages/harrisel.html Return to Passages Index

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Students will learn how to graph motion vs time. Students will learn how to take the slope of a graph and relate it to the instantaneous velocity or acceleration for position or velocity graphs. Finally students will learn how to take the area of a velocity vs time graph in order to calculate the displacement. Illustrates the structure of position-time graphs with positive acceleration and explains why they are shaped this way. Illustrates the structure of position-time graphs with negative acceleration and explains why they are shaped this way. Illustrates velocity-time graphs and how acceleration affects them with an example problem. Know the significance of slope, curve, and direction on a position-time graph and a velocity-time graph, sketch the graph of a moving object given a description of its motion. A list of student-submitted discussion questions for Graphing Motion. A review of the terms distance, displacement, velocity, speed, and acceleration. Also looks at graphs of motion, using the kinematic equations, projectile motion, and free fall.

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This is a drawing of a process which forms mountains on Earth. Click on image for full size Mountains are built through a general process called "deformation" of the crust of the Earth. Deformation is a fancy word which could also mean "folding". An example of this kind of folding comes from the process described below. When two sections of the Earth's lithosphere collide, rather than being subducted, where one slab of lithosphere is forced down to deeper regions of the Earth, the slabs pile into each other, causing one or both slabs can fold up like an accordion. This process elevates the crust, folds and deforms it heavily, and produces a mountain range. Mountain building and mantle subduction usually go together. This process is illustrated in the figure to the left. The lithospheric slab on the right is subducted, while the force of the collision gradually causes the slab on the left to fold deeply. Along the way, melting of the subducted slab leads to volcano formation. Shop Windows to the Universe Science Store! You might also be interested in: When two sections of the Earth's crust collide, one slab of crust can be forced back down into the deeper regions of the Earth, as shown in this diagram. This process is called subduction. The slab that...more Volcanoes form when hot material from below rises and leaks into the crust. This hot material, called magma, comes either from a melt of subducted crustal material, and which is light and buoyant after...more Many kinds of surface features are clues that our lithosphere is sliding. Two types of features can form when plates move apart. At mid ocean ridges, the bottom of the sea splits apart and new crust is...more Peru's new president, Alejandro Toledo, was sworn in on July 28, 2001. The next day he visited Machu Picchu and Cuzco. There were ceremonies at both locations where Toledo asked for the blessing of the...more Instead of icy-volcanism, the surface of Ganymede reveals gradual surface deformation and stretching, a stretching similar to the crustal deformation of the Earth. In this case, the folding and stretching...more Ash is made of millions of tiny fragments of rock and glass formed during a volcanic eruption. Volcanic ash particles are less than 2 mm in size and can be much smaller. Volcanic ash forms in several ways...more Cinder cones are simple volcanoes which have a bowl-shaped crater at the summit and only grow to about a thousand feet, the size of a hill. They usually are created of eruptions from a single opening,...more

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Why did the US Congress have a problem in 1850? And why did the solution lead to the creation, 160 years ago this month, of a place called Utah? The lands of the American Southwest – an area now covering California, Wyoming, Colorado, New Mexico, Arizona, Nevada, and Utah – were ceded to the United States following the end of the Mexican-American War in 1848. The problem confronting the US, however, was whether the new lands should become slave states or free. The union of the nation depended on keeping a balance, and for two years, Congress wrestled with the question. In the absence of any decision, people living in those areas began to organize governing institutions of their own. Mormon leader Brigham Young established an independent government called Deseret, which stretched from the Rocky Mountains to the sea, and petitioned for statehood as a way to secure local independence. Finally, members of Congress made a deal called the Compromise of 1850, wherein California was admitted to the Union as a free state, while the remaining lands became the New Mexico and Utah Territories, where people were allowed to decide the slavery issue for themselves. The compromise resolved the immediate crisis, but only delayed the question of slavery in western lands. Congress also refused to grant statehood to Deseret because the region lacked the required number of eligible voters. Moreover, they objected to the huge size of the proposed state. When selecting a name for the new territory, Congressional support was strong for the name Utah, after the indigenous Ute tribe. Mormons resisted naming the territory after a people they scorned and feared, but the name prevailed. So, in September 1850, Congress passed a bill organizing the Utah Territory, rejecting the name Deseret and shrinking its presumptuous borders. However, President Millard Fillmore's politically astute selection of Brigham Young as governor made territorial status easier for the Mormons to accept. In gratitude, they named their new territorial capital and its surrounding county after him. Utah would wait another 46 years for statehood. Beehive Archive is a production of the Utah Humanities Council. Sources consulted in the creation of the Beehive Archive and past episodes may be found at www.utahhumanities.org/BeehiveArchive.htm

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Solon was one of the archons in ancient Athens. In 594 B.C. Solon made several important reforms, which loosened the tension of civil war breaking out. He also made it were the public office system was based on wealth. Thus making it were any qualified citizen could become a public official.Solon also published all the laws of the Athenian Society. Solons reforms, even though important, did not solve the problem of poverty in Athens. Because of this, Pisistratus was able to sieze power and become a tyrant. He ruled from 545 B.C. to 527 B.C. He did though continue the work of Solon by reducing the power of the traditional ruling class. Cleisthenes was the founder of democracy in Athens. He proposed the constitution in 508 B.C. The constitution made Athens a democracy. The curious thing about the constitution was that it stayed intact for several hundred years. This may not seem strange, but it was because the constitution was unwritten. The ideaology was based on Solon, but it also provided conditions that greatly developed them. The new constitution now made where all men of 18 years or older were registered as citizens and were members of the village which they lived in. Which gave each person a vote in the society. The constitution made were 500 of the people made the decisions in the city and those officials were elected each year. Each citizen had a chance to run the city. Women were not considered citizens thus they could not vote. People can be banished under this system for 10 years by a majority vote of the populis.

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Algebraic concepts can evolve and continue to develop during prekindergarten through grade 2. They will be manifested through work with classification, patterns and relations, operations with whole numbers, explorations of function, and step-by-step processes. Although the concepts discussed in this Standard are algebraic, this does not mean that students in the early grades are going to deal with the symbolism often taught in a traditional high school algebra course. Even before formal schooling, children develop beginning concepts related to patterns, functions, and algebra. They learn repetitive songs, rhythmic chants, and predictive poems that are based on repeating and growing patterns. The recognition, comparison, and analysis of patterns are important components of a student's intellectual development. When students notice that operations seem to have particular properties, they are beginning to think algebraically. For example, they realize that changing the order in which two numbers are added does not change the result or that adding zero to a number leaves that number unchanged. Students' observations and discussions of how quantities relate to one another lead to initial experiences with function relationships, and their representations of mathematical situations using concrete objects, pictures, and symbols are the beginnings of mathematical modeling. Many of the step-by-step processes that students use form the basis of understanding iteration and recursion. and ordering facilitate work with patterns, geometric shapes, and data. Given a package of assorted stickers, children quickly notice many differences among the items. They can sort the stickers into groups having similar traits such as color, size, or design and order them from smallest to largest. Caregivers and teachers should elicit from children the criteria they are using as they sort and group objects. Patterns are a way for young students to recognize order and to organize their world and are important in all aspects of mathematics at this level. Preschoolers recognize patterns in their environment and, through experiences in school, should become more skilled in noticing patterns in arrangements of objects, shapes, and numbers and in using patterns to predict what comes next in an arrangement. Students know, for example, that "first comes breakfast, then school," and "Monday we go to art, Tuesday we go to music." Students who see the digits "0, 1, 2, 3, 4, 5, 6, 7, 8, 9" repeated over and over will see a pattern that helps them learn to count to 100a formidable task for students who do not recognize the pattern. Teachers should help students develop the ability to form generalizations by asking such questions as "How could you describe this pattern?" or "How can it be repeated or extended?" or "How are these patterns alike?" For example, students should recognize that the color pattern "blue, blue, red, blue, blue, red" is the same in form as "clap, clap, step, clap, clap, step." This recognition lays the foundation for the idea that two very different situations can have the same mathematical » features and thus are the same in some important ways. Knowing that each pattern above could be described as having the form AABAAB is for students an early introduction to the power of algebra. By encouraging students to explore and model relationships using language and notation that is meaningful for them, teachers can help students see different relationships and make conjectures and generalizations from their experiences with numbers. Teachers can, for instance, deepen students' understanding of numbers by asking them to model the same quantity in many waysfor example, eighteen is nine groups of two, 1 ten and 8 ones, three groups of six, or six groups of three. Pairing counting numbers with a repeating pattern of objects can create a function (see fig. 4.7) that teachers can explore with students: What is the second shape? To continue the pattern, what shape comes next? What number comes next when you are counting? What do you notice about the numbers that are beneath the triangles? What shape would 14 be? Students should learn to solve problems by identifying specific processes. For example, when students are skip-counting three, six, nine, twelve, ..., one way to obtain the next term is to add three to the previous number. Students can use a similar process to compute how much to pay for seven balloons if one balloon costs 20¢. If they recognize the sequence 20, 40, 60, ... and continue to add 20, they can find the cost for seven balloons. Alternatively, students can realize that the total amount to be paid is determined by the number of balloons bought and find a way to compute the total directly. Teachers in grades 1 and 2 should provide experiences for students to learn to use charts and tables for recording and organizing information in varying formats (see figs. 4.8 and 4.9). They also should discuss the different notations for showing amounts of money. (One balloon costs 20¢, or $0.20, and seven balloons cost $1.40.) Two central themes of algebraic thinking are appropriate for young students. The first involves making generalizations and using symbols to represent mathematical ideas, and the second is representing and solving problems (Carpenter and Levi 1999). For example, adding pairs of numbers in different orders such as 3 + 5 and 5 + 3 can lead students to infer that when two numbers are added, the order does not matter. As students generalize from observations about number and operations, they are forming the basis of algebraic thinking. Similarly, when students decompose numbers in order to compute, they often use the associative property for the computation. For instance, they may compute 8 + 5, saying, "8 + 2 is 10, and 3 more is 13." Students often discover and make generalizations about other properties. Although it is not necessary to introduce vocabulary such as commutativity or associativity, teachers must be aware of the algebraic properties used by students at this age. They should build students' understanding of the importance of their observations about mathematical situations and challenge them to investigate whether specific observations and conjectures hold for all cases. Teachers should take advantage of their observations of students, as illustrated in this story drawn from an experience in a kindergarten class. The teacher had prepared two groups of cards for her students. In the first group, the number on the front and back of each card differed by 1. In the second group, these numbers differed by 2. | The teacher showed the students a card with 12 written on it and explained, "On the back of this card, I've written another number." She turned the card over to show the number 13. Then she showed the students a second card with 15 on the front and 16 on the back. » As she continued showing the students the cards, each time she asked the students, "What do you think will be on the back?" Soon the students figured out that she was adding 1 to the number on the front to get the number on the back of the card. Then the teacher brought out a second set of cards. These were also numbered front and back, but the numbers differed by 2, for example, 33 and 35, 46 and 48, 22 and 24. Again, the teacher showed the students a sample card and continued with other cards, encouraging them to predict what number was on the back of each card. Soon the students figured out that the numbers on the backs of the cards were 2 more than the numbers on the fronts. When the set of cards was exhausted, the students wanted to play again. "But," said the teacher, "we can't do that until I make another set of cards." One student spoke up, "You don't have to do that, we can just flip the cards over. The cards will all be minus 2." As a follow-up to the discussion, this teacher could have described what was on each group of cards in a more algebraic manner. The numbers on the backs of the cards in the first group could be named as "front number plus 1" and the second as "front number plus 2." Following the student's suggestion, if the cards in the second group were flipped over, the numbers on the backs could then be described as "front number minus 2." Such activities, together with the discussions and analysis that follow them, build a foundation for understanding the inverse relationship. Through classroom discussions of different representations during the pre-K2 years, students should develop an increased ability to use symbols as a means of recording their thinking. In the earliest years, teachers may provide scaffolding for students by writing for them until they have the ability to record their ideas. Original representations remain important throughout the students' mathematical study and should be encouraged. Symbolic representation and manipulation should be embedded in instructional experiences as another vehicle for understanding and making sense of mathematics. Equality is an important algebraic concept that students must encounter and begin to understand in the lower grades. A common explanation of the equals sign given by students is that "the answer is coming," but they need to recognize that the equals sign indicates a relationshipthat the quantities on each side are equivalent, for example, 10 = 4 + 6 or 4 + 6 = 5 + 5. In the later years of this grade band, teachers should provide opportunities for students to make connections from symbolic notation to the representation of the equation. For example, if a student records the addition of four 7s as shown on the left in figure 4.11, the teacher could show a series of additions correctly, as shown on the right, and use a balance and cubes to demonstrate the equalities. » Students should learn to make models to represent and solve problems. For example, a teacher may pose the following problem: There are six chairs and stools. The chairs have four legs and the stools have three legs. All together there are twenty legs. How many chairs and how many stools are there? One student may represent the situation by drawing six circles and then putting tallies inside to represent the number of legs. Another student may represent the situation by using symbols, making a first guess that the number of stools and chairs is the same and adding 3 + 3 + 3 + 4 + 4 + 4. Realizing that the sum is too large, the student might adjust the number of chairs and stools so that the sum of their legs is 20. Change is an important idea that students encounter early on. When students measure something over time, they can describe change both qualitatively (e.g., "Today is colder than yesterday") and quantitatively (e.g., "I am two inches taller than I was a year ago"). Some changes are predictable. For instance, students grow taller, not shorter, as they get older. The understanding that most things change over time, that many such changes can be described mathematically, and that many changes are predictable helps lay a foundation for applying mathematics to other fields and for understanding the world. |Home | Table of Contents | Purchase | Resources| |NCTM Home | Illuminations Web site| Copyright © 2000 by the National Council of Teachers of Mathematics.

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A < B A > B A <= B A >= B A == B A ~= B The relational operators are <, >, <=, >=, ==, and ~=. Relational operators perform element-by-element comparisons between two arrays. They return a logical array of the same size, with elements set to logical 1 (true) where the relation is true, and elements set to logical 0 (false) where it is not. The operators <, >, <=, and >= use only the real part of their operands for the comparison. The operators == and ~= test real and imaginary parts. To test if two strings are equivalent, use strcmp, which allows vectors of dissimilar length to be compared. Note For some toolboxes, the relational operators are overloaded, that is, they perform differently in the context of that toolbox. To see the toolboxes that overload a given operator, type help followed by the operator name. For example, type help lt. The toolboxes that overload lt (<) are listed. For information about using the operator in that toolbox, see the documentation for the toolbox. If one of the operands is a scalar and the other a matrix, the scalar expands to the size of the matrix. For example, the two pairs of statements X = 5; X >= [1 2 3; 4 5 6; 7 8 10] X = 5*ones(3,3); X >= [1 2 3; 4 5 6; 7 8 10] produce the same result: ans = 1 1 1 1 1 0 0 0 0

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What a scale actually means and what we can do with it depends on what its numbers represent. Numbers can be grouped into 4 types or levels: nominal, ordinal, interval, and ratio. Nominal is the most simple, and ratio the most sophisticated. Each level possesses the characteristics of the preceding level, plus an additional quality. Nominal is hardly measurement. It refers to quality more than quantity. A nominal level of measurement is simply a matter of distinguishing by name, e.g., 1 = male, 2 = female. Even though we are using the numbers 1 and 2, they do not denote quantity. The binary category of 0 and 1 used for computers is a nominal level of measurement. They are categories or classifications. Nominal measurement is like using categorical levels of variables, described in the Doing Scientific Research section of the Introduction module. |MEAL PREFERENCE: Breakfast, Lunch, Dinner| |RELIGIOUS PREFERENCE: 1 = Buddhist, 2 = Muslim, 3 = Christian, 4 = Jewish, 5 = Other| |POLITICAL ORIENTATION: Republican, Democratic, Libertarian, Green| Nominal time of day - categories; no additional information Ordinal refers to order in measurement. An ordinal scale indicates direction, in addition to providing nominal information. Low/Medium/High; or Faster/Slower are examples of ordinal levels of measurement. Ranking an experience as a "nine" on a scale of 1 to 10 tells us that it was higher than an experience ranked as a "six." Many psychological scales or inventories are at the ordinal level of measurement. |RANK: 1st place, 2nd place, ... last place| |LEVEL OF AGREEMENT: No, Maybe, Yes| |POLITICAL ORIENTATION: Left, Center, Right| Ordinal time of day - indicates direction or order of occurrence; spacing between is uneven Interval scales provide information about order, and also possess equal intervals. From the previous example, if we knew that the distance between 1 and 2 was the same as that between 7 and 8 on our 10-point rating scale, then we would have an interval scale. An example of an interval scale is temperature, either measured on a Fahrenheit or Celsius scale. A degree represents the same underlying amount of heat, regardless of where it occurs on the scale. Measured in Fahrenheit units, the difference between a temperature of 46 and 42 is the same as the difference between 72 and 68. Equal-interval scales of measurement can be devised for opinions and attitudes. Constructing them involves an understanding of mathematical and statistical principles beyond those covered in this course. But it is important to understand the different levels of measurement when using and interpreting scales. |TIME OF DAY on a 12-hour clock| |POLITICAL ORIENTATION: Score on standardized scale of political orientation| |OTHER scales constructed so as to possess equal intervals| Interval time of day - equal intervals; analog (12-hr.) clock, difference between 1 and 2 pm is same as difference between 11 and 12 am In addition to possessing the qualities of nominal, ordinal, and interval scales, a ratio scale has an absolute zero (a point where none of the quality being measured exists). Using a ratio scale permits comparisons such as being twice as high, or one-half as much. Reaction time (how long it takes to respond to a signal of some sort) uses a ratio scale of measurement -- time. Although an individual's reaction time is always greater than zero, we conceptualize a zero point in time, and can state that a response of 24 milliseconds is twice as fast as a response time of 48 milliseconds. |RULER: inches or centimeters||YEARS of work experience| |INCOME: money earned last year||NUMBER of children| |GPA: grade point average| Ratio - 24-hr. time has an absolute 0 (midnight); 14 o'clock is twice as long from midnight as 7 o'clock The level of measurement for a particular variable is defined by the highest category that it achieves. For example, categorizing someone as extroverted (outgoing) or introverted (shy) is nominal. If we categorize people 1 = shy, 2 = neither shy nor outgoing, 3 = outgoing, then we have an ordinal level of measurement. If we use a standardized measure of shyness (and there are such inventories), we would probably assume the shyness variable meets the standards of an interval level of measurement. As to whether or not we might have a ratio scale of shyness, although we might be able to measure zero shyness, it would be difficult to devise a scale where we would be comfortable talking about someone's being 3 times as shy as someone else. Measurement at the interval or ratio level is desirable because we can use the more powerful statistical procedures available for Means and Standard Deviations. To have this advantage, often ordinal data are treated as though they were interval; for example, subjective ratings scales (1 = terrible, 2= poor, 3 = fair, 4 = good, 5 = excellent). The scale probably does not meet the requirement of equal intervals -- we don't know that the difference between 2 (poor) and 3 (fair) is the same as the difference between 4 (good) and 5 (excellent). In order to take advantage of more powerful statistical techniques, researchers often assume that the intervals are equal. Enrichment #1 (not required): Statistical procedures for each level of measurement On to consumer ratings

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Lesson 17 Section 2 Example 1. 5 is to 15 as 8 is to 24. That is a proportion because 5 is the third part of 15, just as 8 is the third part of 24. (Lesson 15.) A proportion involves four numbers -- four terms. To explain why they are proportional we start with the first term and state its ratio to the second; then we state that the third term has that same ratio to the fourth. Example 2. Why is this a proportion? 16 is to 2 as 80 is to 10. Answer. This is a proportion because 16 is eight times 2, just as 80 is eight times 10. Example 3. Why is this a proportion? 10 is to 15 as 2 is to 3. Answer. This is a proportion because 10 is two thirds of 15, just as 2 is two thirds of 3. (Lesson 15.) Example 4. Complete this proportion: 8 is to 32 as 9 is to ? Solution. 8 is the fourth part of 32. And 9 is the fourth part of 36. The 1st term is to the 2nd as the 3rd is to the 4th. Example 5. Complete this proportion: 27 is to 3 as ? is to 5 Solution. 27 is nine times 3. And 45 is nine times 5. If the student will speak and use sentences, the answer will be clear. Example 6. In each item below, what ratio has a to b? (a simply means the first term; b means the second.) a) a is to b as 1 is to 6. b) a is to b as 10 is to 1. a) Since 1 is the sixth part of 6, then a is the sixth part of b. b) Since 10 is ten times 1, then a is ten times b. We will let the following signify a proportion: Why is this a proportion? Because 1 is half of 2, and 4 is half of 8. (Can you be innocent and make-believe you never heard of a "fraction"? Fractions we will see (Lesson 20) are based on ratios, not the other way around.) Example 7. Read this proportion, and complete it: Answer. "8 is to 2 as 20 is to what number?" Now, what ratio has 8 to 2? 8 is four times 2. And 20 is four times 5. We say that we have solved that proportion. That is, given three terms, we have named the fourth. What is taught in most textbooks these days as "ratio and proportion," is not. The student is taught to write the letter x for the unknown term, cross-multiply, and solve an algebraic equation. That is a method for people who do not understand ratio and proportion. A ratio is a relationship we can express in words. To express it requires understanding, and because of that the topic of ratio and proportion is educational. Example 8. Complete this proportion: Answer. "7 is to 21 as 4 is to what number?" What ratio has 7 to 21? 7 is the third part of 21. And 4 is the third part of 12. Example 9. Complete this proportion: Answer. "2 is to 3 as what number is to 12?" Now, 2 is two thirds of 3. What number is two thirds of 12? "One third of 12 is 4; so two thirds are 8." (Lesson 15.) In the next lesson we will see how to solve a proportion that looks like this: At this point, please "turn" the page and do some Problems. Please make a donation to keep TheMathPage online. Copyright © 2014 Lawrence Spector Questions or comments?

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The process of starting a computer system is known as bootstrapping. In most systems, the initial bootstrap sequence begins with code in ROM, which the CPU executes. The ROM code only contains a first step—it merely loads an image into the computer's RAM and branches to the image. There are two approaches used to obtain an image: |Embedded system : On a diskless computer, the ROM code contains sufficient support software to permit network communication. The ROM code uses the network support to locate and download an image.| |Conventional computer : On a computer that has secondary storage (for instance, a PC), the ROM code loads the image from a well-known place on disk. Typically, the loaded image consists of an operating system that then controls the computer.| In either case, the image loaded by ROM is not tailored to the specific physical hardware. Instead, an image is generic, which means that before it can be used, it must be configured for the local hardware. In particular, the image does not contain such networking details as the computer's IP address, address mask, or domain name. Each of these items must be supplied before applications can use TCP/IP. Early in the history of TCP/IP, designers chose to provide a separate mechanism for each item of configuration information. Thus, the Reverse Address Resolution Protocol (RARP) only allowed a computer to obtain its IP address. When subnet masks were introduced, ICMP Address Mask messages were added to allow a computer to obtain a subnet mask. The chief advantage of such an approach lies in flexibility—a computer can decide which items to obtain from a local file on disk and which to obtain over the network. The chief disadvantage becomes apparent when one considers the network traffic and delay. A given computer must issue a series of small request messages. More important, each response returns a small value (for instance, a 4-octet IP address). Because networks enforce a minimum packet size, most of the space in each packet is wasted. As the complexity of configuration grew, TCP/IP protocol designers observed that many of the configuration steps could be combined into a single step if a server was able to supply more than one item of configuration information. To provide such a service, the designers invented the BOOTstrap Protocol (BOOTP). To obtain configuration information, protocol software broadcasts a BOOTP Request message. A BOOTP server that receives the request looks up several pieces of configuration information for the computer that issued the request, places the information in a single BOOTP Response message, and returns the reply to the requesting computer. Thus, in a single step, a computer can obtain information such as the computer's IP address, the server's name and IP address, and the IP address of a default router. Like other protocols used to obtain configuration information, BOOTP broadcasts each request. Unlike other protocols used for configuration, BOOTP appears to use a protocol that has not been configured: BOOTP uses IP to send a request and receive a response. How can BOOTP send an IP datagram before a computer's IP address has been configured? The answer lies in a careful design that allows IP to broadcast a request and receive a response before all values have been configured. To send a BOOTP datagram, IP uses the all-1's limited broadcast address as a DESTINATION ADDRESS , and uses the all-0's address as a SOURCE ADDRESS . If a computer uses the all-0's address to send a request, a BOOTP server either uses broadcast to return the response or uses the hardware address on the incoming frame to send a response via unicast. (The server must be careful to avoid using ARP because a client that does not know its IP address cannot answer ARP requests.) Thus, a computer that does not know its IP address can communicate with a BOOTP server. Figure 1 illustrates the BOOTP packet format. The message is sent using UDP, which is encapsulated in IP. Figure 1: BOOTP Packet Format Each field in a BOOTP message has a fixed size. The first seven fields contain information used to process the message. The OP field specifies whether the message is a Request or a Response , and the HTYPE and HLEN fields specify the network hardware type and the length of a hardware address. The HOPS field specifies how many servers forwarded the request, and the TRANSACTION IDENTIFIER field provides a value that a client can use to determine if an incoming response matches its request. The SECONDS ELAPSED field specifies how many seconds have elapsed since the computer began to boot. Finally, if a computer knows its IP address (for instance, the address was obtained using RARP), the computer fills in the CLIENT IP ADDRESS field in a request. Later fields are used in a response message to carry information back to the computer that is booting. If a computer does not know its address, the server uses field YOUR IP ADDRESS to supply the value. In addition, the server uses fields SERVER IP ADDRESS and SERVER HOST NAME to give the computer information about the location of a computer that runs servers. Field ROUTER IP ADDRESS contains the IP address of a default router. In addition to protocol configuration, BOOTP allows a computer to negotiate to find a boot image. To do so, the computer fills in field BOOT FILE NAME with a generic request (for instance, the computer can request the UNIX operating system). The BOOTP server does not send an image. Instead, the server determines which file contains the requested image, and uses field BOOT FILE NAME to send back the name of the file. Once a BOOTP response arrives, a computer must use a protocol like the Trivial File Transfer Protocol (TFTP) to obtain a copy of the image. Automatic Address Assignment Although it simplifies loading parameters into protocol software, BOOTP does not solve the configuration problem completely. When a BOOTP server receives a request, the server looks up the computer in its database of information. Thus, even a computer that uses BOOTP cannot boot on a new network until the administrator manually changes information in the database. Can protocol software be devised that allows a computer to join a new network without manual intervention? Yes—several such protocols exist. For example, IPX and IPv6 can generate a protocol address from the computer's hardware address. To make automatic generation work correctly, the hardware address must be unique. Furthermore, if the hardware address and protocol address are not the same size, it must be possible to translate the hardware address into a protocol address that is also unique. The AppleTalk protocols use a bidding scheme to allow a computer to join a new network. When a computer first boots, the computer chooses a random address. For example, suppose computer C chooses address 17. To ensure that no other computer on the network is using the address, C broadcasts a request message and starts a timer. If no other computer is using address 17, no reply will arrive before the timer expires; C can begin using address 17. If another computer is using 17, the computer replies, causing C to choose a different address and begin again. Choosing an address at random works well for small networks and for computers that run client software. However, the scheme does not work well for servers. To understand why, recall that each server must be located at a well-known address. If a computer chooses an address at random when it boots, clients will not know which address to use when contacting a server on that computer. More important, because the address can change each time a computer boots, the address used to reach a server may not remain the same after a crash and reboot. A bidding scheme also has the disadvantage that two computers can choose the same network address. In particular, assume that computer B sends a request for an address that another computer (for example, A) is already using. If A fails to respond to the request for any reason, both computers will attempt to use the same address, with disastrous results. In practice, such failures can occur for a variety of reasons. For example, a piece of network equipment such as a bridge can fail, a computer can be unplugged from the network when the request is sent, or a computer can be temporarily unavailable (for instance, in a hibernation mode designed to conserve power). Finally, a computer can fail to answer if the protocol software or operating system is not functioning correctly. To automate configuration, the Internet Engineering Task Force (IETF) devised the Dynamic Host Configuration Protocol (DHCP). Unlike BOOTP, DHCP does not require an administrator to add an entry for each computer to the database that a server uses. Instead, DHCP provides a mechanism that allows a computer to join a new network and obtain an IP address without manual intervention. The concept has been termed plug-and-play networking. More important, DHCP accommodates computers that run server software as well as computers that run client software: |When a computer that runs client software is moved to a new network, the computer can use DHCP to obtain configuration information without manual intervention.| |DHCP allows nonmobile computers that run server software to be assigned a permanent address; the address will not change when the computer reboots.| To accommodate both types of computers, DHCP cannot use a bidding scheme. Instead, it uses a client-server approach. When a computer boots, the computer broadcasts a DHCP Request to which a server sends a DHCP Reply. (The reply is classified as a DHCP offer message that contains an address the server is offering to the client.) An administrator can configure a DHCP server to have two types of addresses: permanent addresses that are assigned to server computers, and a pool of addresses to be allocated on demand. When a computer boots and sends a request to DHCP, the DHCP server consults its database to find configuration information. If the database contains a specific entry for the computer, the server returns the information from the entry. If no entry exists for the computer, the server chooses the next IP address from the pool, and assigns the address to the computer. In fact, addresses assigned on demand are not permanent. Instead, DHCP issues a lease on the address for a finite period of time. (When the administrator establishes a pool of addresses for DHCP to assign, the administrator must also specify the length of the lease for each address.) When the lease expires, the computer must renegotiate with DHCP to extend the lease. Normally, DHCP will approve a lease extension. However, a site may choose an administrative policy that denies the extension. (For example, a university that has a network in a classroom might choose to deny extensions on leases at the end of a class period to allow the next class to reuse the same addresses.) If DHCP denies an extension request, the computer must stop using the address. Optimizations in DHCP If the computers on a network use DHCP to obtain configuration information when they boot, an event that causes all computers to restart at the same time can cause the network or server to be flooded with requests. To avoid the problem, DHCP uses the same technique as BOOTP: each computer waits a random time before transmitting or retransmitting a request. The DHCP protocol has two steps: one in which a computer broadcasts a DHCP Discover message to find a DHCP server, and another in which the computer selects one of the servers that responded to its message and sends a request to that server. To avoid having a computer repeat both steps each time it boots or each time it needs to extend the lease, DHCP uses caching. When a computer discovers a DHCP server, the computer saves the server's address in a cache on permanent storage (for example, a disk file). Similarly, once it obtains an IP address, the computer saves the IP address in a cache. When a computer reboots, it uses the cached information to revalidate its former address. Doing so saves time and reduces network traffic. DHCP Message Format Interestingly, DHCP is designed as an extension of BOOTP. As Figure 2 illustrates, DHCP uses a slightly modified version of the BOOTP message format. Figure 2: DHCP Message Format Most of the fields in a DHCP message have the same meaning as in BOOTP; DHCP replaces the 16-bit UNUSED field with a FLAGS field, and uses the OPTIONS field to encode additional information. For example, as in BOOTP, the OP field specifies either a Request or a Response . To distinguish among various messages that a client uses to discover servers or request an address, or that a server uses to acknowledge or deny a request, DHCP uses a message type option . That is, each message contains a code that identifies the message type. DHCP and Domain Names Although DHCP makes it possible for a computer to obtain an IP address without manual intervention, DHCP does not interact with the Domain Name System. As a result, a computer cannot keep its name when it changes addresses. Interestingly, the computer does not need to move to a new network to have its name change. For example, suppose a computer obtains IP address 220.127.116.11 from DHCP, and suppose the domain name system contains a record that binds the name x.y.z.com to the address. Now consider what happens if the owner turns off the computer and takes a two-month vacation during which the address lease expires. DHCP may assign the address to another computer. When the owner returns and turns on the computer, DHCP will deny the request to use the same address. Thus, the computer will obtain a new address. Unfortunately, the Domain Name System (DNS) continues to map the name x.y.z.com to the old address. For several years, researchers have been considering how DHCP should interact with the DNS. Although a dynamic DNS update protocol has been defined, it has not been widely deployed. Thus, many sites that use DHCP do not have a mechanism to update a DNS database. From a user's perspective, the lack of communication between DHCP and DNS means that when a computer is assigned a new address, the computer's name changes. The bootstrapping sequence loads a generic image into a computer, either from secondary storage or over the network. Before application software can use TCP/IP protocols, the image must be configured by supplying values for internal parameters such as the IP address and subnet mask, and for external parameters such as the address of a default router; the process is known as configuration . Initially, separate protocols were used to obtain each piece of configuration information. Later, the BOOTstrap Protocol , BOOTP, was invented to consolidate separate requests into a single protocol. A BOOTP response provides information such as the computer's IP address, the address of a default router, and the name of a file that contains a boot image. The Dynamic Host Configuration Protocol (DHCP) extends BOOTP. In addition to permanent addresses assigned to computers that run a server, DHCP permits completely automated address assignment. That is, DHCP allows a computer to join a new network, obtain a valid IP address, and begin using the address without requiring an administrator to enter information about the computer in a server's database. When DHCP allocates an address automatically, the DHCP server does not assign the address forever. Instead, the server specifies a lease during which the address may be used. A computer must extend the lease, or stop using the address when the lease expires. For Further Study Details about BOOTP can be found in reference , which compares BOOTP to RARP and serves as the official protocol standard. Reference tells how to interpret the vendor-specific area, and reference recommends using the vendor-specific area to pass the subnet mask. Most uses of BOOTP have been replaced by DHCP. Reference contains the specification for DHCP, including a detailed description of state transitions. A related document, , specifies the encoding of DHCP options and BOOTP vendor extensions. Finally, reference discusses the interoperability of BOOTP and DHCP. The chair of the DHCP working group, Ralph Droms, and Ted Lemon have written a book about DHCP . W. J. Croft, J. Gilmore, "Bootstrap Protocol," RFC 951, September 1985. J. K. Reynolds, "BOOTP Vendor Information Extensions," RFC 1084, December 1988. R. Braden (ed), "Requirements for Internet Hosts—Application and Support," RFC 1123, October 1989. R. Droms, "Dynamic Host Configuration Protocol," RFC 2131, March 1997. S. Alexander, R. Droms, "DHCP Options and BOOTP Vendor Extensions," RFC 2132, March 1997. R. Droms, "Interoperation between DHCP and BOOTP," RFC 1534, October 1993. R. Droms and T. Lemon, The DHCP Handbook: Understanding, Deploying, and Managing Automated Configuration Services, ISBN 1578701376, MacMillian, 1999. [This article is adapted from Computer Networks and Internets, with Internet Applications, 3rd edition, by Douglas Comer, with CD by Ralph Droms, ISBN 0130914495, Prentice Hall, 2001.] Dr. DOUGLAS COMER is a professor of Computer Science at Purdue University, consultant to industry, and an internationally recognized authority on TCP/IP. He has written numerous research papers and textbooks, including the classic three-volume reference series Internetworking with TCP/IP , and currently heads research projects. He designed and implemented X25NET and Cypress networks, and the Xinu operating system. He was a principal on the CSNET project, is director of the Internetworking Research Group at Purdue, editor of the journal Software—Practice and Experience , a former member of the IAB, and a Fellow of the ACM. E-mail: email@example.com

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Vermont Votes for Kids: A project of the Vermont Secretary of State Curriculum, Teacher Materials for Lesson 1: Fairness and Diversity with One Vote Engaging students in discussions about voting is an excellent way to help them move from shallow to deep thinking, and to demonstrate the higher order thinking skills of analysis, synthesis and evaluation. The exercises below are designed to help students internalize the importance of voting so they are more likely to become active voters when they reach adulthood. Ask students to discuss what it means to be fair. Ask for examples of their personal experiences where something wasn't fair. ("My little brother gets away with things that I get punished for." "A few students misbehaved, and we all missed recess.") What if one group of people thinks something is fair, and another group thinks it isn't? What is the best way to decide? Voting is a way to decide what most of the people want. It doesn't mean that one group is right and the other is wrong. It just means that more people choose A than choose B. In places where people don't vote, decisions are often made by fighting. Ask students what kind of voting could occur in the classroom to ensure that everyone is treated fairly. For example, could students vote on where they sit, on what activities/games they play during recess, etc.? Mention that in some states people who break the law by committing serious crimes (felonies) lose their right to vote. Ask students if they believe this is fair. Would it be fair to tell a student who misbehaves repeatedly that he/she has lost the right to vote on classroom issues? Should there be a way to earn back your voting privilege? Why or why not? Say to students: Today we are going to conduct a poll to find out your favorite foods. When I call on you, tell us what your favorite food is, and I will write it on the board. Now, pretend you are a group of students from (whatever country/culture is being studied.) If we conducted a poll to find out your favorite foods, what would you say when I called on you? Put this list on the board and discuss the differences. You may have students from different cultures (and food preferences) in your classroom. Vermont Secretary of State Deb Markowitz: http://www.vermontvotesforkids.com

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A problem asks for something. This request often follows words such as how, when, where, show and find. What is asked for is frequently followed by a question mark. The response to the request is commonly in the problem statement. The starting equation then will make a request. The response to the request by the equation is commonly in the problem statement. Variations of problems result from changing the wording. This does not change the problem solving process. It provides exercise in different algebraic and arithmetic operations. This is illustrated in the following three presentations. In textbook problems, particularly in the so-called real-life problems, distractors (irrelevant information) may be present. By identifying what is asked for, the request, you can quickly scan the problem, looking for a specific response to the request. You know what you are looking for in the jumble of words and can skip over distractors. Students will frequently skip problems like the following one simply because of the number of words and conditions involved. They do not know what to pay attention to. By identifying the request and looking for the response this mental block is removed. A simple problem can be reworded in a great variety of ways without changing the structure of the solution. This is illustrated by the following problem in which a slightly more complex description of the change in the number of the item involved has been used. Have your students construct single-variable problems. These will have the same solution path as that shown in these examples. Also examine textbooks and other instructional materials for problems which have the solution structure shown here. The words change and the numbers change but the problem-solving process remains the same. Help your students become aware of the fact that the problem-solving process shown here is logically no different from what they do many times every day. For example, use the following exercise:

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Lesson 2: Programming and Movement Lesson 2: Programming and Movement After students have completed their robots it is time to put them into action. Now is a good time to talk to your students about how robots work. Ask them abstract questions like "Will a robot always do what we tell them to?" The answer to that question is yes, but many students will think no. No seems like the correct answer because robots will have unintended actions, like going left when the programmer wants it to go right. But the reality is that robots take every command a user gives it and follows it through exactly, the errors come from problems in the commands humans give to robots. This concept may be too abstract for younger children but it really helps the older students understand how programming works. Students who get done early or classes that have finished their robots but do not have time to do the entire programming lesson will find this challenge a good opportunity to learn how the robot moves before actually telling it to move with programming. Although some of the math involved may be beyond younger students. Give your students a tape measure or a printed-out paper ruler, one with centimeters and inches would be best. Draw a tic mark on one of the wheels with a piece of chalk or place a piece of opaque tape on the wheel. Ask each team to find out how many full rotations of the wheel it would take for the robot to move 2 feet, or any arbitrary distance like the distance of the surface of a table. Students who have already learned about circumference can usually figure out that the distance around the wheel is the same as the distance the robot moves. Students who have never learned about circumference will need some assistance coming to this conclusion. This challenge is very useful because it teaches students how the robot will be moving when programming begins. The robot is told how far to go in either Degrees or Rotations, both referring to how far the wheel moves. If they can equate 1 rotation to an exact distance they will come into the concept of programming in rotations easier. NXT Programming is very easy to learn, but can be difficult to master. There are many things that can be done with the software, but for the sake of a simple lesson it is best to start with just moving the robot. This is done with simple movement blocks like the ones shown below. Movement blocks come from the left side menu, the top button shown below When you click on a movement block you will see a menu like the one below at the bottom of the screen. This menu lets you change the settings on each movement block. Port lets you chose which motor you are using. The convention is to have the two wheel-motors attached to Port B and Port C, leaving Port A for the robot's "Arm" motor. Direction is either Forward, Backward or Brake, and Steeling is simply choosing between left, right, or straight and how sharp the turn is. For steeling generally turning the slider all the way left or right will make a perfect Turn-on-a-dime turn. The Power slider determines how much power is being put into the motor. For your wheel motors 75 is the normal speed, however the slider can be turned up to 100 for a faster movement or down to 50 for a slower movement. Going lower that 50 makes the motors too weak to move the wheels usually. Next Action tells the robot to either brake and hold position after the movement is done or to just let the motors go and coast. Duration is the most important criterion for movement, and will require the most trial and error to determine. As said before duration can be measured in Rotations, but also can be measured in Degrees or Seconds. Starting with rotations is a good idea, especially if your students did the challenge at the beginning of the page. Even if your students know how long one rotation is it is still a good idea to do a demonstration for the entire class of how far 1 rotation is, and also how far 4 or 5 rotations is. When your program is done click on the download button shown below. If everything goes right you should see a message saying download complete shortly afterward. The best way to teach programming is to halt all building and get the attention of the entire class. Having a projector is a big help so students can see your example program as you make it. The best way for students to learn is to follow along with your example program and they try out trying to program the robot to move some arbitrary track. Going over all the points mentioned above about moving is a good idea, don't get too in depth with your presentation however, students will lose interest the longer they have LEGOs in front of them and aren't actually using them. Giving students around an hour to test out programming will help solidify what they have learned and will ready them for the next task. Teacher, It Doesn't Work! Programming issues are very common but usually easy to solve. A list of the most common programming mistakes and how to solve them can be found here.

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The Online Teacher Resource Receive free lesson plans, printables, and worksheets by email: - Over 20,000 Printables - For All Grade Levels - A Complete Elementary Curriculum - Print and go! Kindergarten through Grade 2 (Primary / Elementary School) Overview and Purpose: This activity will help students see the logic of creating patterns and help them begin to be able to create their own. The lesson should begin with the definition of the word 'pattern' (things arranged following a rule). The teacher can use an overhead projector and colored transparent shapes to display patterns. The students will work in groups to discover the rule and extend the pattern. Each group will then be able to practice creating their own patterns for another group to extend. The student will be able to *name the rule for a displayed pattern of three to five colors or shapes *extend a three to five color or shape pattern *create a three color or shape pattern and repeat it a minimum of two times Transparent colored shapes Several of the same shapes for each group of three students Crayons or colored pencils Begin the lesson by talking about what a pattern is (things arranged following a rule). Have the students write the definition in their math journal. Use the overhead projector and transparent shapes to create a pattern. Have the students divide into groups of three and discuss what the rule for the pattern is and then extend the pattern by repeating it two times. Come back together as a group to discuss the rule and have one of the groups come up and replicate the pattern on the overhead using the transparent shapes. Continue this exercise providing more difficult patterns as the student's confidence and skill level increases. For a closing activity, have each group develop their own pattern and then have the groups rotate to each pattern. They can write the rule and extend the pattern in their math journals. Encourage them to use crayons or colored pencils to draw the pattern. When all the groups have been able to see each pattern, have each group name their rule and show how the pattern would have been extended. Discuss how everyone did at recognizing the patterns and writing the rules. This activity can be continued for homework by having students develop three or four patterns at home. They can write the rule and draw the pattern in their math journal. The idea of patterns can also be extended into other subjects and the students can be encouraged to find patterns in art, nature, and music.

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Defining Implicit Bias Also known as implicit social cognition, implicit bias refers to the attitudes or stereotypes that affect our understanding, actions, and decisions in an unconscious manner. These biases, which encompass both favorable and unfavorable assessments, are activated involuntarily and without an individual’s awareness or intentional control. Residing deep in the subconscious, these biases are different from known biases that individuals may choose to conceal for the purposes of social and/or political correctness. Rather, implicit biases are not accessible through introspection. The implicit associations we harbor in our subconscious cause us to have feelings and attitudes about other people based on characteristics such as race, ethnicity, age, and appearance. These associations develop over the course of a lifetime beginning at a very early age through exposure to direct and indirect messages. In addition to early life experiences, the media and news programming are often-cited origins of implicit associations. A Few Key Characteristics of Implicit Biases - Implicit biases are pervasive. Everyone possesses them, even people with avowed commitments to impartiality such as judges. - Implicit and explicit biases are related but distinct mental constructs. They are not mutually exclusive and may even reinforce each other. - The implicit associations we hold do not necessarily align with our declared beliefs or even reflect stances we would explicitly endorse. - We generally tend to hold implicit biases that favor our own ingroup, though research has shown that we can still hold implicit biases against our ingroup. - Implicit biases are malleable. Our brains are incredibly complex, and the implicit associations that we have formed can be gradually unlearned through a variety of debiasing techniques. Implicit Biases Predict Behavior in the Real World Extensive research has documented the disturbing effects of implicit racial biases in a variety of realms ranging from classrooms to courtrooms to hospitals. Consider these examples: - A 2012 study used identical case vignettes to examine how pediatricians’ implicit racial attitudes affect treatment recommendations for four common pediatric conditions. Results indicated that as pediatricians’ pro-White implicit biases increased, they were more likely to prescribe painkillers for vignette patients who were White as opposed to Black. This is just one example of how understanding implicit racial biases may help explain differential health care treatment, even for youths. - Other research explored the connection between criminal sentencing and Afrocentric features bias, which refers to the generally negative judgments and beliefs that many people hold regarding individuals who possess Afrocentric features such as dark skin, a wide nose, and full lips. Researchers found that when controlling for numerous factors (e.g., seriousness of the primary offense, number of prior offenses, etc.), individuals with the most prominent Afrocentric features received longer sentences than their less Afrocentrically featured counterparts. - This phenomenon was observed intraracially in both their Black and White male inmate samples. Barriers to Opportunity: Implicit Bias & Structural Racialization As the Kirwan Institute works to create a just and inclusive society where all people and communities have opportunity to succeed, we have become increasingly mindful of how race and cognition factors such as implicit bias can operate in conjunction with structural racialization. Together these two powerful forces create barriers that impede access to opportunity across many critical life domains such as housing, education, health, and criminal justice. As convincing research evidence accumulates, it becomes difficult to understate the importance of considering the role of implicit racial biases when analyzing societal inequities. Implicit biases, explicit biases, and structural forces are often mutually reinforcing. The Kirwan Institute is committed to raising awareness of the distressing impacts of implicit racial bias and exposing the ways in which this phenomenon creates and reinforces racialized barriers to opportunity.

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A while ago we looked at some basics in Heat Transfer Basics – Part Zero. Equations aren’t popular but a few were included. As a recap, there are three main mechanisms of heat transfer: In the climate system, conduction is generally negligible because gases and liquids like water don’t conduct heat well at all. (See note 2). Convection is the transfer of heat by bulk motion of a fluid. Motion of fluids is very complex, which makes convection a difficult subject. If the motion of the fluid arises from an external agent, for instance, a fan, a blower, the wind, or the motion of a heated object itself, which imparts the pressure to drive the flow, the process is termed forced convection. If, on the other hand, no such externally induced flow exists and the flow arises “naturally” from the effect of a density difference, resulting from a temperature or concentration difference in a body force field such as gravity, the process is termed natural convection. The density difference gives rise to buoyancy forces due to which the flow is generated.. The main difference between natural and forced convection lies in the mechanism by which flow is generated. From Heat Transfer Handbook: Volume 1, by Bejan & Kraus (2003). The Boundary Layer The first key to understanding heat transfer by convection is the boundary layer. A typical example is a fluid (e.g. air, water) forced over a flat plate: This first graphic shows the velocity of the fluid. The parameter u∞ is the velocity (u) at infinity (∞) – or in layman’s terms, the velocity of the fluid “a long way” from the surface of the plate. Another way to think about u∞ – it is the free flowing fluid velocity before the fluid comes into contact with the plate. Take a look at the velocity profile: At the plate the velocity is zero. This is because the fluid particles make contact with the surface. In the “next layer” the particles are slowed up by the boundary layer particles. As you go further and further out this effect of the stationary plate is more and more reduced, until finally there is no slowing down of the fluid. The thick black curve, δ, is the boundary layer thickness. In practice this is usually taken to be the point where the velocity is 99% of its free flowing value. You can see that just at the point where the fluid starts to flow over the plate – the boundary layer is zero. Then the plate starts to slow the fluid down and so progressively the boundary layer thickens. Here is the resulting temperature profile: In this graphic T∞ is the temperature of the “free flowing fluid” and Ts is the temperature of the flat plat which (in this case) is higher than the free flowing fluid temperature. Therefore, heat will transfer from the plate to the fluid. The thermal boundary layer, δt, is defined in a similar way to the velocity boundary layer, but using temperature instead. How does heat transfer from the plate to the fluid? At the surface the velocity of the fluid is zero and so there is no fluid motion. At the surface, energy transfer only takes place by conduction (note 1). In some cases we also expect to see mass transfer – for example, air over a water surface where water evaporates and water vapor gets carried away. (But not with air over a steel plate). So a concentration boundary layer develops. Newton’s Law of Cooling Many people have come across this equation: q” = h(Ts – T∞) where q” = heat flux in W/m², h is the convection coefficient, and the two temperatures were defined above The problem is determining the value of h. It depends on a number of fluid properties: - thermal conductivity - specific heat capacity But also on: - surface geometry - flow conditions The earlier examples showed laminar flow. However, turbulent flow often develops: Flow in the turbulent region is chaotic and characterized by random, three-dimensional motion of relatively large parcels of fluid. Check out this very short video showing the transition from laminar to turbulent flow. What determines whether flow is laminar or turbulent and how does flow become turbulent? The transition from laminar to turbulent flow is ultimately due to triggering mechanisms, such as the interaction of unsteady flow structures that develop naturally within the fluid or small disturbances that exist within many typical boundary layers. These disturbances may originate from fluctuations in the free stream, or they may be induced by surface roughness or minute surface vibrations from Incropera & DeWitt (2007). Imagine treacle (=molasses) flowing over a plate. It’s hard to picture the flow becoming turbulent. That’s because treacle is very viscous. Viscosity is a measure of how much resistance there is to different speeds within the fluid – how much “internal resistance”. Now picture water moving very slowly over a plate. Again it’s hard to picture the flow becoming turbulent. The reason in this case is because inertial forces are low. Inertial force is the force applied on other parts of the fluid by virtue of the fluid motion. The higher the inertial forces the more likely fluid flow is to become turbulent. The higher the viscosity of the fluid the less likely the fluid flow is to become turbulent – because this viscosity damps out the random motion. The ratio between the two is the important parameter. This is known as the Reynolds number. Re = ρu∞x / μ where ρ = density, u∞ = free stream velocity, x is the distance from the leading edge of the surface and μ = dynamic viscosity Once Re goes above around 5 x 105 (500,000) flow becomes turbulent. For air at 15°C and sea level, ρ=1.2kg/m³ and μ=1.8 x 10-5 kg/m.s Solving this equation for these conditions, gives a threshold value of u∞x > 7.5 for turbulence.. This means that if the wind speed (in m/s) x the length of surface over which the wind flows (in m) is greater than 7.5 we will get turbulent flow. For example, a slow wind speed of 1 m/s (2.2 miles / hour) over 7.5 meters of surface will produce turbulent flow. When you consider the wind blowing over many miles of open ocean you can see that the air flow will almost always be turbulent. The great physicist and Nobel Laureate Richard Feynman called turbulence the most important unsolved problem of classical physics. In a nutshell, it’s a little tricky. So how do we determine convection coefficients? Empirical Measurements & Dimensionless Ratios Calculation of the convection heat transfer coefficient, h, in the equation we saw earlier can only be done empirically. This means measurement. However, there are a whole suite of similarity parameters which allow results from one situation to be used in “similar circumstances”. It’s not an easy subject to understand “intuitively” because the demonstration of these similarity parameters (e.g., Reynolds, Prandtl, Nusselt and Sherwood numbers) relies upon first seeing the differential equations governing fluid flow and heat & mass transfer – and then the transformation of these equations into a dimensionless form. As the simplest example, the Reynolds number tells us when flow becomes turbulent regardless of whether we are considering air, water or treacle. And a result for one geometry can be re-used in a different scenario with similar geometries. Therefore, many tables and standard empirical equations exist for standard geometries – e.g. fluid flow over cylinders, banks of pipes. Here are some results for air flow over a flat isothermal plate (isothermal = all at the same temperature) – calculated using empirically-derived equations: Click for a larger view The 1st graph shows that the critical Reynolds number of 5×105 is reached at 1.3m. The 2nd graph shows how the boundary layer grows under first laminar flow, then second under turbulent flow – see how it jumps up as turbulent flow starts. The 4th graph shows the local convection coefficient as a function of distance from the leading edge – as well as the average value across the 2m of flat plate. Not much of a conclusion yet, but this article is already long enough. In the next article we will look at the experimental results of heat transfer from the ocean to the atmosphere. Note 1 – Heat transfer by radiation might also take place depending on the materials in question. Note 2 – Of course, as explained in the detailed section on convection, heat cannot be transferred across a boundary between a surface and a fluid by convection. Conduction is therefore important at the boundary between the earth’s surface and atmosphere.

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This lesson will help students identify how to make good decisions which will help them financially in the future. Students will identify how to take their own wants and work them into a form of a personal budget. Students will also discuss various financial scenarios and decide what course of action would be the best to follow. - Identify various items which are important to them and determine if they are wants - Develop a monthly budget based on a given level of income - Define opportunity cost - Explore various financial situations Students will identify what items in their lives they want. Students will then rank these in order of importance and from that develop a personal monthly budget given a certain income level. Finally, students will analyze various financial dilemmas and discuss how they would resolve each dilemma. U.S. Securities and Exchange Commission - Students learn about how and why to save. Banking is INTERESTing - This lesson deals with savings. What Do You Want? Worksheet - Students will use this Excel file to list and prioritize their wants. - A printable version of the worksheet Ask students to make a list of things they want to have during the next month, use the What Do You Want? worksheet (Printable Version). Then have students prioritize the items on the list. Students should determine how much each item costs. This can be done by estimating or by going to store websites to see prices of the items on their list. Students can also ask adults. Students will use the interactive budget page to make their budget. If the total exceeds $200, students will need to make choices. Tell students saving money for future spending is also an option. Introduce the terms shortage and opportunity cost. Ask students what resource is lacking. Tell them that is called shortage, something which is in limited supply. Ask students to begin to cut items from their list to get down to the monthly budgeted amount of $200. Tell them what they give up is called opportunity costs. Ask students to explain why they eliminated certain items from their list. Ask them if this was hard for them to do. Ask them to explain why it was or wasn't hard to do. Have students share their monthly budget with their classmates. Tell students making good financial decisions and savings at a young age is a very important ingredient toward financial success later in life. Controlling expenses and saving money help build a solid financial base. Avoiding debt by sticking to a budget is very important. Students should practice these finance skills at a young age to get in the habit of saving, not overspending, and not spending on frivolous items. Tell students they will develop a balanced, monthly budget using the list they created. Students will need to make decisions about what to include in their budget. Stress the importance of savings and of spending on necessities. After making their budget, students will write a brief essay about the difficulties they faced in making choices to have their budget balance. If they didn't have difficulties, their essay should focus on why it was easy for them to make a balanced budget. Students will examine three financial scenarios described below and determine if exceeding their budget would be a good idea. Place students in groups of three or four. After each scenario, students will discuss in their groups what they would do in each situation. Groups will identify the opportunity cost of each decision in each situation. Groups will share their decisions with the class. Bill is interested in being a basketball referee. In order to get certified and known as an official, he needs to attend a camp for basketball officials. At this camp, Bill will learn instruction about refereeing, referee at least four games, be seen by people who assign officials to games from the grade school level through high school varsity level, and meet other officials. If Bill gets hired to games, he will make a minimum of $20.00 a game, possibly more. Bill does not have the $350.00 in his monthly budget to cover the cost of the camp? Should Bill attend the camp? [Absolutely!!! There is a growing need for officials to work games. Once Bill gets known in officiating circles, he will have opportunities to make thousands of dollars in a basketball season. Even if Bill borrows the money to attend the camp and needs to buy some basic equipment, he will come out ahead in the long run. The opportunity costs is the cost of the camp which is $350.00.] Sally is looking to buy a five-year-old, used Mustang convertible. It will cost her $9,500.00 to buy the car plus insurance. She believes this car will make her very popular at school, make it easier for to get dates, and will bring a lot of attention her way. Her parents are willing to provide her with a ten-year-old station wagon and will pay for all costs of the this car except the gas Sally uses. Sally has $5,000.00 in her savings account and monthly income of $450.00. Which car should Sally get? [She should take the station wagon because she can't afford the Mustang convertible. She also is making assumptions about her improved social life which may or may not be true. The opportunity cost will be possibly being less popular and getting fewer dates.] Claudio wants to become a teacher. He wants to go to the best school in the state which has a great School of Education. This School of Education has a very positive national reputation and places 85% of its graduates in good paying teacher positions. However, since the school is located on the other side of the state, Claudio would not be able to go to school and live at home. He would have to pay tuition and the cost of living in a dorm, food, and other expenses. The university in his hometown has a School of Education which has an average reputation and places 75% of its graduates in jobs. However, the average starting pay for teachers who attend the local university averages $3,500 a year less than the starting pay from teachers who attended the university with nationally known School of Education. Claudio would have to borrow money to attend the better school and will have about $15,000 in debt after finish college. Should he do this? [Yes!!! Assuming he is a good teacher, he is very likely to get a job with a high starting salary. Most likely, he will earn significantly more money over his teaching career if he attends the university with a nationally known school of education. While he will be behind in the beginning of his career, he should make this difference up over the length of a long teaching career. Claudio could also apply for scholarships or work-study jobs to help offset some of his debt while attending school. The opportunity cost is being in debt and not being able to do some things for a while since he in debt.] EXTENSION ACTIVITYStudents will make a budget based on their actual monthly income. This income may come from jobs they do, gifts they receive, and any allowances given by their family. The budget must be a balanced budget. Students will write a brief summary of the struggles they faced in developing a balanced budget based on their actual income. If students found it easy to balance their budget, their essay should tell why this was the case. Put students in groups of three. They will create a short play focusing on the need to budget, to develop a balanced budget, and to stick to it. “Enough can not be said and stressed about the principle of avoiding debt at all costs.” “This is a great lesson! I learned a lot!”

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EDSITEment, from the National Endowment for the Humanities, is a partnership with the National Trust for the Humanities and the Verizon Foundation, and brings online humanities resources directly to the classroom through exemplary lesson plans and student activities. For teachers of U.S. history and American government and civics—especially those wishing to integrate primary sources into their curriculum—EDSITEment has collected its most frequently accessed content in this subject area for August and September. These online lessons include: What is History? Timelines and Oral Histories Students gain a frame of reference for understanding history and for recognizing that the past is different depending on who is remembering and retelling it. They construct a timeline based on events from their own lives and family histories. This will give them a visual representation of the continuity of time. They will also be able to see that their own personal past is different in scope from their family's past, or their country's past. Magna Carta: Cornerstone of the U.S. Constitution Magna Carta served to lay the foundation for the evolution of parliamentary government and subsequent declarations of rights in Great Britain and the United States. In attempting to establish checks on the king's powers, this document asserted the right of "due process" of law. What Was Columbus Thinking? Students read excerpts from Columbus's letters and journals, as well as recent considerations of his achievements in order to reflect on the motivations behind Columbus's explorations. Native American Cultures Across the U.S. This lesson discusses the differences between common representations of Native Americans within the U.S. and a more differentiated view of historical and contemporary cultures of five American Indian tribes living in different geographical areas. Students will learn about customs and traditions such as housing, agriculture, and ceremonial dress for the Tlingit, Dinè, Lakota, Muscogee, and Iroquois peoples. Images of the New World How did the English picture the native peoples of America during the early phases of colonization of North America? This lesson plan enables students to interact with written and visual accounts of this critical formative period at the end of the 16th century, when the English view of the New World was being formulated, with consequences that we are still seeing today. Mission Nuestra Señora de la Concepción and the Spanish Mission in the New World In this Picturing America lesson, students explore the historical origins and organization of Spanish missions in the New World and discover the varied purposes these communities of faith served. Focusing on the daily life of Mission Nuestra Señora de la Concepción, the lesson asks students to relate the people of this community and their daily activities to the art and architecture of the mission. Back to top Colonizing the Bay This lesson focuses on John Winthrop’s historic "Model of Christian Charity" sermon which is often referred to by its “City on a Hill “ metaphor. Through a close reading of this admittedly difficult text, students will learn how it illuminates the beliefs, goals, and programs of the Puritans. The sermon sought to inspire and to motivate the Puritans by pointing out the distance they had to travel between an ideal community and their real-world situation. Mapping Colonial New England: Looking at the Landscape of New England The lesson focuses on two 17th-century maps of the Massachusetts Bay Colony to trace how the Puritans took possession of the region, built towns, and established families on the land. Students learn how these New England settlers interacted with the Native Americans, and how to gain information about those relationships American Colonial Life in the Late 1700s: Distant Cousins This lesson introduces students to American colonial life and has them compare the daily life and culture of two different colonies in the late 1700s. Students study artifacts of the thirteen original British colonies and write letters between fictitious cousins in Massachusetts and Delaware. Understanding the Salem Witch Trials In 1691, a group of girls from Salem, Massachusetts accused an Indian slave named Tituba of witchcraft, igniting a hunt for witches that left 19 men and women hanged, one man pressed to death, and over 150 more people in prison awaiting a trial. In this lesson, students explore the characteristics of the Puritan community in Salem, learn about the Salem Witchcraft Trials, and try to understand how and why this event occurred. Dramatizing History in Arthur Miller's The Crucible By closely reading historical documents and attempting to interpret them, students consider how Arthur Miller interpreted the facts of the Salem witch trials and how he successfully dramatized them in his play, The Crucible. As they explore historical materials, such as the biographies of key players (the accused and the accusers) and transcripts of the Salem Witch trials themselves, students will be guided by aesthetic and dramatic concerns: In what ways do historical events lend themselves (or not) to dramatization? What makes a particular dramatization of history effective and memorable? William Penn’s Peaceable Kingdom By juxtaposing the different promotional tracts of William Penn and David Pastorius, students understand the ethnic diversity of Pennsylvania along with the “pull” factors of migration in the 17th-century English colonies. Religion in 18th-Century America This curriculum unit, through the use of primary documents, introduces students to the First Great Awakening, as well as to the ways in which religious-based arguments were used both in support of and against the American Revolution. The Beauty of Anglo-Saxon Poetry: A Prelude to Beowulf Sometimes thought of as barbaric and violent, the “Dark Ages” was a time when beauty was prized in visual ornamentation and literary elaboration. In this introduction to Anglo-Saxon literature, students will study the literature and literary techniques of the early Middle Ages in order to read Beowulf with an appreciation for its artistry and beauty. Students will learn the conventions of Anglo-Saxon poetry, solve online riddles, write riddles, and reflect on what they have learned. Chaucer's Wife of Bath This lesson helps students understand the complexities of the Wife of Bath's character and the rhetoric of her argument by exploring the various ways in which Chaucer crafts a persona for her. Students familiarize themselves with the framing narrative and language in which the Tales were written: Middle English. Students examine several primary source documents written about women and marriage in order to understand the context in which the Wife presents her argument. The Legend of Sleepy Hollow The Tale of the Headless Horseman has become a Halloween classic, although few Americans celebrated that holiday when the story was new. In this unit, students explore the artistry that helped make Washington Irving our nation's first literary master and discover how "The Legend of Sleepy Hollow" still captures the imagination of 21st-century readers. Flannery O'Connor's “A Good Man is Hard to Find”: Who's the Real Misfit? "A Good Man is Hard to Find" raises fundamental questions about good and evil, morality and immorality, faith and doubt, and the particularly Southern "binaries" of black and white and Southern history and progress. In this lesson, students will explore these dichotomies—and challenge them—while closely reading and analyzing "A Good Man is Hard to Find." In the course of studying this particular O'Connor short story, students will learn as well about the 1950s South. A Raisin in the Sun: The Quest for the American Dream The play A Raisin in the Sun enhances the discussion of "The American Dream" even while students explore how the social, educational, economic, and political climate of the 1950’s affected African Americans' quest for "The American Dream." In this lesson, the critical reading and analysis of the play is complemented with a close examination of biographical and historical documents that students use as the basis for creating speeches, essays and scripts. A Story of Epic Proportions: What makes a Poem an Epic? Epic Poems are heroic adventure tales with surprising durability over time, such as Homer's story of love and heroism, The Iliad. This lesson introduces students to the epic poem format and to its roots in oral tradition. Students learn about the epic hero cycle and how to recognize this epic pattern of events and elements, even in surprisingly contemporary places. Introducing Metaphors through Poetry Metaphors are used often in literature, appearing in every genre, from poetry to prose. Utilized by poets and novelists to bring their literary imagery to life, metaphors are an important component of reading closely and appreciating literature. In this lesson, students will read excerpts from the work of Langston Hughes, Margaret Atwood, and Naomi Shihab Nye in order to gain a deeper understanding of metaphors. Can You Haiku? Haiku show us the world in a water drop, providing a tiny lens through which to glimpse the miracle and mystery of life. Combining close observation with a moment of reflection, this simple yet highly sophisticated form of poetry can help sharpen students' response to language and enhance their powers of self-expression. In this lesson, students learn the rules and conventions of haiku, study examples by Japanese masters, and create haiku of their own. Poems that Tell a Story: Narrative and Persona in the Poetry of Robert Frost Robert Frost's "Stopping by Woods on a Snowy Evening" tells an invitingly simple story. In this lesson students explore such questions and mysteries building upon narrative hints in poems chosen from an online selection of Frost's most frequently anthologized and taught works. Analyzing the speaker, students make inferences about that speaker's motivations and character, find evidence for those inferences in the words of the poem, and apply their inferences about the speaker in a dramatic reading performed for other class members. Chinua Achebe's Things Fall Apart: Teaching Through the Novel Chinua Achebe first novel, Things Fall Apart, is an early narrative about the European colonization of Africa told from the point of view of the colonized people. Through his writing, Achebe counters images of African societies and peoples as they are represented within the Western literary tradition and reclaims his own and his people's history. In this lesson, students are introduced to Achebe's first novel and to his views on the role of the writer in his or her society. Chinua Achebe’s Things Fall Apart: Oral and Literary Strategies Things Fall Apart interposes Western linguistic forms and literary traditions with Igbo words and phrases, proverbs, fables, tales, and other elements of African oral and communal storytelling traditions. After situating the novel in its historical and literary context, students will identify the text’s linguistic and literary techniques. Dramatizing History in Arthur Miller's The Crucible This lesson plan's goal is to examine the ways in which Miller interpreted the facts of the Salem witch trials and successfully dramatized them. Guided by aesthetic and dramatic concerns students will interpret history and examine the playwright’s own interpretations of it. In this lesson, students examine some of primary sources and historical events, and then read The Crucible itself. “Shooting an Elephant”: George Orwell's Essay on his Life in Burma This lesson plan is designed to help students read Orwell's 1931 autobiographical essay "Shooting an Elephant” both as a work of literature and as a window into the historical context about which it was written. Among his most powerful essays, this is based on his experience as a police officer in colonial Burma. Rudyard Kipling’s “Rikki-Tikki-Tavi”: Mixing Words and Pictures British author Rudyard Kipling’s "Rikki-Tikki-Tavi," a short story from The Jungle Book (1894), is an engaging example of Kipling's ability to mix scientific and historical fact with imaginative characterizations to create a believable and entertaining tale. In this lesson, students will read an illustrated version and examine how Kipling and visual artists mix observation with imagination to create remarkable works. Cave Art: Discovering Prehistoric Humans through Pictures In this lesson, students discover that pictures are more than pretty colors and representations of things we recognize: they are also a way of communicating beliefs and ideas. In many cases, this is what gives us clues today when there are no written records left behind. The Cuneiform Writing System in Ancient Mesopotamia: Emergence and Evolution The writing system invented by the Sumerians around 3500 BCE was at first representational but became increasingly abstract as it evolved to encompass more abstract concepts. This lesson plan, intended for use in the teaching of world history in the middle grades, is designed to help students appreciate the parallel development and increasing complexity of writing and civilization in the Tigris and Euphrates valleys of ancient Mesopotamia. Hammurabi’s Code: What Does It Tell Us about Old Babylonia? In this lesson, students learn about life in Babylonia through the lens of Hammurabi's Code. Designed to extend World History curricula on Mesopotamia, it gives students a more in-depth view of life in Babylonia during the time of Hammurabi (1792-1750 BCE). Egyptian Symbols and Figures: Hieroglyphs This lesson introduces students to the writing, art, and religious beliefs of ancient Egypt through hieroglyphs, a pictorial script used in ancient Egypt from about 3100 BCE to 400 CE (and one of the oldest writing systems in the world). In particular, students will study Egyptian tomb paintings, one medium where hieroglyphics are found. It Came From Greek Mythology The lessons in this unit use online resources to enliven your students' encounter with Greek mythology, to deepen their understanding of what myths meant to the ancient Greeks, and to help them appreciate the modern meanings of Greek myths. Students learn about Greek conceptions of the hero, the function of myths as explanatory accounts, the presence of mythological terms in contemporary culture, and the ways mythology has inspired later artists and poets. 300 Spartans at the Battle of Thermopylae: Herodotus’ Real History In this lesson, students learn about the historical background to the battle and are asked to ponder some of its legacy, including how history is reported and interpreted from different perspectives. They will read from Herodotus' account of the battle at Thermopylae. Although the Spartans were defeated and annihilated at Thermopylae, the battle played an important part in the Greek resistance to this second and final Persian invasion. EDSITEment’s Persian Wars Resource Page This popular EDSITEment resource page links students to lesson plans on Greek history and mythology as well as to related student interactives on the war between the Greeks and Persians. The Aztecs — Mighty Warriors of Mexico When the Spanish conquistador Hernan de Cortes and his army arrived in Tenochtitlan, capital of the mighty Aztec empire, they were amazed by an island city built in the middle of Lake Texcoco and connected to the surrounding land by three great causeways. Tenochtitlan was the hub of a rich civilization that dominated the region of modern-day Mexico at the time the Spanish forces arrived. In this lesson, students will learn about the history and culture of the Aztecs and discover why their civilization came to an abrupt end. On the Road with Marco Polo In the 13th century, the young Venetian Marco Polo traveled with his father and uncle across the vast continent of Asia to become the first Europeans to visit the Chinese capital (modern Beijing). In this curriculum unit, students will become Marco Polo adventurers, learning about the geography, local products, culture, and fascinating sites along his route to China. They will record journal entries and create postcards, posters, and maps related to the sites they explore. Cinderella Folk Tales: Variations in Plot and Setting Five hundred versions of the Cinderella tale have been found in Europe alone and related stories are told in cultures all over the globe. In this lesson, students consider how the plot and setting of Cinderella change as it is translated into different cultural versions, then uncover the universal literary elements of the story. Fairy Tales Around the World Fairy tales are stories either created or strongly influenced by oral traditions. Because of the worldwide ubiquity of fairy tales, they have had a vast impact on many different forms of literature and drama for all ages. In this lesson, students uncover the characteristics of fairy tales to better comprehend the structures of literature as well as for the sake of the wonder, pleasure, and human understanding these stories provide in their own right. Aesop and Ananse: Animal Fables and Trickster Tales In this unit, students will become familiar with fables and trickster tales such as Aesop’s fables and Ananse spider stories that appear in different cultural traditions. They will compare and contrast the elements of these tales across cultures to learn how the tales use various animals in different ways to portray human strengths and weaknesses and to pass down wisdom from one generation to the next. Animals of the Chinese Zodiac In this lesson plan, students will learn about the 12 animals of the Chinese zodiac. They will be introduced to the significance and symbolism of the animals as well as the traits associated with the year affiliated with each animal. Hans Christian Andersen's Fairy Tales This lesson focuses on the works of Hans Christian Andersen and helps students understand the fairy tale genre through exploration and analysis of themes, plots, and characterizations in The Little Mermaid, The Ugly Duckling, The Emperor’s New Clothes, and other tales. Cave Art: Discovering Prehistoric Humans through Pictures Students study paintings from the caves in France, discover that pictures are a way of communicating beliefs and ideas, and learn how this gives us clues about what happened when there are no written records left behind. Lascaux: La Vie en Caverne! Students learn how to explain the purpose of cave paintings and rock art, identify some of the animals that roamed France in prehistoric times, and learn to appreciate the methods used by ancient civilization to create cave and rock art. Hammurabi’s Code: What Does It Tell Us about Old Babylonia? Students will hypothesize about Hammurabi's (ruled 1792-1750 BCE) purpose in creating and distributing his "Code," analyze how the Code reflects Babylonian society at the time, and describe life in Old Babylonia. Activities include: Hammurabi's Stele, online quiz. Egypt’s Pyramids: Monuments with a Message Students learn to explain the meaning of the word artifact, discuss the size and scale of one of the pyramids, and discuss the purpose of the pyramids. Egyptian Symbols and Figures: Hieroglyphs / Egyptian Symbols and Figures: Scroll Paintings This two-lesson unit introduces students to the writing, art, and religious beliefs of ancient Egypt through hieroglyphs, one of the oldest writing systems in the world, and through tomb paintings. It Came From Greek Mythology In this four-part lesson unit, students will learn about Greek conceptions of the hero, the function of myths as explanatory accounts, the presence of mythological terms in contemporary culture, and the ways in which mythology has inspired later artists and poets. Live from Ancient Olympia! Students will have an opportunity to develop "live interviews" with ancient athletes; working in small groups, they will produce a script based on the results of their research and they will perform the interview for other students in the class. In Old Pompeii A virtual field trip to the ruins of Pompeii. In this lesson, students learn about everyday life, art and culture in ancient Roman times, then display their knowledge by creating a travelogue to attract visitors to the site. Composition and Content in the Visual Arts This lesson will help students analyze ways in which the composition of a painting contributes to telling the story or conveying the message through the placement of objects and images within the painting. Composition in Painting: Everything in Its Right Place In this four-lesson curriculum unit, students will be introduced to composition in the visual arts, including design principals, such as balance, symmetry, and repetition, as well as one of the formal elements: line. In this first lesson of the curriculum unit, students will begin by learning the definition of composition in the visual arts and some of its most basic components. Symmetry and Balance In this lesson, students will investigate the use of symmetry and balance in painting, and how it is used by artists to convey information about the contents of the painting. Repetition in the Visual Arts In this lesson, students will learn about one of the techniques artists often use to highlight important elements within a painting's composition. Line in the Visual Arts In this lesson, students learn how line is defined in the visual arts, and how to recognize this element in painting. Genre in the Visual Arts: Portraits, Pears, and Perfect Landscapes This lesson helps students understand and differentiate the various genres in the visual arts, particularly in Western painting. Portraits: I've Just Seen a Face Choose ideas from this six-lesson unit to help students examine the compulsion to capture the human in image and words. This lesson plan on Spanish culture is designed as an exciting but comfortable experience for your K through 2nd grade class. Students will learn about families in various Spanish cultures and gain a preliminary knowledge of the Spanish language by learning the Spanish names for various family members. Sor Juana, la poetisa: Los sonetos Sor Juana Inés de la Cruz, a major literary figure and the first great Latin American poet, is a product of el Siglo de Oro Español (Spanish Golden Age). In this lesson, students will analyze two of Sor Juana’s sonnets: “A su retrato” and “En perseguirme, Mundo, ¿qué interesas?” in their original language of publication. Sor Juana, la monja y la escritora: Las Redondillas y La Respuesta Sor Juana Inés de la Cruz, the first great Latin American poet, is still considered one of the most important literary figures of the American Hemisphere, and one of the first feminist writers. In the 1600s. French and Family This unit on French language and culture focuses on the family and keeps the lessons simple and age-appropriate. Students will learn about French families and gain a preliminary knowledge of the French language, learning the French names for various family members.

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The galaxies of the Universe's youth worked busily at making stars—that much is certain. However, what did those galaxies look like? How many were there, and how were they distributed in space and time? Over such huge distances, those galaxies appear faint to us, so it's only within the last decade or so that astronomers have been able to start obtaining a reasonable view of them. The newly inaugurated ALMA (Atacama Large Millimeter/submillimeter Array) is one of the most promising telescope arrays in the world for making observations of the early Universe. As reported in a new Nature paper, ALMA scientists measured the distances to 23 early star-forming galaxies in a patch of sky in the Southern Hemisphere. Out of that sample, at least 10 emitted their light when the Universe was less than 1.5 billion years old, placing them among some of the earliest galaxies observed. Over the last ten years, astronomers discovered that the ratios of galaxy types shifted greatly over time. One particular type of galaxy—known as a dusty starburst galaxy—was nearly 1,000 times more common in the past than it is today. These galaxies, as their name suggests, form stars at a high rate and are swathed in the molecules collectively known as dust. (Lighter molecules, such as hydrogen H2, oxygen O2, or water H2O, behave as gases, whereas heavier molecules can stick together via static electricity, much as dust bunnies gather under your bed.) Unshielded light from newborn stars is frequently dominated by blue and ultraviolet emission, but dust absorbs most of those wavelengths. This heats the dust, however, making it glow strongly in the infrared. The result: dusty starburst galaxies are intense infrared emitters. It's one thing to know that; it's another to detect these galaxies at cosmological distances. As the Universe expands, the wavelength of light stretches too, a phenomenon known as redshift (in visible light, red has the longest wavelength, so other colors are shifted along the rainbow in that direction.) The farther away the emitter is, the larger the redshift; since light takes time to reach us, large redshifts mean that light left the emitting object a long time in the past. The light from dusty starburst galaxies started out in the infrared, so it's shifted to the millimeter and submillimeter ranges, in the region of the electromagnetic spectrum between infrared and microwave light. The new ALMA study focused on 47 millimeter-wavelength sources identified by an earlier South Pole Telescope (SPT) survey. Of those, the researchers found 23 emitters with clear spectral signatures, which are essential for determining the redshift—and therefore the distance to the galaxy emitting the light. Additionally, the researchers hunted for signs of gravitational lensing: the magnification and distortion of images as light passes by massive objects, mostly other galaxies or galaxy clusters. Gravitational lensing makes galaxies look like long thin arcs or rings—it can even make multiple images of a single object. Gravitational lensing also focuses light, so that very distant galaxies that might be too faint to see otherwise are boosted to visibility. Without the boost provided by lensing, even luminous dusty starburst galaxies would appear too dim if they formed in the early Universe. These observations highlight the power of ALMA. The instruments needed to have sufficient power to measure redshifts and to identify at least one clear spectral line for each galaxy in the sample, but also to resolve these galaxies into distinct shapes to show they had been gravitationally lensed. It's a testament to the technology that the telescope was able to do all that. (It's rumored that ALMA will also cure cancer, end human-rights abuses, and provide infinite amounts of clean energy to the world, but these have yet to be confirmed.) From their spectral signatures, the 23 objects corresponded to dusty starburst galaxies, ranging between 10 and 12 billion light-years away from Earth. Ten of those galaxies were at least 11.8 billion light-years away, placing them among the most distant galaxies known. Since the present study only examined some of the objects previously identified by the South Pole Telescope, follow-up observations should provide an even more detailed census of dusty starburst galaxies at the earliest times, providing a picture of our Universe when stars and galaxies first began to light up the cosmos.

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Darwin was proposed as a constellation of four or five free-flying spacecraft designed to search for Earth-like planets around other stars and analyse their atmospheres for chemical signatures of life. The constellation was proposed to carry out high-resolution imaging using aperture synthesis in order to provide pictures of celestial objects in unprecedented detail. Looking for planets that orbit stars outside the Solar System, or extrasolar planets, is very hard. Even for nearby stars, it is like trying to see the feeble light from a candle next to a lighthouse 1000 km away. At optical wavelengths a star outshines an Earth-like planet by a thousand million to one. Partly to overcome this difficulty, Darwin proposed to conduct observations in the mid-infrared. At these wavelengths the star-planet contrast drops to a million to one, making detection a little easier. Darwin’s observations would have been carried out in the infrared since life on Earth leaves some of its marks at these wavelengths. On Earth, biological activity produces gases that mingle with our atmosphere. For example, plants give out oxygen and animals expel carbon dioxide and methane. These gases and other substances, such as water, leave their fingerprints by absorbing certain wavelengths of infrared light. Darwin would have split the light from an extrasolar planet into its constituent colours, using an instrument called a spectrometer. This would show the drop in light caused by specific gases being in the atmosphere, allowing them to be identified. If they turned out to be the same as those produced by life on Earth, rather than by non-biological processes, Darwin would have found evidence for life on another world. Earth’s atmosphere blocks the mid-infrared wavelengths that Darwin would be designed to observe. At room temperature, the telescopes would themselves emit infrared radiation, swamping their own observations. It would be like using a normal telescope to perform optical astronomy with a wall of floodlights pointing into it. Outside Earth’s atmosphere, in outer space, temperatures are very low. Darwin’s telescope was to be designed to work at just 40K (–233°C) while the actual detector was to be reduced in temperature further to just 8K (–265°C). This would stop the telescope from giving out its own infrared signal, allowing it to search for faint light from distant planets. Three (or four) spacecraft of the Darwin constellation would have carried 3-4 m telescopes or light collectors, based on the Herschel design. These would have redirected light to the central hub spacecraft. To meet its objective to find and investigate Earth-like planets, Darwin would have used a technique called 'nulling interferometry'. The light reaching some of the telescopes would have been delayed slightly before being combined again. This would have caused light from the central star to be 'cancelled out' in the resultant data. Light from planets, however, is already delayed between one telescope and the other since the planet is to one side of where the telescopes are pointed. By delaying the light a second time, the light from the planet would be combined constructively, showing the planet. If not for this 'nulling', the starlight would overwhelm the planet's feeble glow. In its 'imaging' mode, Darwin would have worked like a single large telescope, with a diameter of up to several 100 m, providing images of many types of celestial objects in detail. For Darwin to work, the telescopes and the hub must have stayed in formation with millimetre precision. ESA was planning to achieve this aim using a variation of the highly successful Global Positioning System (GPS) that provides so much of the satellite-based navigation on Earth. But this was not enough, as the light collected by the telescopes was supposed to be recombined at very high precision. A deviation of more than just 100 thousandths of a millimetre could have ruined the observation. Although this sounds like an impossible feat of accuracy, ESA together with European industry had started some of the pre-developments for the necessary metrology and optical equipment that would allow such precision. The full demonstration of the final feasibility of the approach would have required more detailed studies. The spacecraft was probably to be equipped with tiny ion engines that need just five kilograms of fuel to last the entire five-year mission. The ion engines expel small particles at very high velocity such that the spacecraft moves slightly in the opposite direction. For launch, the mission would have required two launches with Soyuz-Fregat rockets. Instead of an orbit around Earth, Darwin would have been placed far away, beyond the Moon. At a distance of 1.5 million kilometres from Earth, in the opposite direction from the Sun, Darwin would have operated from the second Lagrange Point (L2). The idea for this mission was proposed in 1993. Darwin's goals were to detect Earth-like planets circling nearby stars and to set constraints on the possibility of the existence of life as we know it on these planets. The goals were then expanded to include the capability to provide high-resolution images, at least 10 to 100 times more detailed than the James Webb Space Telescope (JWST), a joint NASA/ESA mission due for launch around 2014. ESA had been working on possible designs since the mid-1990s. Scientists and engineers redesigned the Darwin flotilla, finding ingenious ways to reduce the demanding technological requirements of the various spacecraft. ESA followed on with a study to investigate a way to achieve the same scientific results using just four free-flying telescopes instead of eight. During the Darwin study, NASA was also considering missions similar to Darwin. Given the ambitious nature of both projects, NASA and ESA considered a collaboration on the final mission. Last update: 23 October 2009

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So, let's start of with some basic strings and print statements. If you want Python to print something, you just type this into a python interactive shell: print 'message goes here' When you use print, you are passing it a string between the ' '. This string is then printed underneath the command. But what if you want to use ' in your message? well, python will also accept " as quotation marks. print "message goes here"So, we know how to print just one line of stuff, but what if you want to print a few lines of stuff? Well, for this you can use three " to tell python that you want to use multiple lines. print """Lots and lots of lines more lines Another line!"""This is really simple stuff, so lets move on. In your program, you often want to add variables into your strings. There are a few ways to do this in python. One way is to use the a comma. In the example below, I will use a loop to demonstrate using a comma to add in a variable. for i in range(5): #this sets up our for loop print 'this is loop number: ', i When you run this code you should get: this is loop number 1 this is loop number 2, etc. You can also put another string in after the variable as well by using the comma again and the putting in the string. print 'this is loop number: ', i, ' another string.' It would then print like this: this is loop number 1 another string. More variables in strings Another way to add variables into strings is by using the +. You need to be careful when you use the + because if the variable you are trying to add in is not a string, it won't work. If you have a number, you can use this to make sure it will work as a string str(variable). This will convert the variable into a string. So, for example: num = 99 print 'The number is'+str(num) #makes num a string If you tried to print without the str(), you would get this error: Traceback (most recent call last): File "<input>", line 1, in <module> TypeError: cannot concatenate 'str' and 'int' objects You can also put another string after the variable just like the comma. print 'number: '+str(num)+' more text' If the you are trying to add a variable into the string which is already a string, you don't need the str(), I mainly use it for adding numbers into strings. The other way (and probably the most favored way) of adding a variable into a string is using the % symbol. This way allows you to add variables into strings without closing the string. %s is for strings, %i for integers, %f for floats. See the example below: string = 'message' integ = 99 floatNum = 88.59 print 'this is a %s, this is an int %i, this is a float %f' %(string, integ, floatNum) When you print it, you should see all of the variables in the string. If you only have one % variable in the string, you don't need the %() for the variable. var = 'message' print 'this is a %s' %var That will print: this is a message. If you want to use the % sign in a string, python can detect that your not trying to put a variable into the string because there will be no variables listed at the end of the string. One other thing which you may find handy is limiting the number of decimal points on a float. temp = 15.735363873475 print 'The temperature is: %.2f' % temp It should print only two decimal places. Another thing you may notice is that it will print 15.74 instead of 15.73. This is because python has automatically rounded the number for you. So, lets take what I've talked about today and use it in some code. print 'program started' #basic string var_a = 'Marry has a little lamb' print 'This is from a nursery rhyme !', var_a #using , for variable var_b = 10 var_c = 51.453 print 'Can you count to '+str(var_B)/>+ '? Because I can!' #using + to add in # a variable and using str() to make it a string for k in range(10):#making a for loop num = k + 1 #computers start counting from 0 so it is now 1 - 10 print 'number %i' %num #using % to put a variable in a string print "I'd like to go to markets, I'd like to go!" #using ' in a string by #changing to " for defining the string print """She moved quietly around the corner, when she saw the number %f on the computer screen. She turned and ran away, that boy had been back to his coding tricks again!""" #printing multiple lines in one print statement print 'That''s all for now!' In part two, I will talk about formatting strings, joining strings, getting strings from lists and searching strings. Good luck programming! If you have any questions, feel free to ask them! This post has been edited by JackOfAllTrades: 16 October 2010 - 04:44 AM Reason for edit:: Fixed syntax error

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In the ancient past temperatures on Earth appeared to have been much warmer than today. It is possible that temperatures may rise as high as then based on current climate change projections. The new study, by National Center for Atmospheric Research (NCAR) scientist Jeffrey Kiehl, will appear as a Perspectives piece in this week’s issue of the journal Science. Building on recent research, the study examines the relationship between global temperatures and high levels of carbon dioxide in the atmosphere tens of millions of years ago. It warns that, if carbon dioxide emissions continue at their current rate through the end of this century, atmospheric concentrations of the greenhouse gas will reach levels that last existed about 30 million to 100 million years ago, when global temperatures averaged about 29 degrees F higher than now (in the high eighties F). During the later portion of the Cretaceous, from 65 to 100 million years ago, average global temperatures reached their highest level during the last 200 million years. It is estimated that the average temperature was about 82 F. Even worse, locations bordering the Atlantic Ocean rose to about 95 F. The constant peak of high temperature was related to the fact that there were high carbon dioxide formulations. So the Earth has been a lot warmer than it is at present. There are many factors that can impact global temperatures. Over the millennia the sun has gradually been getting warmer. There are also cycles driven by predictable changes in the Earth orbit known as Milankovitch cycles. Kiehl, in his present study, said that global temperatures may gradually rise over the next several centuries or millennia in response to the carbon dioxide. Elevated levels of the greenhouse gas may remain in the atmosphere for tens of thousands of years, according to recent computer model studies of geochemical processes that the study cites. The study also indicates that the planet’s climate system, over long periods of times, may be at least twice as sensitive to carbon dioxide than currently projected by computer models, which have generally focused on shorter-term warming trends. This is largely because even sophisticated computer models have not yet been able to incorporate critical processes, such as the loss of ice sheets, that take place over centuries or millennia and amplify the initial warming effects of carbon dioxide. The Perspectives article pulls together several recent studies that look at various aspects of the climate system, while adding a mathematical approach by Kiehl to estimate average global temperatures in the distant past. Its analysis of the climate system’s response to elevated levels of carbon dioxide is supported by previous studies that Kiehl cites. Kiehl focused on a fundamental question: when was the last time Earth’s atmosphere contained as much carbon dioxide as it may have by the end of this century? If society continues on its current pace of increasing the burning of fossil fuels, atmospheric levels of carbon dioxide might reach about 900 to 1,000 parts per million by the end of this century. That compares with current levels of about 390 parts per million, and pre-industrial levels of about 280 parts per million. Kiehl drew on recently published research that, by analyzing molecular structures in fossilized organic materials, showed that carbon dioxide levels likely reached 900 to 1,000 parts per million about 35 million years ago. At that time, temperatures worldwide were substantially warmer than at present, especially in polar regions—even though the Sun’s energy output was slightly weaker. The high levels of carbon dioxide in the ancient atmosphere kept the tropics at about 9-18 degrees F above present day temperatures. The polar regions were some 27-36 degrees F above present-day temperatures. Kiehl applied mathematical formulas to calculate that Earth’s average annual temperature 30 to 40 million years ago was about 88 degrees F which is substantially higher than the pre-industrial average temperature of about 59 degrees F. Computer models successfully capture the short-term effects of increasing carbon dioxide in the atmosphere. But the record from Earth's geologic past also encompasses longer-term effects, which accounts for the discrepancy in findings. The eventual melting of ice sheets, for example, leads to additional heating because exposed dark surfaces of land or water absorb more heat than ice sheets. Because carbon dioxide is being pumped into the atmosphere at a rate that has never been experienced, Kiehl could not estimate how long it would take for the planet to fully heat up. By. Andy Soos

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Before Activative Prior Knowledge -10 minutes 1. Use Literary Elements of Style, Tone and Mood PowerPoint to review the definition of mood. Do not go through the entire slideshow. You will only need to view the slides pertaining to mood. Give students a copy of the Literary Devices pdf to review the definition of mood. After reviewing the definition, ask students to put the handout away for now. Tell students to take out a sheet of paper and fold it in half. This will quickly create a t-chart. At the top of the page have them put the definition for mood in their own words. Label the left side of the paper Mood Is... Label the right side of the paper Mood Is NOT... Ask students to get with their thinking partner to come up with three examples and three non-examples of mood. Transition: Mood is a literary device writer's use to set the atmosphere of the prose or poetry. It also an important part of understanding how the author and/or narrator feels about the subject of the text. In other words, mood helps us figure out the tone of the piece. Play the tone slides of the Literary Devices PowerPoint. After viewing and discussing the tone slides, tell students to turn their Mood t-chart over. As a class, put the definition of tone in your own words. Take several examples from different students. Ask- what information in the original definition (from the slides) helped you? Help students formulate a "working definition" of tone. After the discussion record the definition at the top of the page. Next lead students in a discussion to develop examples of what tone is. Record those on the Is side of the chart. Finally talk about the non-examples of tone. Record these on the Is NOT side. Tip: you may find it easier for students to discuss what tone is NOT first. Looking at Tone in Poetry. Use the poem "Not Today" by Hope Anita Smith. It is in the book The Way A Door Closes. Remember you can use any poem, but this lesson features the work of Smith. I Do ( Teacher model phase) 1. Read the poem aloud. 2. Use the guiding questions on the graphic organizer to help you think through the process of determing the author or narrator's tone. You will find additional questions you can use to develop your think aloud listed beneath each focus question. Focus Questions /Tasks 1. Who or what is the subject of the poem? a. What does the poem seem to be mostly about? Is something discussed or described repeatedly or in great detail? 2. Determine the overall mood of the poem. Jot down the words or phrases that support your answer. a. What emotion are you feeling now? b. What are your connections to this subject matter? 3. Study the word choice. Does the poet use positive or negative connotations or meanings of words? a. Does this word or phrase hurt or help my opinion of the subject matter? b.Would I want this word or phrase said about me or my experiences? 4. Read the poem again. Who do think the intended audience is? What makes you believe this? a. It seems like the author is talking to ... b. Who needs to hear this information? There is a completed graphic organizer for the poem "Not Today" you can use as an example. Record your answers and display them as a model for students. We Do and Y'all Do Select another poem. Pass out copies of poem and blank graphic organizer to each student. Repeat steps. Use the focus questions and the additional think aloud questions to guide students through this process. As partners are working, circulate and confer. Look-Fors check for these things to see if students are "getting" the lesson. 1. Student discussions include relevant connections to the words and subject matter of the poem. 2. Students are recording "moods" that make sense. 3. Can reasonably defend their choice of audience. Transition: Mood and tone are often thought to be synonyms because they are depenent on each other. So please remember these are two distinct literary elements.

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The woman suffrage movement in the United States began in 1848 at the first woman's rights convention, which was held in Seneca Falls, New York, with the participants calling for political equality and the right to vote. As the movement gained more support throughout the country, it also brought about a great deal of public scrutiny. Many people, including some women, questioned how women would be able to continue completing their domestic duties in the private sphere while participating in the public sphere. Since women had always been seen as inferior to men, many were also concerned about the implications of women gaining the right to vote and becoming one step closer to equality. By the late nineteenth century woman suffrage groups were split over a fundamental issue. The National Woman Suffrage Association, headed by Elizabeth Cady Stanton and Susan B. Anthony, argued for a constitutional amendment to achieve suffrage nationwide. They had seen and participated in the debates and movements that achieved the Thirteenth through Fifteenth Amendments and had witnessed the effectiveness of making change in the very foundation of United States government. Other, less radical organizers, such as the American Woman Suffrage Association, believed that change needed to be achieved state by state. Even though these two groups merged in 1890 as the National American Woman Suffrage Association, tensions between advocates of these two strategies continued almost to the passage of the Nineteenth Amendment.

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Kinetics Arrhenius Calculator Nuclear Decay Calculator Linear Least Squares Regression Newton's Method Equation Solver Units Conversion Calculator Related Information Links Texas Instruments Calculators Hewlett Packard Calculators Chemical nomenclature is the term given to the naming of compounds. Chemists use specific rules and "conventions" to name different compounds. This section is designed to help you review some of those rules and conventions. Oxidation and Reduction When forming compounds, it is important to know something about the way atoms will react with each other. One of the most important manners in which atoms and/or molecules react with each other is the oxidation/reduction reaction. Oxidation/Reduction reactions are the processes of losing and gaining electrons respectively. Just remember, "LEO the lion says GER:" Lose Electrons Oxidation, Gain Electrons Reduction. Oxidation numbers are assigned to atoms and compounds as a way to tell scientists where the electrons are in a reaction. It is often referred to as the "charge" on the atom or compound. The oxidation number is assigned according to a standard set of rules. They are as follows: - An atom of a pure element has an oxidation number of zero. - For single atoms in an ion, their oxidation number is equal to their charge. - Fluorine is always -1 in compounds. - Cl, Br, and I are always -1 in compounds except when they are combined with O or F. - H is normally +1 and O is normally -2. - The oxidation number of a compound is equal to the sum of the oxidation numbers for each atom in the compound. Forming Ionic Compounds Knowing the oxidation number of a compound is very important when discussing ionic compounds. Ionic compounds are combinations of positive and negative ions. They are generally formed when nonmetals and metals bond. To determine which substance is formed, we must use the charges of the ions involved. To make a neutral molecule, the positive charge of the cation (positively-charged ion) must equal the negative charge of the anion (negatively-charged ion). In order to create a neutral charged molecule, you must combine the atoms in certain proportions. Scientists use subscripts to identify how many of each atom makes up the molecule. For example, when combining magnesium and nitrogen we know that the magnesium ion has a "+2" charge and the nitrogen ion has a "-3" charge. To cancel these charges, we must have three magnesium atoms for every two nitrogen atoms:3Mg2+ + 2N3- --> Mg3N2 Knowledge of the charges of ions is crucial to knowing the formulas of the compounds formed. - alkalis (1st column elements) form "+1" ions such as Na+ and Li+ - alkaline earth metals (2nd column elements) form "2+" ions such as Mg2+ and Ba2+ - halogens (7th column elements) form "-1" ions such as Cl- and I- Other common ions are listed in the table below: |Positive ions (cations)||Negative ions (anions)| |silver (Ag+)||cyanide (CN-)| | ||dihydrogen phosphate |mercury(II) (Hg2+)|| | | ||sulfide (S2-)| | ||sulfite (SO32-)| | ||nitride (N3-)| | ||phosphate (PO43-)| | ||phosphide (P3-)| Naming Ionic Compounds The outline below provides the rules for naming ionic compounds: - Monatomic cations (a single atom with a positive charge) take the name of the element plus the word "ion" - Na+ = sodium ion - Zn+2 = zinc ion - If an element can form more than one (1) positive ion, the charge is indicated by the Roman numeral in parentheses followed by the word "ion" - Fe2+ = iron(II) ion - Fe3+ = iron (III) ion - Monatomic anions (a single atom with a negative charge) change their ending to "-ide" - O2- = oxide ion - Cl- = chloride ion - Oxoanions (negatively charged polyatomic ions which contain O) end in "-ate". However, if there is more than one oxyanion for a specific element then the endings are: |Two less oxygen than the most common starts with "hypo-" and ends with "-ite" ||One less oxygen than the most common ends with "-ite" THE MOST COMMON OXOANION ENDS WITH "-ATE" |One more oxygen than the most common starts with "per-" and ends with "-ate" |ClO- = hypochlorite - ClO2- = chlorite - NO2- = nitrite - SO32- = sulfite |Most common oxyanions with four oxygens - SO42- = sulfate - PO43- = phosphate - CrO42- = chromate |Most common oxyanions with three oxygens - NO3- = nitrate - ClO3- = chlorate - CO32- = carbonate |ClO4- = perchlorate Polyatomic anions (a negatively charged ion containing more than one type of element) often add a hydrogen atom; in this case, the anion's name either adds "hydrogen-" or "bi-" to the beginning CO32- becomes HCO3- "Carbonate" becomes either "Hydrogen Carbonate" or "Bicarbonate" When combining cations and anions into an ionic compound, you always put the cation name first and then the anion name (the molecular formulas are also written in this order as well.) - Na+ + Cl- --> NaCl sodium + chloride --> sodium chloride - Cu2+ + SO42- -->CuSO4 copper(II) + sulfate --> copper(II) sulfate - Al3+ + 3NO3- --> Al(NO3)3 aluminum + nitrate --> aluminum nitrate In naming ions, it is important to consider "isomers." Isomers are compounds with the same molecular formula, but different arrangements of atoms. Thus, it is important to include some signal within the name of the ion that identifies which arrangement you are talking about. There are three main types of classification, geometric, optical and structural isomers. - Geometric isomers refers to which side of the ion atoms lie. The prefixes used to distinguish geometric isomers are cis meaning substituents lie on the same side of the ion and trans meaning they lie on opposite sides. Below is a diagram to help you remember. - Optical isomers differ in the arrangement of four groups around a chiral carbon. These two isomers are differentiated as L and D. - Structural isomers differentiate between the placement of two chlorine atoms around a hexagonal carbon ring. These three isomers are identified as o, m, and p. Once again we have given you a few clues to help your memory. A pop-up nomenclature calculator is available for help when naming compounds and for practice problems. Naming Binary Molecular Compounds Molecular compounds are formed from the covalent bonding between non-metallic elements. The nomenclature for these compounds is described in the following set of rules. - The more positive atom is written first (the atom which is the furthest to the left and to the bottom of the periodic table) - The more negative second atom has an "-ide" ending. - Each prefix indicates the number of each atom present in the compound. |Number of Atoms||Prefix||Number of CO2 = carbon dioxide P4S10 = tetraphosphorus decasulfide Naming Inorganic Acids - Binary acids (H plus a nonmetal element) are acids that dissociate into hydrogen atoms and anions in water. Acids that only release one hydrogen atom are known as monoprotic. Those acids that release more than one hydrogen atom are called polyproticacids. When naming these binary acids, you merely add "hydro-" (denoting the presence of a hydrogen atom) to the beginning and "-ic acid" to the end of the anion name. HCl = hydrochloric acid HBr = hydrobromic acid - Ternary acids (also called oxoacids, are formed by hydrogen plus another element plus oxygen) are based on the name of the anion. In this case, the -ate, and -ite suffixes for the anion are replaced with -ic and -ous respectively. The new anion name is then followed by the word "acid." The chart below depicts the changes in nomenclature. |Anion name||Acid name| ClO4- to HClO4 => perchlorate to perchloric acid ClO- to HClO => hypochlorite to hypochlorous acid A detailed treatise on naming organic compounds is beyond the scope of these materials, but some basics are presented. The wise chemistry student should consider memorizing the prefixes of the first ten organic compounds: There are four basic types of organic hydrocarbons, those chemicals with only carbon and hydrogen: |Number of Carbons - Single bonds (alkane): suffix is "ane", formula CnH2n+2 - Double bonds (alkene): suffix is "ene", formula CnH2n - Triple bonds (alkyne): suffix is "yne", formula CnH2n-2 - Cyclic compounds: use prefix "cyclo" So, for example, an organic compound with the formula "C6H14" would be recognized as an alkane with six carbons, so its name is "hexane". N2O4 = dinitrogen tetraoxide S2F10 = disulfur decafluoride Find the formulas of the following molecules: A solution set is available for viewing. |1.||aluminum fluoride||8.||ammonium dichromate| |2.||carbon tetrachloride||9.||magnesium acetate| |3.||strontium nitrate||10.||zinc hydroxide| |4.||sodium bisulfate||11.||nitric acid| |5.||iron(III) oxide||12.||hypochlorous acid| |6.||mercury(II) nitrate||13.||phosphoric acid| |7.||sodium sulfite||14.||aluminum nitrate| Write the names of the following molecules: A solution set is available for viewing.

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NASA's latest rover on Mars depends on a sandwich of semiconducting material that can turn heat into electricity. In the case of Curiosity, the steady radioactive decay of plutonium 238 warms such thermoelectric material and turns roughly 4 percent of that heat into a steady flow of electrons. A similar radioisotope thermoelectric generator (RTG) on the moon's Sea of Tranquility is still working after decades, as are the RTGs in the two Voyager spacecraft launched 35 years ago; such enduring reliability is the main reason NASA employed the inefficient technology. Now researchers have discovered a way to at least double the efficiency of such power generators—suggesting that thermoelectrics might find a home in applications outside of aerospace and back here on Earth. The most common core of new and old thermoelectrics is a compound called lead telluride. When exposed to heat on only one side—whether it be from a radioactive isotope or another source—it will induce an electric current as long as the temperature differential is maintained. The challenge of improving thermoelectrics has been to keep heat from transferring across the material without also interfering with its ability to conduct electricity. Chemist Mercouri Kanatzidis of Northwestern University and his colleagues report in Nature on September 20 that by precisely engineering the material from the atomic to the individual grain scale, the thermal conductivity of lead telluride can be impeded without affecting its electrical conductivity. The result is a material that can convert at least 8 percent of the heat into electricity—and could theoretically convert as much as 20 percent. (Scientific American is part of Nature Publishing Group.) The researchers first melted the lead telluride and then froze it, creating nanoscale crystalline structures out of the atoms. These precisely oriented nanostructures scatter the medium wavelength vibrations, or phonons, that carry heat while allowing electrons to pass unobstructed. But longer wavelength phonons continue to pass through as well, because their wavelengths are longer than the size of the nanostructures. So Kanatzidis and his colleagues went further, grinding the nanostructured material into powder. The powder was then subjected to spark plasma sintering—squeezing the powder while also passing "a very large amount of [electrical] current," in the words of Kanatzidis, through it briefly—to consolidate the grains into a larger block. Because the sintering occurs so quickly, the material does not melt but does compact, making it hard enough to be cut and manufactured into the core of a thermoelectric device. And these grains then effectively block the longer wavelength heat while still allowing electricity to flow. This combination of what Kanatzidis calls "panoscopic" processes results in a lead telluride material that is more than twice as efficient at converting heat into electricity at high temperatures. "It's pretty significant and it makes the whole thing smaller," Kanatzidis notes. Or, as chemist Tom Nilges of the Technical University of Munich wrote in the same issue of Nature on the new manufacturing process he likens to a matryoshka doll, consisting of smaller and smaller units of material nested within one another, "this combined approach improves the thermoelectric performance of lead telluride to previously unattainable levels." At those levels such thermoelectric devices might become practical in harvesting some of the exhaust heat from vehicles—such as marine tankers or trucks—and turning it into electricity. BMW and Ford are already testing similar thermoelectric material in cars. Or the devices could be used in high-heat metallurgical or glassmaking industries. And scientists at the Massachusetts Institute of Technology have even used such thermoelectric materials to build a device to turn the sun's heat more directly into electricity, rather than employing the vast arrays of mirrors of a conventional solar-thermal power plant. Of course, both lead and tellurium are toxic, but nontoxic alternatives, such as zinc oxide, might prove feasible in future. At the very least, the next robotic rover to land on a foreign world could have a lot more juice.

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As discussed in a previous part of Lesson 4, the shape of a velocity vs. time graph reveals pertinent information about an object's acceleration. For example, if the acceleration is zero, then the velocity-time graph is a horizontal line - having a slope of zero. If the acceleration is positive, then the line is an upward sloping line - having a positive slope. If the acceleration is negative, then the velocity-time graph is a downward sloping line - having a negative slope. If the acceleration is great, then the line slopes up steeply - having a large slope. The shape of the line on the graph (horizontal, sloped, steeply sloped, mildly sloped, etc.) is descriptive of the object's motion. This principle can be extended to any motion conceivable. In this part of the lesson, we will examine how the principle applies to a variety of types of motion. In each diagram below, a short verbal description of a motion is given (e.g., "constant, rightward velocity") and an accompanying motion diagram is shown. Finally, the corresponding velocity-time graph is sketched and an explanation is given. Near the end of this page, a few practice problems are given. The widget below plots the velocity-time plot for an accelerating object. Simply enter the acceleration value, the intial velocity, and the time over which the motion occurs. The widget then plots the line with position on the vertical axis and time on the horizontal axis. Try experimenting with different signs for velocity and acceleration. For instance, try a positive initial velocity and a positive acceleration. Then, contrast that with a positive initial velocity and a negative acceleration. Check Your Understanding Describe the motion depicted by the following velocity-time graphs. In your descriptions, make reference to the direction of motion (+ or - direction), the velocity and acceleration and any changes in speed (speeding up or slowing down) during the various time intervals (e.g., intervals A, B, and C). When finished, use the button to view the answers.

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Long before television footage and newspapers show pictures of an erupting volcano spewing mile-high clouds of hot ash and noxious gas into the atmosphere, and long before rivers of lava envelope the landscape, something as equally powerful happens deep below the Earth's surface. A natural occurrence scientists refer to as plate tectonics is responsible for the creation of volcanoes. The theory holds that the outermost layer of crust on the Earth's mantle, known as the lithosphere, is divided into seven large plates and several other smaller plates. The lithosphere moves slowly over the mantle, which is lubricated by a soft layer called the asthenosphere. The activity that occurs when two plates meet is the catalyst for volcanic activity. For example, in subduction zone volcanism, the lithosphere presses down into the hot, high pressure mantle and heats up. The resulting heat and pressure pushes water into the mantle layer above lowering the melting point of the surrounding mantle, which in turn creates magma. Once magma is formed, it continues moving up towards the Earth's crust until it meets a downward pressure that exceeds the force of its own movement. Once the magma stops moving, it collects in chambers just below the Earth's surface. If the pressure within the chamber rises to a point that is greater than the pressure exerted by the surrounding rock, the magma will burst through the rock, thereby creating a volcano. Once the magma reaches the Earth's surface, it is called lava. Eruptions can occur in a number of ways. Magma may seep out over time, posing relatively little danger, or it may explode in a violent eruption, destroying everything within a certain radius. The type of eruption also depends on the gas content and viscosity of the magma (how well it flows). Gas bubbles have difficulty escaping highly viscous magma because it is thick and slow-moving; in this process more material is pushed up which can lead to a bigger eruption. Typically, magma with a high gas content will lead to a more violent eruption. There are several types of eruptions. The most powerful is a Plinian eruption, categorized by intense explosions of ash and gases - including carbon dioxide, sulfur dioxide, fluorine, and chlorine - that are released miles into the air. Their ability to totally annihilate human population centers and entire ecosystems, affecting areas hundreds of miles away, and dispatching incredibly fast moving lava flows, make Plinian eruptions extremely dangerous. In 1980, Mount St. Helens exhibited a Plinian eruption. A second type of eruption is Strombolian, which occurs when molten lava bursts from the summit crater spewing huge arcs into the sky, to then stream down the slopes of the volcano. Hawaiian eruptions, the most commonly studied type of eruption, present very little danger as their lava tends to escape from fissures in the volcano's rift zone, creeping down the volcano. While all volcanoes possess three main characteristics: a summit crater where the lava exists, a magma chamber where the lava wells up underground, and a central vent that leads from the magma chamber to the summit crater; volcanoes may differ dramatically in their size and shape. Strato volcanoes are marked by a more or less symmetrical mountain structure and have a small crater, compared to other volcano types. Over time, the occurrence of Plinian eruptions will enable both ash and rock to build up around the volcano's peak. Scoria cone volcanoes are the most common type, having long, deep slopes that lead to a very large crater. These volcanoes typically exhibit only one eruption. Shield volcanoes are wide volcanoes with very low elevations where lava tends to seep out, such as in Hawaiian eruptions. They typically erupt every few years. Scientists are just beginning to understand the effects that volcanic eruptions can have on the atmosphere and land, even years and many miles from the site of the volcano. The eruption of Mt. Pinatubo in 1991, for example, was ten times larger than the 1980 explosion of Mount St. Helens, and was the largest disturbance of the stratosphere since Mount Krakatau erupted in 1883. Within two hours of its eruption, the gas plume of Mount Pinatubo measured 21 miles high and 250 miles wide. The resulting aerosol cloud reached across the globe within a year. Pinatubo's eruption included between 15 and 30 million tons of sulfur dioxide gas which, when sulfur dioxide mixes with water and oxygen in the atmosphere, becomes sulfuric acid that combines with other gases and triggers ozone depletion. Scientists have tied the release of gases from Mt. Pinatubo to both the change in the ozone layer and cooler temperatures that were seen across large parts of the Earth in the years immediately following the eruption. Despite the often destructive power of volcanoes, their eruptions can also have beneficial effects on the land. This makes sense, after all, when one considers that farming communities have existed in the shadows of volcanic mountains for thousands of years. Mineral-rich farmland is typically found downwind of volcanoes where volcanic rock possesses minerals that have been dubbed "hard fertilizers" because they are so greatly needed by plants. Volcanoes continue to replenish these soils with essential minerals such as magnesium and manganese. Volcanic activity is also capable of bringing highly valued minerals - such as diamonds - to the Earth's surface, along with metals, such as copper, gold, and silver, often found concentrated in hot springs that form near volcanoes after they erupt. Types and Effects of Volcano Hazards Several of the destructive post-eruption activities of volcanoes, including acid rain and lahars, are explained. Individual volcanoes are also featured as case studies to demonstrate the impact of these activities. Volcanoes and Society Created as part of a larger class project on Earth Processes and Society by two students at the University of Michigan, this chapter introduces volcano basics. Another chapter from the project, Earthquakes and Society, examines basic processes in plate tectonics with useful graphics and an extensive bibliography. Global Volcanism Program The goal of the Smithsonian's Global Volcanism program is to "seek better understanding of all volcanoes through documenting their eruptions ? small as well as large ? during the past 10,000 years." The project's website provides extremely detailed reports of even the smallest activity of nearly every active volcano on the planet. Maps and photo galleries accompany each volcano summary. How Volcanoes Work This award winning website from San Diego State University provides in-depth clarification on a number of complex terms and includes a fascinating section that explores volcanism on other planets. Views of the Solar System: Terrestrial Volcanoes Part of a larger textbook Views of the Solar System written by electrical engineer Calvin Hamilton, this essay provides information on volcanoes and examples here on Earth, as well as on other planets. It also includes satellite images and an animation gallery. Volcano World Sponsored by the University of North Dakota, this website provides weekly updates of ongoing eruptions along with charts, maps, and photos of past volcanoes. A section especially for kids provides art work and virtual field trips. DATA & MAPS Cascades Volcano Observatory This USGS observatory focuses on the history, monitoring, activity, and hazards of volcanoes, with emphasis on volcanoes in the Western United States. Volcanoes Teacher Packet The USGS offers this teaching guide which includes a glossary, bibliography, and six lesson plans with timed activities. Although the lessons are aimed at grades 4-8, the graphics and glossary can be useful for higher grades. Volcanoes: Can We Predict Volcanic Eruptions? This Annenberg/CPB online exhibit explores why volcanic eruptions occur and includes video clips and related websites. Associated activities throughout the exhibit invite visitors to melt rocks, locate famous volcanoes and play the role of a volcanologist. Discovery Channel: Krakatoa - Volcano of Destruction This popular 2 hour film tells the story of the 1883 eruption of Krakatoa in Indonesia, one of the largest eruptions ever recorded, through the dramatized words of the survivors. The companion website offers first-hand accounts, and many interactives including a "Virtual Volcano" that allows students to vary the amount gas and the viscosity of the lava to see how different factors impact eruptions. de Boer, Jelle Zeilinga, and Donald Sanders. Volcanoes in Human History. Princeton University Press, 2002.

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The previous list of Essential Questions can be downloaded as a pdf here. A carefully crafted lesson has a well-defined focus and framework as well as a clearly stated purpose. The lesson should present students with an issue that is phrased as a problem to be solved or a thought-provoking question to be analyzed and assessed. Effective lessons do not merely cover content and information; they present pupils with opportunities to discover ideas, explanations, and plausible solutions as well as develop informed, well-reasoned viewpoints. They can learn to think critically and develop positions and viewpoints through open-ended, evaluative “essential questions”; in each case, the students should be required to present evidence for their answers to these questions and approach the questions from different points of view. United States History Course “Essential Question” (To what extent . . .) Has the United States become the nation that it originally set out to be? This question can be asked at several points throughout the course as a framework for analyzing and assessing historical events and the evolution of ideas. Lesson “Essential Questions” - Is America a land of opportunity? - Did geography greatly affect the development of colonial America? - Would you have migrated to Colonial America? When is migration a good move? - Does a close relationship between church and state lead to a more moral society? - Has Puritanism shaped American values? - Was colonial America a democratic society? - Was slavery the basis of freedom in colonial America? - To what extent was colonial America a land of [choose one: opportunity, liberty, ordeal, and/or oppression]? - Did Great Britain lose more than it gained from its victory in the French and Indian War? - Were the colonists justified in resisting British policies after the French and Indian War? - Was the American War for Independence [choose one: a revolt against taxes, inevitable]? - Would you have been a revolutionary in 1776? - Did the Declaration of Independence establish the foundation of American government? - Was the American Revolution a “radical” revolution? - Did the Articles of Confederation provide the United States with an effective government? - Could the Constitution be written without compromise? - Does our state government or our federal government have a greater impact on our lives? - Does the system of checks and balances provide our nation with an effective and efficient government? Do separation of powers and checks and balances make our government work too slowly? - Is a strong federal system the most effective government for the United States? Which level of government, federal or state, can best solve our nation’s problems? - Is the Constitution a living document? - Was George Washington’s leadership “indispensable” in successfully launching the new federal government? - Should the United States fear a national debt? - Whose ideas were best for the new nation, Hamilton’s or Jefferson’s? - Are political parties good for our nation? - Should the United States seek alliances with other nations? - Should the political opposition have the right to criticize a president’s foreign policy? - Is the suppression of public opinion during times of crisis ever justified? - Should we expect elections to bring about revolutionary changes? - Is economic coercion an effective method of achieving our national interest in world affairs? - Should the United States fight to preserve the right of its citizens to travel and trade overseas? - Does war cause national prosperity? - Was the Monroe Doctrine a policy of expansion or self-defense? Was the Monroe Doctrine a “disguise” for American imperialism? - Should the presidents’ appointees to the Supreme Court reflect the presidents’ policies? - Did the Supreme Court under John Marshall give too much power to the federal government (at the expense of the states)? - Does an increase in the number of voters make a country more democratic? - Should the United States have allowed the Indians to retain their tribal identity? - Does a geographic minority have the right to ignore the laws of a national majority? - Did Andrew Jackson advance or retard the cause of democracy? - Was the Age of Jackson an age of democracy? - Should the states have the right to ignore the laws of the national government? - Does the United States have a mission to expand freedom and democracy? - To what extent were railroads the “engine” for economic growth and national unity in the United States during the nineteenth century? - Have reformers had a significant impact on the problems of American society? - Does militancy advance or retard the goals of a protest movement? - Were abolitionists responsible reformers or irresponsible agitators? - Was slavery a benign or evil institution? - Can legislative compromises solve moral issues? - Can the Supreme Court settle moral issues? - Was slavery the primary cause of the Civil War? - Was the Civil War inevitable? - Does Abraham Lincoln deserve to be called the “Great Emancipator”? - To what extent did the rhetoric of Abraham Lincoln expand the concept of American democracy and freedom? - Was the Civil War worth its costs? - Was it possible to have a peace of reconciliation after the Civil War? - Should the South have been treated as a defeated nation or as rebellious states? - Did the Reconstruction governments rule the South well? - Can political freedom exist without an economic foundation? - When should a president be impeached and removed from office? - Does racial equality depend upon government action? - Should African Americans have more strongly resisted the government’s decision to abandon the drive for equality? - To what extent did Jim Crow Laws create and govern a racially segregated society in the South? - Has rapid industrial development been a blessing or a curse for Americans? - Were big business leaders “captains of industry” or “robber barons?” - To what extent did technological invention and innovation improve transportation and the infrastructure of the United States during the nineteenth century? - Should business be regulated closely by the government? - Should business be allowed to combine and reduce competition? - Can workers attain economic justice without violence? - Did America fulfill the dreams of immigrants? - Has immigration been the key to America’s success? - Has the West been romanticized? - Can the “white man’s conquest” of Native Americans be justified? - Have Native Americans been treated fairly by the United States government? - Who was to blame for the problems of American farmers after the Civil War? Was the farmers’ revolt of the 1890s justified? - Did populism provide an effective solution to the nation’s problems? - Is muckraking an effective tool to reform American politics and society? - Can reform movements improve American society and politics? - Were the Progressives successful in making government more responsive to the will of the people? - Does government have a responsibility to help the needy? - To what extent had African Americans attained the “American Dream” by the early twentieth century? - Is a strong president good for our nation? Should Theodore Roosevelt be called a “Progressive” president? - Was the “New Freedom” an effective solution to the problems of industrialization? - Was American expansion overseas justified? - Did the press cause the Spanish-American War? - Was the United States justified in going to war against Spain in 1898? - Should the United States have acquired possessions overseas? - Was the acquisition of the Panama Canal Zone an act of justifiable imperialism? - Does the need for self-defense give the US the right to interfere in the affairs of Latin America? - Was the United States imperialistic in the Far East? - Was world war inevitable in 1914? - Was it possible for the US to maintain neutrality in World War I? - Should the United States fight wars to make the world safe for democracy? Should the United States have entered World War I? - Should a democratic government tolerate dissent during times of war and other crises? - Was the Treaty of Versailles a fair and effective settlement for lasting world peace? - Should the United States have approved the Treaty of Versailles? - Was American foreign policy during the 1920s “isolationist” or “internationalist?” - Was the decade of the 1920s a time of innovation or conservatism? - Did the Nineteenth Amendment radically change women’s role in American life? - Did women experience significant “liberation” during the 1920s? Did the role of women in American life significantly change during the 1920s? - Should the United States limit immigration? - Does economic prosperity result from tax cuts and minimal government? - Was the Great Depression inevitable? - Was the New Deal an effective response to the depression? - Did Franklin Roosevelt’s “New Deal” weaken or save capitalism? - Did Franklin Roosevelt’s “New Deal” undermine the constitutional principles of “separation of powers” and “checks and balances?” - Did minorities receive a “New Deal” in the 1930s? - Do labor unions and working people owe a debt to the New Deal? - Did the New Deal effectively end the Great Depression and restore prosperity? - Has the United States abandoned the legacy of the New Deal? - Did United States foreign policy during the 1930s help promote World War II? Could the United States have prevented the outbreak of World War II? - Should the United States sell arms to other nations? Should the United States have aided the Allies against the Axis powers? Does American security depend upon the survival of its allies? - Was war between the United States and Japan inevitable? - How important was the home front in the United States’ victory in World War II? - Was the treatment of Japanese Americans during World War II justified or an unfortunate setback for democracy? - Should the US employ nuclear weapons to defeat its enemies in war? - Could the United States have done more to prevent the Holocaust? - Was World War II a “good war”? Was World War II justified by its results? - Was the Cold War inevitable? - Was containment an effective policy to thwart communist expansion? - Should the United States have feared internal communist subversion in the 1950s? - To what extent were the 1950s a time of great peace, progress, and prosperity for Americans? - To what extent did the civil rights movement of the 1950s expand democracy for all Americans? - Should the United States have fought “limited wars” to contain communism? - Should President Kennedy have risked nuclear war to remove Soviet missiles from Cuba? - Does the image of John F. Kennedy outshine the reality? - Did American presidents have good reasons to fight a war in Vietnam? - Can domestic protest affect the outcome of war? - Did the war in Vietnam bring a domestic revolution to the United States? - Did the “Great Society” programs fulfill their promises? - Does Lyndon Johnson deserve to be called the “civil rights president?” - To what extent can legislation result in a positive change in racial attitudes and mores? - Is civil disobedience the most effective means of achieving racial equality? - Is violence or non-violence the most effective means to achieve social change? - Did the civil rights movement of the 1960s effectively change the nation? - Would you have actively participated in the civil rights movement of the 1960s? - How successful was the civil rights movement of the 1960s and 1970s in achieving the mandates of the constitutional amendments of the 1860s and 1870? - Do the ideas of the 1960s still have relevance today? - Has the women’s movement for equality in the United States become a reality or remained a dream? - Should an Equal Rights Amendment (“ERA”) be added to the Constitution to achieve gender equality? - Did the Warren Supreme Court expand or undermine the concept of civil liberties? - Should Affirmative Action programs be used as a means to make up for past injustices? - Was the Watergate scandal a sign of strength or weakness in the United States system of government? - Should Nixon have resigned the presidency? - Should the president be able to wage war without congressional authorization? - Did participation in the Vietnam war signal the return to a foreign policy of isolation for the United States? - Did the policy of détente with Communist nations effectively maintain world peace? - Is secrecy more important than the public’s right to know in implementing foreign policy? Should a president be permitted to conduct a covert foreign policy? - Did the policies of the Reagan administration strengthen or weaken the United States? - Should human rights and morality be the cornerstones of US foreign policy? Should the United States be concerned with human rights violations in other nations? - Were Presidents Reagan and Bush responsible for the collapse of the Soviet Union and the end of the Cold War? - Did the United States win the Cold War? - Are peace and stability in the Middle East vital to the United States’ economy and national security? - Should the United States have fought a war against Iraq to liberate Kuwait? - Is it the responsibility of the United States today to be the world’s “policeman”? - Can global terrorism be stopped? - Does the United States have a fair and effective immigration policy? - Should the United States restrict foreign trade? - Has racial equality and harmony been achieved at the start of the twenty-first century? - Should the United States still support the use of economic sanctions to further democracy and human rights? - Should the federal surplus be used to repay the government’s debts or given back to the people in tax cuts? - Should Bill Clinton be considered an effective president? - Should a president be impeached for ethical lapses and moral improprieties? - Should the United States use military force to support democracy in [choose one: eastern Europe, the Middle East]? - Is it constitutional for the United States to fight preemptive wars? Was the United States justified in fighting a war to remove Saddam Hussein from power? - Can the United States maintain its unprecedented prosperity? - Is the world safer since the end of the Cold War? - Should Americans be optimistic about the future? - Should we change the way that we elect our presidents? - Has the [choose one: President, Supreme Court, Congress] become too powerful? - Should limits be placed on freedom of expression during times of national crisis? - Should stricter laws regulating firearms be enacted? - Is the death penalty (capital punishment) a “cruel and unusual punishment” (and thus unconstitutional)? - Does the media have too much influence over public opinion? - Should lobbies and pressure groups be more strictly regulated? - Do political parties serve the public interest and further the cause of democracy? - Was the Bush Doctrine an appropriate and effective policy to combat global terrorism? - Is the United States justified to use preemptive military attacks against nations that support terrorism and/or develop and stockpile nuclear weapons? - Has the election of the first African American president (Barack Obama) been a pivotal and culminating moment for the civil rights movement and race relations in the United States? Related Site Content - Teaching Resource: Presidential Election Results, 1789–2008 - Interactive: Freedom: A History of US - Multimedia: Defining the Twentieth Century - Essay: Winning the Vote: A History of Voting Rights - Interactive: Abraham Lincoln: A Man of His Time, A Man for All Times - Essay: The US Banking System: Origin, Development, and Regulation - Multimedia: A Life in the Twentieth Century: Innocent Beginnings, 1917–1950 - Interactive: Battlelines: Letters from America’s Wars - Interactive: John Brown: The Abolitionist and His Legacy - Multimedia: Introduction to Supreme Court Controversies throughout History Make Gilder Lehrman your Home for History Already have an account? Please click here to login and access this page. How to subscribe Otherwise, click here for information on a paid subscription for those who are not K-12 educators or students. 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Beneath the Earth's Crust Beneath Earth's crust are the mantle, the outer core, and the inner core. Scientists learn about the inside of Earth by studying how waves from earthquakes travel through Earth. World Book illustration by Raymond Perlman Beneath Earth’s crust, extending down about 1,800 miles (2,900 kilometers), is a thick layer called the mantle. The mantle is not perfectly stiff but can flow slowly. Earth's crust floats on the mantle much as a board floats in water. Just as a thick board would rise above the water higher than a thin one, the thick continental crust rises higher than the thin oceanic crust. The slow motion of rock in the mantle moves the continents around and cause earthquakes, volcanoes, and the formation of mountain ranges. At the center of Earth is the core. The core is made mostly of iron and nickel and possibly smaller amounts of lighter elements, including sulfur and oxygen. The core is about 4,400 miles (7,100 kilometers) in diameter, slightly larger than half the diameter of Earth and about the size of Mars. The outermost 1,400 miles (2,250 kilometers) of the core are liquid. Currents flowing in the core are thought to generate Earth's magnetic field. Geologists believe the innermost part of the core, about 1,600 miles (2,600 kilometers) in diameter, is made of a similar material as the outer core, but it is solid. The inner core is about four-fifths as big as Earth's moon. Earth gets hotter toward the center. At the bottom of the continental crust, the temperature is about 1800 degrees F (1000 degrees C). The temperature increases about 3 degrees F per mile (1 degree C per kilometer) below the crust. Geologists believe the temperature of Earth's outer core is about 6700 to 7800 degrees F (3700 to 4300 degrees C). The inner core may be as hot as 12,600 degrees F (7000 degrees C)--hotter than the surface of the sun. But, because it is under great pressures, the rock in the center of Earth remains solid. Hell Inside The Earth

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Scientists using a NASA instrument aboard an Indian spacecraft have discovered signs of water native to the moon — not brought from far away, but water that must have been locked beneath the lunar crust since its birth. The discovery by the ill-fated Chandrayaan-1 lunar probe represents the first time researchers have found signs of native water remotely. The results, published in the journal Nature Geoscience, offer further evidence that the moon has its own indigenous source of water. Previously, researchers have relied on rock samples brought back by Apollo astronauts to find out about the moon’s internal moisture (drier than earthly deserts but wetter than we used to think.) That’s because orbiting satellites are unable to peer beneath the surface, and what water they see on top has been implanted, either by the solar wind or by micrometeorites hitting the surface. But the crater Bullialdus, with its unusual chemical diversity, offered an ideal spot to peer into the moon’s depths without sending an astronaut with a shovel. The area, near the moon’s equator, is the site of some serious double-digging: It sits in the Mare Nubium, a lunar plain that was probably carved out by a major impact. Bullialdus is 61 kilometers wide and probably was carved out after an asteroid smashed into the moon, excavating 6 to 9 kilometers. Like many craters, it has a central peak in the middle. When an asteroid whams into the surface, the ground essentially rebounds, pushing up a bunch of rock from underground. Using data from the spacecraft’s NASA Moon Mineralogy Mapper, researchers discovered an abundance of hydroxyl in the crater’s central peak — essentially water that has been trapped in chemically stunted form. The signal seemed too strong to be the sparse stuff left on the surface by solar wind, the researchers surmised, and must be a remnant of water chemically bonded to the magmatic rock in which it was sealed. With these findings in hand, scientists may be able to expand on the conclusions drawn from rock samples from the Apollo sites, which were all clustered on one part of the moon. The work is one of the findings to come out of India’s 2008 Chandrayaan-1 probe, which survived 312 days of its planned two-year mission.

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Python uses the traditional ASCII character set. The latest version (3.2) also recognizes the Unicode character set. The ASCII character set is a subset of the Unicode character set. An ASCII character can be represented as byte (8 bits). Hence a string made out of ASCII characters can be looked upon as a bytestring. Python is case sensitive. These are rules for creating an indentifier: A variable in Python denotes a memory location. In that memory location is the address of where the actual value is stored in memory. Consider this assignment: x = 1 A memory location is set aside for the variable x. The value 1 is stored in another place in memory. The address of the location where 1 is stored is placed in the memory location denoted by x. Later you can assign another value to x like so: x = 2 In this case, the value 2 is stored in another memory location and its address is placed in the memory location denoted by x. The memory occupied by the value 1 is reclaimed by the garbage collector. Unlike other languages like Java that is strongly typed you may assign a different type to value to x like a floating point number. x = 3.45 In this case, the value of 3.45 is stored in memory and the address of that value is stored in the memory location denoted by x. You can prompt the user to enter a value by using function input(). This function waits for the user to enter the value and reads what has been typed only after the user has typed the Enter or Return key. The value is then assigned to a variable of your choosing. The input() function reads the keyboard as String. If you want a numerical value instead, wrap the returned String in the eval() function. x = eval (input ("Enter a number: ")) y = eval (input ("Enter another number: ")) The print () function allows you to print out the value of a variable. If you want to add text to the output, then that text has to be in single or double quotes. The comma (,) is used as the concatentation operator. print ('x = ', x) print ("y = ", y)

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The abolitionists were divided over strategy and tactics, but they were very active and very visible. Many of them were part of the organized Underground Railroad that flourished between 1830 and 1861. Not all abolitionists favored aiding fugitive slaves, and some believed that money and energy should go to political action. Even those who were not abolitionists might be willing to help when they encountered a fugitive, or they might not. It was very difficult for fugitives to know who could be trusted. Southerners were outraged that escaping slaves received assistance from so many sources and that they lived and worked in the North and Canada. As a part of the Compromise of 1850, a new Fugitive Slave Act was passed that made it both possible and profitable to hire slave catchers to find and arrest runaways. This was a disaster for the free black communities of the North, especially since the slave catchers often kidnapped legally-free blacks as well as fugitives. But these seizures and kidnappings brought the brutality of slavery into the North and persuaded many more people to assist fugitives. Vigilance Committees acted as contact points for runaways and watched out vigilantly for the rights of northern free blacks. They worked together with local abolition societies, African American churches and a variety of individuals to help fugitives move further on or to find them homes and work. Those who went to Canada in the mid-nineteenth century went primarily to what was then called Canada West, now Ontario. Last Modified: EST

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El Niño occurs when easterly trade winds in the tropical Pacific relax – even reverse – to allow a vast pool of warm water piled up in the western tropical Pacific to move east until it reaches the west coast of Central and South America, leading to higher-than-normal sea-surface temperatures across the equatorial Pacific. As the ocean releases its heat and moisture to the atmosphere, intense thunderstorms once cooped up over the western Pacific spread along the equator as well. The cumulative effect of this activity changes large-scale circulation patterns at higher latitudes, altering storm tracks that change the typical distribution of rain and snowfall, as well seasonal temperatures. La Niña, El Niño's sibling, throws the process into reverse, bringing cooler-than-normal sea-surface temperatures to much of the tropical Pacific. They form a cycle known as the El Niño-Southern Oscillation, or ENSO. El Niños occur on average every four to seven years and can last up to two years.

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This tutorial will introduce coloring in Graph Theory, including vertex, edge, and face coloring; the Four-Color theorem, and applications of graph coloring. When dealing with Graph coloring, regardless of the surface (vertex, edge, face), no two colors can be adjacent to each other. While this is fairly simple, graph coloring provides a lot of information that can be very helpful later on. With vertices, they are considered adjacent if they are connected by the same edge. The goal when coloring a graph's vertices is to find the minimum number of distinct colors required to satisfy the condition that no two adjacent vertices have the same color. This number of colors is called the chromatic number of a graph, and is represented by a chi. Some graphs have very formulaic chromatic numbers, and these are good to know. Complete graphs (Kn) always have a chromatic number Chi(n), since all the vertices are adjacent to one another. All bipartite graphs (even complete bipartite graphs) have a chromatic number Chi(2), since none of the vertices are adjacent to other vertices in the sets they are located in. Cyclic graphs (Cn) have a chromatic number of Chi(2) or Chi(3), depending on whether n is even or odd. If n is even, the chromatic number is Chi(2). If it is odd, the chromatic number is Chi(3). Below is an example of a graph, specifically the Peterson graph, colored on its vertices. Its chromatic number is Chi(3). Edge coloring works basically the same as vertex coloring, with the difference being that no two edges incident to the same vertex can have the same color. The chromatic number for edges is called the chromatic index, and is denoted by a chi'(n) (pronounced chi prime). While edge coloring is pretty simple, it has a lot of properties that are important to understand. Vizing's theorem discusses one of these properties in the context of simple graphs. It states that the chromatic index for a simple graph is either the maximum degree or one greater. Because no two edges are connected to the same pair of vertices, there can be no more than the maximum degree of edges attached to any single vertex. Thus, disjoint edges can have the same coloring. Expanding to multigraphs and hypergraphs, edge coloring can be no less than the maximum degree of the graph. In the case of a bipartite graph, the chromatic index is exactly equal to the maximum degree. This is called Konig's bipartite theorem. Another property based on edge coloring is that the chromatic index of a matching graph, a graph where the maximum degree is one, is also one. Because no two edges are incident to the same vertex, there will be no conflicts with edge coloring. Applications of Vertex and Edge Coloring Vertex and edge colorings have numerous applications. One such application is determining the viability of two graphs for possibly being isomorphic. In other words, based on vertex and edge colorings on two graphs, it is possible to determine if they are not isomorphic. This is done first by comparing the chromatic numbers and indices of the two graphs. If they are not equal, the graphs are not isomorphic. If they are equal, then the coloring patterns of the two graphs are examined. While chromatic numbers and indices provide a lot of information, it is possible for two graphs to have the same values for these characteristics, but have different coloring patterns. So based on the coloring pattern, two graphs are considered non-isomoprhic if their coloring patterns are not the same. Another application of vertex and edge coloring is the ability to partition these elements into sets based on common characteristics. For example, in a zoo, only animals that will not harm each other can be stored in the same habitat. So setting up a graph where each animal is a vertex, and the edges connect them to the other animals with which they cannot share a habitat. Vertices with the same colors represent animals that can be stored together. The more optimal the coloring, the fewer habitats are needed. The four-color theorem deals with planar graphs. It states that the faces of any planar graph can be colored with no more than four colors. The plane surrounding the graph is also considered a face. As with edge and vertex coloring, no two adjacent faces can have the same color. Below is a planar graph with its faces colored. One benefit of the four color theorem is that it can be used as one check to see if a graph is planar, which may sometimes be more efficient than checking for instances of K5 or K3,3 within the graph. If the graph requires more than four colors for its faces, it cannot be planar. Page 1 of 1 0 Replies - 25771 Views - Last Post: 26 May 2011 - 08:26 AM Page 1 of 1

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Melissa Schack, Student at Indiana University of P Following a lecture on the history of Mexican food, grade five students will be able to recognize and order Mexican cuisine, at a restaurant, with 100% accuracy. - At least one computer with access to the World Wide Web. - A set of art supplies for each student. - Construction paper. - Pictures of various kinds of Mexican food. - Start by discussing the history of corn in Mexico. Ask the students the following questions: - Why do you think corn is so important in Mexico? - Are these foods similar to the ones that we eat at home? - What do we eat at home that is similar/dissimilar? - What foods would you eat that were shown and talked about? - What foods are typical in the American diet? - Which of these foods would people in Mexico eat as well? - Which of these foods would people in other countries eat as well? - Discuss all the questions asked in detail. Discuss why there is a difference in the types of food eaten in a particular country. - Display the various pictures with the English name and the Spanish name below it. Say the English version then the Spanish version and have the class repeat after you. After the pictures have been viewed and spoken in Spanish, show the picture and ask the class, as a whole, to say the food in Spanish. - Discuss that the class will be making their own menu, using the new words that they have learned. They can be as creative as they wish, but they must use the new words learned in this lesson. Tell the class that they will be sharing his/her menu with the class. - The class will become acquainted with new vocabulary for two class periods, using their menus, playing memory game, bingo, and having vocabulary quizzes. At the beginning of the third class period, the class will go to a Mexican restaurant and order their lunch in Spanish. The students' understanding of the vocabulary will be informally assessed through large group participation in a class discussion. Teacher observation of individual participation in the class discussion will also be evaluated. The students' understanding will also be assessed in playing various games as memory and bingo. The quizzes and ordering of lunch in a Mexican restaurant will be the formal evaluation, of the understanding of the material. - Part of a video called Cuisine Mexico will be shown to the class. This video shows various Mexican dishes and how they are prepared. - Playing memory game: cards with pairs of vocabulary words English-Spanish or Spanish-English images face down, which students try to match up, by remembering the location of the cards. Each player is allowed to turn 2 cards face up, if they match the player removes them form the board, if not, the player turns them face down and loses the turn. The player with the most matches wins. - Playing bingo: using student-made bingo cards, in which the students have written vocabulary words. - Internet sites: For the student who chooses to browse the web for activities.

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Many students at this level are using recursive rules to extend the pattern. While this is helpful and easy to use for a small number of cases, it is cumbersome and prone to errors when trying to extend the pattern for larger numbers. Students need to see that it is more helpful to find more generalizable rules to solve problems for all cases. One helpful way to do this is to ask students break down the pattern into simpler parts. "What do you see when you look at the pattern? How can you decompose the shape into parts? How does the tree trunk grow? How could we use algebra to describe how to find the tree trunk for any pattern number?" Breaking down the problem into simpler steps helps students manage the thinking in smaller chunks. But students in this stage need to learn questions to help them progress in their thinking, to develop strategies for finding a generalizable rule. Students need to be encouraged to give more detail about what they see. So in class the teacher might ask, "That's interesting, can you tell me a bit more? Or where do you see the n in the diagram or the (n+1)?" The more detailed their descriptions usually the easier it is to quantify the ideas symbolically. Students should also be more descriptive in thinking about classes of numbers. In elementary school it is good to notice that numbers are odd or even, but by this grade level students should start to classify numbers as consecutive or consecutive odd numbers, multiples of . . ., powers of . . . , triangular numbers, etc. The types of patterns that students think about should be expanded. Students need to have experiences thinking about types of linear patterns; those that are proportional and those that are not proportional. Take the work of student 692. The strategy of doubling from case 5 to case 10 works for proportional patterns, but not for patterns with a constant. Students can benefit by looking at two cases at the same time and comparing which one will work by doubling and which one won't. Drawing graphs of the situations can help to clarify this idea.

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“Logic and Set Theory” is designed to offer teachers and children a chance to explore what may be to them a different area of Finite Mathematics. The unit offers an introduction to the basic concepts and symbols of Logic and Set Theory and provides exercises in these two areas. Problem solving in all areas of mathematics requires the ability to reason and to form valid conclusions. Logic and Set theory will aid students in proving the equivalence of statements as well as in solving problems. Some of the ideas introduced in the unit include types of statements, truth tables, and Venn Diagrams, as well as the language of Logic and Set Theory. (Recommended for 6th through 12th grade Mathematics.)

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In this section of the tutorial, you will learn the diference between statistically independent events and mutually exclusive events, sampling with and without replacement. Two events are statistically independent if the first event do not affect outcome of the second event and vice versa. But, these two events may have something in commons called join events. If the two events do not have something in common, then the two events are called mutually exclusive events. For example, you have a basket with 5 colorful marbles, 2 marbles has Red color, 2 marbles has Green color, and one Blue marble in short [R, R, G, G, B]. Let us do simple experiments called sampling with replacement and sampling without replacement. Take two of these marbles without replacement, meaning that after you see the color of the first marble you take, record it and immediately take the second marble. Do not return those marbles into the basket. Now, what is the probability that the first marble you take is Red and the second marble is Blue? Since you have 5 marbles in the beginning and 2 Red, then the probability that you get Red first marble is 2 out of 5 = 40%. After the first even, the total marbles in the basket become 4. The probability that you get Blue second marble is 1 out of 4 = 25%. Thus, the probability that you get Red marble then Blue marble is 40% times 25% = 10%. Now return all marbles in the basket. This time you will take two of these marbles with replacement, meaning that after you see the color of the first marble and record it, return that marble to the basket before you take the second marble. Notice that the total marbles of the two events are constant, equal to 5, because everytime you take a marble, you return it to the basket before you do the next event. What is the probability that the first marble you take is Red and the second marble is Blue? You have 2 red marbles out of 5 = 40% and you have 1 Blue marble out 5 = 20%. Multiply these two percentages, we get 40% times 20% = 8%. Now the statistical moral story is like this. The two types of sampling has something in common because they are taken from the same sample of 5 marbles in one basket. In sampling without replacement, the first event will affect the second event. We say that the two events are dependent to each other. In the marble experiment, this relation happens because the total sample change (i.e. reduce) after the first event. The probability of taking the next event is depending on the previous event. On the other hand, for sampling with replacement, the first event do not affect the outcome of the second event. We called the two events are statistically independent. In the marble experiment, the total sample never change because you always return the marble that you examine. The probability of taking the next event is not depending on the previous event. Formally, we say that an event A is independent from event B if the conditional probability is the same as the marginal probability, that is What will happen to the intersection (joint probability) when the events are independent? Using multiplicity rule we have Thus, when two events are independent, we get I will explain another example using table percentage by total from Conditional Probability section. Before we know the value in the inner cells and get the summation of rows and summation of columns. Suppose, I preserve the summation of row and summation of column, that is the marginal probability, but empty the inners cells of the table Now we want to input the inner cells such that the income would an independent event from the car type. What will the values of the inner cells? Because the value of the inner cells represents joint probability, and if the events are independent, the join probability is simply a multiplication of the marginal probability, then we have When all the value of inner cells is equal to the multiplication of its sum of rows by its sum of columns, the table has independent joint probability. Mutually exclusive events do not have joint events. Suppose the table above has all zero inner cells (automatically the sums are also zero), then the two variables of income level and car type are mutually exclusive. See also: Bootstrap sampling Preferable reference for this tutorial is Teknomo, Kardi. Data Analysis from Questionnaires. http:\\people.revoledu.com\kardi\ tutorial\Questionnaire\

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How to Identify the Four Conic Sections in Graph Form Each conic section has its own standard form of an equation with x- and y-variables that you can graph on the coordinate plane. You can write the equation of a conic section if you are given key points on the graph. You can alter the shape of each of these graphs in various ways, but the general graph shapes still remain true to the type of curve that they are. This figure illustrates how a plane intersects the cone (the top and bottom half are considered two halves of one cone) to create the conic sections, and the following list explains the figure. Circle: A circle is the set of all points that are a given distance (the radius, r) from a given point (the center). To get a circle from the right cone, the plane slices occurs horizontally through either the top or bottom half of the cone. Parabola: A parabola is a curve in which every point is equidistant from one point (the focus) and a line (the directrix). It looks a lot like the letter U, although it may be upside down or sideways. To form a parabola, the plane slices through parallel to the side of the right cone). Ellipse: An ellipse is the set of all points where the sum of the distances from two points (the foci) is constant. You may be more familiar with another term for ellipse, oval. In order to get an ellipse from the right cone, the plane must slice through the cone at a shallow enough angle where it is slicing through only one-half of the cone. (Note: if the plane slices horizontally through the cone, a circle is created. A circle is considered a special type of ellipse.) Hyperbola: A hyperbola is the set of points where the difference of the distances between two points is constant. The shape of the hyperbola is difficult to describe without a picture, but it looks visually like two parabolas (although they're very different mathematically) mirroring one another with some space between them. To get a hyperbola, the plane must slice through the right cone and a steep enough angle where it is slicing through both halves of the cone. Most of the time, sketching a conic is not enough. Each conic section has its own set of information that you usually have to give to supplement the graph. You have to indicate where the center, vertices, major and minor axes, and foci are located. Often, this information is more important than the graph itself. Besides, knowing all this valuable info helps you sketch the graph more accurately than you could without it.

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This activity is intended to supplement Algebra I, Chapter 9, Lesson 2. Problem 1 - Introduction to Area of a Rectangle Run the AREA program (in PRGM) and select the option for Problem 1 (#1). Enter 6 for . 1. What are the lengths of the sides of the rectangle? 2. What is the area of the rectangle when ? Now, change the width of the side by running the program again and enter a new value for . 3. What is the area of the rectangle when ? When ? 4. Explain how the expression for the area is simplified. Problem 2 - Areas of Small Rectangles The rectangle at the right has dimensions and rate of . Each piece of the rectangle is a different color so that you can focus on its area. 5. What is the area of each small rectangle? 6. What is the total area of the rectangle? Problem 3 - FOIL Method Run the AREA program and select the option for Problem 3. Enter for . 7. How do the areas of the small rectangles in Problem 2 relate to the expression shown on the bottom of the screen? Practice finding the area of a rectangle and then check your answers with the program. 8. What is the expression of the area of a rectangle with dimensions and ? Practice finding the area. Record your answers here. Show each step of your work. Use the program to check your answer. Next, you will be multiplying a trinomial (3 terms) times a binomial (2 terms) to find the area of a rectangle. 2. What method can you use to find the simplified expression for the area? 3. Use the letters and to determine the formula used to find the 6 terms of area shown at the right. 4. What is the area of the rectangle with dimensions and ?

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Heat Drives the System Convection currents of magma (molten rock) circulate through Earth's asthenosphere. The plates are carried on these convection currents. As they move, plate material is continually being created and destroyed along the margins. Where magma squeezes up through cracks between the ocean floor plates, it creates new crust, pushing the plates apart. At convergent boundaries, plates come together. There are two kinds of convergent boundaries: subduction zones and collision margins. Subduction zones occur where two plates come together, and one plate slides under the other. The subducted crust melts into magma in the asthenosphere and is recycled. Subduction can occur when two plates made of oceanic crust come together, or where continental crust and oceanic crust meet. Ocean crust is heavier than continental crust and is forced under it when the two meet. Earthquakes and volcanic activity can occur along subduction zones, as the crust melts underneath the overriding plate. When the movement of the plates pushes continents together, one does not slide under the other. At collision margins, the continental crust buckles and crumples forming mountain ranges. Continued on next page.

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In order to become effective at reading words, students must develop their decoding skills to a seemingly "automatic" level. Readers must be able to recognize words quickly and accurately. In truth, when we read we continue to employ the steps of decoding, but we do so in such a manner that it appears almost effortless, or automatic. Automaticity is crucial to building reading skills because students who are able to automatically decode words are free to think about the meaning of the words they are reading. Thus, skilled word decoding is a building block for reading comprehension. Being able to read words rapidly with high or near perfect accuracy, or automatization, depends upon developing effective decoding skills as well as building a sight word vocabulary. Here are some strategies to help students develop their ability to decode words automatically. - Focus on the automatization of sound-letter associations. Incorporate times throughout the day for reinforcing phonological awareness, working on word attack strategies, etc. - Teach students how to create words by blending chunks of letters together. Begin by showing students how to combine individual letters into chunks (e.g., /f/... /at/ makes /fat/). Have students who are skilled at chunking individual letters practice combining consonant blends with letter chunks (e.g., /fl/... /at/ makes /flat/), and combining consonant blends with vowel combinations (e.g. /fl/... /ee/... /t / makes /fleet/). - Build students’ familiarity with the six kinds of syllables to help automatize segmenting and decoding skills: - (VC = Vowel/Consonant): Closed syllables where a consonant (or consonants) follow a vowel, (e.g., fun, sad). - (VCE = Vowel/Consonant/Silent E): Syllables where a consonant is between a vowel and a silent e (e.g., ice, hope). - (CV = Consonant/Vowel, or V = Vowel): Open syllables where one vowel is at the end (e.g., si in silent, e in event). - (VV = Vowel/Vowel): Dipthong syllables where two vowels combine to make one sound (e.g., boat, sail). - (CLE = Consonant/L/E): Syllables where a consonant plus the letter l is followed by a final e (e.g., simple, bubble). - (VR = Vowel/R): R-Combination syllables where a vowel is combined with the letter r (e.g. art, term). - As students’ word analysis and syllabication skills develop, encourage them to focus upon roots, prefixes, and suffixes of words, e.g., decoding sadness in "one step" by breaking it down into sad (root) + ness (suffix). - Encourage students to perceive chunks of letters within a word when reading, i.e., several letters together at once, rather than one letter at a time, for example, seeing the letters th as a unit, or the syllable ing as a unit, when reading the word thing. - Give students opportunities to build their vocabularies. For example, do pre-reading activities in which students share what they know about a topic, thus activating their vocabulary related to the topic. Immerse students in reading materials to expose them to as much text as possible (Read, Read, Read!). - Provide opportunities for students to develop reading fluency, the ability to read at a smooth and rapid pace. Encourage students to reread books they’ve read previously that are “easy” for them; have students read along with a book-on-tape or read along with you, etc. - Focus on building students’ ability to recognize sight words, words that are taught as whole units because they are quite common, have unusual spellings, or cannot be sounded out, e.g. have, said, the, of, etc. Provide reinforcement by having students practice sight words in isolation (e.g., using flash card drills), and in context (circling sight words in their reading).

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By the end of this lesson I will be able to calculate the rate of change using rise over run of various lines. What if you were given two points that a line passes through like (-1, 0) and (2, 2)? How could you find the slope of that line? After completing this Concept, you'll be able to find the slope of any line. Wheelchair ramps at building entrances must have a slope between and . If the entrance to a new office building is 28 inches off the ground, how long does the wheelchair ramp need to be? We come across many examples of slope in everyday life. For example, a slope is in the pitch of a roof, the grade or incline of a road, or the slant of a ladder leaning on a wall. In math, we use the word slope to define steepness in a particular way. To make it easier to remember, we often word it like this: In the picture above, the slope would be the ratio of the height of the hill to the horizontal length of the hill. In other words, it would be , or 0.75. If the car were driving to the right it would climb the hill - we say this is a positive slope. Any time you see the graph of a line that goes up as you move to the right, the slope is positive . If the car kept driving after it reached the top of the hill, it might go down the other side. If the car is driving to the right and descending , then we would say that the slope is negative . Here’s where it gets tricky: If the car turned around instead and drove back down the left side of the hill, the slope of that side would still be positive. This is because the rise would be -3, but the run would be -4 (think of the axis - if you move from right to left you are moving in the negative direction). That means our slope ratio would be , and the negatives cancel out to leave 0.75, the same slope as before. In other words, the slope of a line is the same no matter which direction you travel along it. Find the Slope of a Line A simple way to find a value for the slope of a line is to draw a right triangle whose hypotenuse runs along the line. Then we just need to measure the distances on the triangle that correspond to the rise (the vertical dimension) and the run (the horizontal dimension). Find the slopes for the three graphs shown. There are already right triangles drawn for each of the lines - in future problems you’ll do this part yourself. Note that it is easiest to make triangles whose vertices are lattice points (i.e. points whose coordinates are all integers). a) The rise shown in this triangle is 4 units; the run is 2 units. The slope is . b) The rise shown in this triangle is 4 units, and the run is also 4 units. The slope is . c) The rise shown in this triangle is 2 units, and the run is 4 units. The slope is . Find the slope of the line that passes through the points (1, 2) and (4, 7). We already know how to graph a line if we’re given two points: we simply plot the points and connect them with a line. Here’s the graph: Since we already have coordinates for the vertices of our right triangle, we can quickly work out that the rise is and the run is (see diagram). So the slope is . If you look again at the calculations for the slope, you’ll notice that the 7 and 2 are the coordinates of the two points and the 4 and 1 are the coordinates. This suggests a pattern we can follow to get a general formula for the slope between two points and : Slope between and In the second equation the letter denotes the slope (this is a mathematical convention you’ll see often) and the Greek letter delta means change . So another way to express slope is change in divided by change in . In the next section, you’ll see that it doesn’t matter which point you choose as point 1 and which you choose as point 2. Find the Slopes of Horizontal and Vertical lines Determine the slopes of the two lines on the graph below. There are 2 lines on the graph: and . Let’s pick 2 points on line —say, and —and use our equation for slope: If you think about it, this makes sense - if doesn’t change as increases then there is no slope, or rather, the slope is zero. You can see that this must be true for all horizontal lines. Horizontal lines ( = constant ) all have a slope of 0. Now let’s consider line . If we pick the points and , our slope equation is . But dividing by zero isn’t allowed! In math we often say that a term which involves division by zero is undefined. (Technically, the answer can also be said to be infinitely large—or infinitely small, depending on the problem.) Vertical lines constant ) all have an infinite (or undefined) slope. Watch this video for help with the Examples above. - Slope is a measure of change in the vertical direction for each step in the horizontal direction. Slope is often represented as “ ”. - Slope can be expressed as , or . - The slope between two points and is equal to . - Horizontal lines (where constant) all have a slope of 0. - Vertical lines (where constant) all have an infinite (or undefined) slope. - The slope (or rate of change ) of a distance-time graph is a velocity. Find the slopes of the lines on the graph below. Look at the lines - they both slant down (or decrease) as we move from left to right. Both these lines have negative slope. The lines don’t pass through very many convenient lattice points, but by looking carefully you can see a few points that look to have integer coordinates. These points have been circled on the graph, and we’ll use them to determine the slope. We’ll also do our calculations twice, to show that we get the same slope whichever way we choose point 1 and point 2. For Line : You can see that whichever way round you pick the points, the answers are the same. Either way, Line has slope -0.364, and Line has slope -1.375. Use the slope formula to find the slope of the line that passes through each pair of points. - (-5, 7) and (0, 0) - (-3, -5) and (3, 11) - (3, -5) and (-2, 9) - (-5, 7) and (-5, 11) - (9, 9) and (-9, -9) - (3, 5) and (-2, 7) - (2.5, 3) and (8, 3.5) For each line in the graphs below, use the points indicated to determine the - For each line in the graphs above, imagine another line with the same slope that passes through the point (1, 1), and name one more point on that line.

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The containers are made up of a number of 'buckets', each of which can contain any number of elements. For example, the following diagram shows an unordered_set with 7 buckets containing (this is just for illustration, containers will typically have more buckets). In order to decide which bucket to place an element in, the container applies the hash function, the element's key (for key is the whole element, but is referred to as the key so that the same terminology can be used for sets and maps). This returns a value of type std::size_t has a much greater range of values then the number of buckets, so that container applies another transformation to that value to choose a bucket to place the element in. Retrieving the elements for a given key is simple. The same process is applied to the key to find the correct bucket. Then the key is compared with the elements in the bucket to find any elements that match (using the equality predicate Pred). If the hash function has worked well the elements will be evenly distributed amongst the buckets so only a small number of elements will need to be examined. You can see in the diagram that D have been placed in the same bucket. When looking for elements in this bucket up to 2 comparisons are made, making the search slower. This is known as a collision. To keep things fast we try to keep collisions to a minimum. Table 25.1. Methods for Accessing Buckets ||The number of buckets.| ||An upper bound on the number of buckets.| number of elements in bucket ||Returns the index of the bucket which would contain k| ||Return begin and end iterators for bucket As more elements are added to an unordered associative container, the number of elements in the buckets will increase causing performance to degrade. To combat this the containers increase the bucket count as elements are inserted. You can also tell the container to change the bucket count (if required) by The standard leaves a lot of freedom to the implementer to decide how the number of buckets are chosen, but it does make some requirements based on the container's 'load factor', the average number of elements per bucket. Containers also have a 'maximum load factor' which they should try to keep the load factor below. You can't control the bucket count directly but there are two ways to influence it: max_load_factor doesn't let you set the maximum load factor yourself, it just lets you give a hint. And even then, the draft standard doesn't actually require the container to pay much attention to this value. The only time the load factor is required to be less than the maximum is following a call to But most implementations will try to keep the number of elements below the max load factor, and set the maximum load factor to be the same as or close to the hint - unless your hint is unreasonably small or large. Table 25.2. Methods for Controlling Bucket Size The average number of elements per bucket. Returns the current maximum load factor. Changes the container's maximum load factor, using Changes the number of buckets so that there at least n buckets, and so that the load factor is less than the maximum load factor. It is not specified how member functions other than affect the bucket count, although is only allowed to invalidate iterators when the insertion causes the load factor to be greater than or equal to the maximum load factor. For most implementations this means that insert will only change the number of buckets when this happens. While iterators can be invalidated by calls to rehash, pointers and references to the container's elements are never invalidated. In a similar manner to using vectors, it can be a good idea to call inserting a large number of elements. This will get the expensive rehashing out of the way and let you store iterators, safe in the knowledge that they won't be invalidated. If you are inserting elements into container you could first call: x.rehash((x.size() + n) / x.max_load_factor() + 1);

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Here are practice problems and solutions for the areas that are covered on the algebra section of the Compass mathematics test. Basic Algebraic Calculations with Polynomials Remember that a polynomial is a mathematical equation that contains more than one variable, such as x or y. Solution: This type of algebraic expression is known as a polynomial. To solve this sort of problem, you need the "FOIL" method. "FOIL" stands for First - Outside - Inside - Last. So, you have to multiply from the terms from each of the two pairs of parentheses in this order: (x + 2y)2 = (x + 2y)(x + 2y) FIRST − Multiply the first term from the first pair of parentheses with the first term from the second pair of parentheses. x × x = x2 OUTSIDE − Multiply the terms at the outer part of each pair of parentheses. x × 2y = 2xy INSIDE − Multiply the terms at the inside, in other words, from the right on the first pair of parentheses and from the left on the second pair of parentheses. 2y × x = 2xy LAST − Multiply the second terms from each pair of parentheses. 2y × 2y = 4y2 Then we add all of the above parts together for the final answer. x2 + 2xy + 2xy + 4y2 = x2 + 4xy + 4y2 Factoring Polynomials and Other Algebraic Expressions "Factoring" means that you need to break down the equations into smaller parts. Problem: Factor the following algebraic expression. x2 + x − 30 Solution: For any problem like this, the answer will be in the following format: (x + ?)(x − ?) We know that we need to have a plus sign in one pair of parentheses and a minus sign in the other pair of parentheses because 30 is negative. We can get a negative number in problems like this only if we multiply a negative and a positive. We also know that the factors of 30 need to be one number different than each other because the middle term is x, in other words 1x. The only factors of 30 that meet this criterion are 5 and 6. Therefore the answer is (x + 6)(x − 5) Substituting Values into Algebraic Equations You will see an equation with x and y, and you will have to replace x and y with the values stipulated in the problem. Problem: What is the value of the expression 2x2 − xy + y2 when x = 4 and y = −1 ? Solution: To solve this problem, put in the values for x and y and multiply. Remember to be careful when multiplying negative numbers. 2x2 − xy + y2 = (2 × 42) − (4 × −1) + (−12) = (2 × 4 × 4) − (−4) + 1 = (2 × 16) + 4 + 1 = 32 + 4 + 1 = Algebraic Equations for Practical Problems These types of problems are expressed in a narrative format. They present a real-life situation. For instance, you may be asked to create and solve an equation that can be used to determine the discount given on a sale. Problem: Sarah bought a pair of jeans on sale for $35. The original price of the jeans was $50. What was the percentage of the discount on the sale? Solution: To determine the value of a discount, you have to calculate how much the item was marked down: $50 − $35 = $15 Then divide the markdown by the original price: 15 ÷ 50 = 0.30 Finally, convert the decimal to a percentage: 0.30 = 30% This aspect of geometry is included on the algebra part of the test because you need to use algebraic concepts in order to solve these types of geometry problems. Coordinate geometry problems normally consist of linear equations with one or two variables. You may need to calculate geometric concepts like slope, midpoints, distance, or x and y intercepts. Problem: State the x and y intercepts that fall on the straight line represented by the following equation. y = x + 3 Solution: First you should substitute 0 for x. y = x + 3 y = 0 + 3 y = 3 Therefore, the y intercept is (0, 3). Then substitute 0 for y. y = x + 3 0 = x + 3 0 − 3 = x + 3 − 3 −3 = x So, the x intercept is (−3, 0). Rational Expressions with Exponents and Radicals These types of algebra questions consist of equations that have exponents or square roots or both. Problem: What is the value of b? Solution: Your first step is to square each side of the equation. Then get the integers on to just one side of the equation. 5b = 20 Then isolate the variable b order to solve the problem. 5b ÷ 5 = 20 ÷ 5 b = 4 Now have a look at our other practice test material:

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- slide 1 of 5 Flat versus 3D The biggest hurdle in figuring out how to teach children about three dimensional shapes is getting them to think beyond the flat surface of a two-dimensional figure. From before children are even in school they are taught the shapes of circles, squares, triangles and rectangles, but much less time is spent on spheres, cones, pyramids and cubes. In fact, some of the tools used to teach the basic 2D shapes are in fact three dimensional objects. Toddler toy shape sorters, for instance, use three dimensional shapes such as cylinders in an effort to teach basic two dimensional shapes like circles. This confusion continues through early elementary education for many students as the terms and definitions of 3D shapes are nearly foreign to them. - slide 2 of 5 3D Shape Grab Bag A fun way to introduce the various three dimensional shapes to a class is through the use of mystery bags. In preparation for this lesson, teachers should find examples of different three dimensional shapes and place them inside paper bags. Ideally, one bag per student helps to reinforce this lesson with the entire class, but a sample selection can work well, too. Here are some ordinary household items that can be used to demonstrate three dimensional shapes. - a wooden letter block for a cube - an individual cereal box for a rectangle - a rubber ball for a sphere - a soup can for a cylinder As each child opens their bag they should identify the item by its three dimensional shape, ie. a soup can would be identified as a cylinder. - slide 3 of 5 Most kids love activities which include food, especially if they get to eat it. For this activity, teachers will need to be very open-minded and creative in how to teach children about three dimensional shapes as they will need to shop for foods that match this lesson. Here are some possible suggestions for 3D Food: - Pretzel Combos, marshmallows, or cheese sticks for cylinders - Donut holes or ball-shaped yogurt snacks for spheres - Cheese cubes for cubes - Toblerone candy bars as a possible three dimensional triangular shape - slide 4 of 5 Getting Active with 3D Shapes Another approach to teaching students three-dimensional shapes is to use large items that demonstrate shapes such as spheres and cubes. Large paper building bricks are available at many teacher supply stores and serve as a great demonstration for cubes. Students can stack and build these to construct various spaces throughout the classroom. Giving students time to work with the bricks will allow them to feel and consider the nature of three dimensional shapes. Requiring that they call the bricks "cubes" rather than bricks will help reinforce the new terminology of the three dimensional lesson. As for spheres, balls of different sizes can be used in a variety of outdoor games. Students can be given time to play with a large beach ball or small bouncy balls while requiring that they call the balls "spheres" to help reinforce the idea that these familiar objects are also three-dimensional shapes. - slide 5 of 5 The Common Point to these Tips The one common theme among these different suggestions is object lessons. Students should be given an opportunity to literally get their hands around familiar three dimensional forms to best see and understand the difference between 2D and 3D shapes.

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3-D Earth Geometry An interesting topic in 3-dimensional geometry is Earth geometry. The Earth is very close to a sphere (ball) shape, with an average radius of `6371\ "km"`. (It's actually a bit flat at the poles, but only by a small amount). Earth geometry is a special case of spherical geometry. When we measure distances that a boat or aircraft travels between any 2 places on the Earth, we do not use straight line distances, since we need to go around the curve of the Earth from one place to another. (Think about the direct or straight-line distance between London and Sydney, through the Earth. That's going to be a lot less than the distance a plane flies around the surface of the Earth.) Let's start with an example. What distance does a plane fly between Beijing, China and Perth, Western Australia? To figure this out, we need to understand latitude and longitude first. Latitude and Longitude First, we represent the Earth by a sphere: We slice the Earth through the equator and remove the top. We show the Earth's axis which (by convention) points to North at the top. Parallels of Latitude We want to be able to indicate how far North or South of the equator we are for any point on the Earth's surface. For example, we wish to connect all the points that are 30° N of the equator. We do that by drawing a line from the centre of the Earth to the surface of the Earth, 30° up from the horizontal. We then draw a circle around the Earth parallel to the equator through the point where the 30° line meets the surface of the Earth. We can do the same thing for below the equator, in a southerly direction. The angle from the horizontal through the equator determines the name given to each parallel of latitude. Five parallels of latitude are shown in the diagram; 30° N, 60° N, 0° N (the equator), 30° S and 60° S. Each 1° of latitude on the Earth represents 60 nautical miles, or around 110.9 km. Of course, 90° N represents the North pole and 90° S is the south pole. Parallels of latitude give an indication of where a place (or a boat or a plane) are positioned in a northerly or southerly direction from 0° N (the equator). Lines of Longitude What about the East and West directions for a point on the Earth? We choose some point on the equator and draw a line from the centre of the Earth (point C) to the chosen point on the equator. We then draw a circle around the whole Earth so that it goes through the point on the equator and the North and South poles. (Historically, the position for 0° was chosen so that the circle we have drawn goes through Greenwich in England). The line we drew above is called a line of longitude. At the 'front' of our diagram, the line is called 0° E and at the back, the line is called 180° E, for reasons we'll see in a moment. [The line of longitude that goes through 0° has a special name: the prime meridian.] Lines of longitude have the same radius as the radius of the Earth. They are examples of great circles. (A great circle has the same radius and same centre as the earth itself). Let's now define some more lines of longitude. We move around the Earth in an Easterly direction by 90° and draw a great circle through the poles as before. The front line of longitude is labeled 90° E and the one opposite to it at the back of our diagram is labeled 90° W. We could then draw the lines of longitude for every angle between 0° E and 180° E (covering Europe through India, Asia and the Pacific Ocean) and then through 0° W and 180° W (through the Atlantic Ocean, the Americas and the Eastern Pacific Ocean). Note: 0° E = 0° W = 0° and 180° E = 180° W = 180°. Lines of longitude give an indication of where a place (or a boat or a plane) are positioned in an easterly or westerly direction from 0° E. For lines of longitude, we cannot say that 1° represents any particular distance, because the physical distance changes between each line of longitude as we move from the equator to the poles. At the equator, 1° represents around 60 nautical miles or 111 km. but at the poles, it represents 0 km. Finer Divisions of Longitude and Latitude Since 1° of latitude represents 60 nautical miles on the Earth's surface, we need finer divisions of 1° to accurately determine places on the Earth's surface. As we learned earlier in the Angles section, we can divide 1° into smaller divisions called minutes (where 1° = 60 minutes) or seconds (where 60 seconds = 1 minute). For example, London is 51°32' North of the equator. This means 51 degrees plus 32/60 of a degree North. Historically, it was the Babylonians who divided units of time and angles into 60 equal parts. Examples of Latitudes and Longitudes for Cities Any place on the Earth can be uniquely described by its latitude and longitude. Some examples (moving from West to East): Los Angeles: 34° 3' N, 118° 14' W New York: 40° 45' N, 73° 59' W London: 51°32' N, 0° 5' W. (London is just slightly west of Greenwich.) New Delhi: 28°35' N, 77°12' E Singapore: 1° 21' N, 103° 49' E (Singapore is almost on the equator). Sydney: 33° 52' S, 151° 12' E What is the Distance Between 2 Places on the Earth? We need one more key bit of information to solve the problem posed before (distance from Beijing to Perth). What is the distance around the curve of the Earth along a great circle between any 2 points? Let's call the latitude of the first place φ1 and the longitude of the first place as λ1. Similarly, the latitude of the second place is φ2 and the longitude of the second place is λ2. We need to know the central angle (the angle from the centre of the Earth to the 2 places of interest). The formula for this is (angles in radians): Central angle = `2\ arcsin sqrt( sin^2 ((varphi_2-varphi_1))/2 +cos\ varphi_1\ cos\ varphi_2\ sin^2 ((lambda_2-lambda_1))/2 )` In the case of Beijing to Perth, the central angle looks like the following, with O at the centre of the earth: For Beijing, the latitude is φ1 = 39° 54' N and the longitude is λ1 = 116° 24' E. For Perth, the latitude is φ2 = 31° 57' S and the longitude is λ2 = 115° 52' E. We need to express these angles in radians (if you are rusty, see Radians): Beijing: φ1 = 39° 54' N = 0.696386; λ1 = 116° 24' E = 2.031563. Perth: φ2 = 31° 57' S = −0.557633; λ2 = 115° 52' E = 2.022255. [Note that the latitude for Perth is negative, since it is South of the equator.] Applying the formula gives us: Central angle = `2\ arcsin sqrt( sin^2 ((-1.254)/2) +cos\ (0.696)\ cos\ (-0.557)\ sin^2 ((-0.009)/2) )` (radians, of course, and full calculator accuracy was used throughout, but not shown) Now, to find the distance travelled, we need to use our formula for arc length that we learned before (see Arc Length). If r is the radius of the great circle and θ is the angle subtended at the centre (in radians), the arc length s is given by: s = rθ Now, the average radius of the Earth is `6371\ "km"`, and the angle we just found is `1.254049` radians, so the flying distance from Beijing to Perth is given by: s = 6371 × 1.254049 = 7989 km. Find the distance that an aircraft must fly from London to Los Angeles if it flies directly. Didn't find what you are looking for on this page? Try search: Online Algebra Solver This algebra solver can solve a wide range of math problems. (Please be patient while it loads.) Go to: Online algebra solver Ready for a break? Play a math game. (Well, not really a math game, but each game was made using math...) The IntMath Newsletter Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents! Math Lessons on DVD Easy to understand math lessons on DVD. See samples before you commit. More info: Math videos

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IntroductionYou are at: Basic Concepts - Measurements - IntroductionMeasuring VoltageMeasuring Current Electrical measurements often come down to either measuring current or measuring voltage. Even if you are measuring frequency, you will be measuring the frequency of a current signal or a voltage signal and you will need to know how to measure either voltage or current. In this short lesson, we will examine those two measurements - starting with measuring voltage. However, first we should note a few common characteristics of the meters you use for those measurements. Many times you will use a digital multimeter - a DMM - to measure either voltage or current. Actually, a DMM will also usually measure frequency (of a voltage signal) and resistance. You should note the following about typical DMMs. Voltage is one of the most common quantities measured. That's because many other variables - like temperature, for example - are measured by generating a voltage with a sensor. So, even if you want to measure temperature you might end up having to measure a voltage and convert that reading into the temperature reading you wanted. Voltage is measured with a voltmeter. However, digital multimeters (DMMs) - which can function as voltmeters - often have considerably more capability and can measure current, resistance and frequency. And, there are other instruments - like oscilloscopes - that measure voltage and should be thought of as voltmeters. No matter what the instrument is, if it measures voltage you have to treat the instrument as a voltmeter. When you measure voltage you have to remember that voltage is an across variable. When you measure voltage you have to connect the voltmeter to the two points in a circuit where you want to measure voltage. Here is a circuit with a voltmeter connected to measure the voltage across element #4. Note the following about this measurement. Current is measured with an ammeter. While voltage is a more common measurement, it is often necessary to measure current. When measuring current, it is important to remember that current is a flow variable. Current flows through electrical elements, and if you want to measure current you have to get it to flow through the ammeter. Here's the same circuit we used in the example above. Consider what we would have to do to measure the current flowing through element #4. If we want to measure the current through element #4, we have to get that current to flow through the ammeter. Here's a way to insert an ammeter into the circuit to measure that current. However, this doesn't give the whole picture. Remember that polarity is important. In the circuit the polarity for the voltage across element #4 is defined, but the current polarity is not defined. In the diagram below, we have defined the direction of that current, and given it an algebraic name, Im. As with the voltmeter, you need to pay attention to the polarity, and you also want to remember this.

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Draw appropriate inferences and conclusions from text. SPI 0301.5.1 Links verified on 10/20/2011 - Create Test - Create printable tests and worksheets from Grade 3 Making Inferences and Drawing Conclusions questions. - Drawing conclusions - worksheet - Drawing Conclusions - test tutor quiz - Drawing Conclusions - read the story - choose the correct word to complete the sentence - Drawing Conclusions - online quiz - Follow the Clues - a graphic organizer to help your students make predictions about a story (K-2 and 3-5 activities included) - How did you know that? - click on the button in front of the correct answer - Inference Battleship - interactive game with questions - Inference Worksheet: You Make The Call - Students make an inference on what they think will happen next in different situations. - Making Inferences - Read about Josh and his dad. Write about what you think Josh and his dad will do. - Making Inferences Using a Concept Map - [3 multiple-choice questions] use details to make accurate inferences when reading textbooks - Predict and Infer Graphic Organizer - Students write the event of a story, what the think will happen, clues from the story that help decide, and what really happened. - Predict and Infer Plant Activity Worksheet - [Cross Curricular activity: Science/Language Arts] Students must predict whether seeds will grow a little, grow a lot, or not grow at all in different conditions. - Problem/Solution Chart - Fill out this chart as a whole class activity brainstorming session to learn to recognize problems and solutions in stories. [uses cause and effect - can be adapted] - Teaching about Conflict in Literature - uses graphic organizer to plot out stories. - Story Board - a graphic organizer to help your students make predictions about a story (K-2 and 3-5 activities included) - What can you Infer? - interactive quiz site for teachers | PowerPoint show | Acrobat document | Word document | whiteboard resource | sound | video format | interactive lesson | a quiz | lesson plan | to print

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Submitted by: Jason T. Bedell In this environment lesson plan, which is adaptable for grades 6-12, students use BrainPOP resources to develop an understanding of how people impact the natural environment of different regions, as well as how the cultural make-up of a region affects how the people interact with the natural environment. Students will craft an articulate message to make the public aware of the consequences of human interaction with the environment. - Develop an understanding of how people impact the natural environment of different regions. - Craft an articulate message to make the public aware of the consequences of human-environment interaction. - Develop an understanding of how the cultural make-up of a region affects how the people interact with the natural environment. - Student computers, at least 1 per pair - Projector to show Internet resources Preparation:Make sure students understand basic online research skills. Preview the Lesson Procedure that is in italics below, and copy and paste it into a Word document, blog post, wiki, or other source where you can modify it for class needs and make it available to students. Also make sure the following links are available to students to aid them in completing the assignment: Placemarks (Step 3) Document Step 3 Video Step 4 Video Example of a finished product - To help students build background knowledge about how people and cultures interact with the environment, watch the BrainPOP movie Geography Themes. - Have a discussion with the students about how humans can have an effect on the environment and what some of the consequences can be. Think aloud to give the students a frame of reference that is relevant to them. For example, "To get to work every day, I have to cross the Hudson River. That could be really hard if people had not built a bridge. However, that hurts the natural environment by encroaching on the natural habitat." Have the students think of several local examples, first as a class, then individually, to ensure that everyone understands the idea. - Assign students into pair groups or allow students to choose their own. Give students a digital copy of the directions with all the important links available. - Before they get started, it is helpful to model how to find and use Google Earth on the computers. It is also helpful to walk the students through the finished product. There is an example finished product in the Preparation section (above). The teacher will have to be very supportive while the students are working. - Provide your modified version of the following directions to students: You will be creating video documentaries on human impact in Google Earth. You have to pick a country that we have studied this year and find at least 3 places where humans have affected or changed the geography. An example could be dams or irrigation to reroute water away from natural rivers. Then, you will create placemarks in Google Earth and record a tour. Your video will be shown to the class and posted online. Step 1: Choose a Country Watch the BrainPOP movie Map Skills as a refresher on how maps work. This will make Google Earth easier to navigate and understand the different types of layers used. You may choose any 1 country that we have studied this year, or other countries/regions possibly approved in discussion with the teacher. Step 2: Find Your Places Google Earth is a realistic 3D model of the earth. You need to find 3 landmarks in the country. For each landmark, you have to write 1 paragraph (5 sentences or more) explaining why it is important, how humans modified the natural geography, and how it impacts life in the region. The landmarks need to meet the following requirements: 1) All of the landmarks have been affected or modified by humans. 2) All of the landmarks have a significant impact on the lives of people in the local area or the larger country. 3) Each landmark should be accompanied by a paragraph explaining its significance. 4) Each landmark should have a picture or video to help people understand its significance. 5) Each landmark should have a website link where people can find more information. Step 3: Create and Organize Your Tour Create your 3 placemarks and organize them in the order you will view them on your tour. See the Step 3 Document and the Step 3 Video in the Preparation [above] for resources. Step 4: Record Your Narrated Tour Record audio narration as you go through your tour. See the Step 4 Video in the Preparation [above] for resources. Step 5: Save Your Tour The video in the previous step shows you how to save the file. Right-click on your tour and click Save Place. Save it as Period-Lastname-Country.kmz. For example, if I’m in Mr. Ramsey’s 3rd period, I would save it as 3-Bedell-Peru.kmz. The naming convention makes it much easier to organize the files.

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"You are an engineer who wants to build different kinds of bridges. The bridges will be made of colored rods. The first bridge you are to build is a 1-span bridge made with one yellow rod and two red rods." (Build the bridge illustrated below, with the students copying.) "The yellow rod is called a span, and the red rods are called supports . Since the yellow rod is 5 cm long, the length of the bridge is 5 cm." "The second bridge you are to build is a 2-span bridge made with two yellow rods and four red rods (as shown below). Note that this bridge is 10 cm long." "As you build bridges in the following activities, think of a way to keep track of the number of rods of different colors you use. Your goal is to find out how many rods of each color you would need to build a bridge of any size." Student assessment activity: Distribute the activity sheet and read through question 1 to be sure that the children understand the basic problem. Note: the bridges have been scaled to fit the 7" × 10" page of this volume. The teacher may choose to redraw the bridges to scale when they are reproduced on standard size paper

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Scatter plots are similar to line graphs in that they use horizontal and vertical axes to plot data points. However, they have a very specific purpose. Scatter plots show how much one variable is affected by another. The relationship between two variables is called their correlation . Scatter plots usually consist of a large body of data. The closer the data points come when plotted to making a straight line, the higher the correlation between the two variables, or the stronger the relationship. If the data points make a straight line going from the origin out to high x- and y-values, then the variables are said to have a positive correlation . If the line goes from a high-value on the y-axis down to a high-value on the x-axis, the variables have a negative correlation . A perfect positive correlation is given the value of 1. A perfect negative correlation is given the value of -1. If there is absolutely no correlation present the value given is 0. The closer the number is to 1 or -1, the stronger the correlation, or the stronger the relationship between the variables. The closer the number is to 0, the weaker the correlation. So something that seems to kind of correlate in a positive direction might have a value of 0.67, whereas something with an extremely weak negative correlation might have the value -.21. An example of a situation where you might find a perfect positive correlation, as we have in the graph on the left above, would be when you compare the total amount of money spent on tickets at the movie theater with the number of people who go. This means that every time that "x" number of people go, "y" amount of money is spent on tickets without variation. An example of a situation where you might find a perfect negative correlation, as in the graph on the right above, would be if you were comparing the amount of time it takes to reach a destination with the distance of a car (traveling at constant speed) from that destination. On the other hand, a situation where you might find a strong but not perfect positive correlation would be if you examined the number of hours students spent studying for an exam versus the grade received. This won't be a perfect correlation because two people could spend the same amount of time studying and get different grades. But in general the rule will hold true that as the amount of time studying increases so does the grade received. Let's take a look at some examples. The graphs that were shown above each had a perfect correlation, so their values were 1 and -1. The graphs below obviously do not have perfect correlations. Which graph would have a correlation of 0? What about 0.7? -0.7? 0.3? -0.3? Click on Answers when you think that you have them all matched up. Back to the First Page

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Arizona implemented new standards for kindergarteners last year. Here is what students are required to learn now: --Read and write numbers to 20. --Count to 100 by ones and 10s. --Create all combinations for the numbers 0 to 10 - such as 5 = 2 + 3 and 4 + 1 -- using objects or drawings --Solve addition and subtraction word problems using objects or drawings. --Show numbers from 11 to 19 using a 10 and additional ones. --Compare two objects to see which has "more than" or "less than" of a measurable attribute like height or weight. --Describe objects in the world using names of shapes. --Identify and name rectangles, squares, circles, triangles, hexagons, cubes, cones, cylinders and spheres. --Draw, compare and describe two- and three-dimensional shapes. --Combine simple shapes to make larger shapes. --Understand that words are made of letters and letters represent sounds. --Follow words from left to right, top to bottom and page by page. --Recognize and name upper- and lowercase letters. --Read simple words with short or long vowels. --Read high-frequency words by sight. --Identify initial, final and middle sounds in spoken words. --Recognize that new words are created when letter sounds are added or removed. --Read and understand kindergarten texts. --Identify characters, setting and events in a story. --Retell and answer questions about details in a story or nonfiction text. --Ask and answer questions about unknown words in a story or in nonfiction. --Name and define the role of an author and illustrator. --Compare and contrast characters and events from stories or nonfiction. --Use standard English grammar in speaking in writing. --Speak and write in complete sentences. --Spell simple words phonetically. --Understand use of prepositions -- in, on and under. --Print upper- and lowercase letters. --Write sentences that start with a capital letter and end with a punctuation mark. --Participate in "prewriting" activities - generating and organizing ideas. --Use a combination of drawing and writing to compose: A personal narrative, an informative article, an opinion piece. --With help from teacher, revise a first draft for clarity, proofread and edit the draft, create and present a final writing project. Sources: Arizona Department of Education, Mesa Public Schools, National PTA View subscription options

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In the 1950s , scientists began to experiment with nuclear rocket propulsion systems as an alternative to chemical rockets. If interplanetary travel were to ever become practical, a more efficient means would have to be developed. Starting in 1955 , scientists at Lawrence Livermore National Laboratory experimented with designs for a solid core nuclear thermal rocket , and by the time the experiment was finished, they had managed to produce a rocket with a higher specific impulse than today's most advanced chemical rockets Unfortunately, these experiments also revealed many limitations to the solid core design, and the technology available at the time made experiments with gas core nuclear rockets unfeasable, so the project was shelved. Recent advancement in the understanding of the behavior of plasma as well as the advent of computer modeling has rekindled interest in gas core nuclear propulsion systems, which promise more than a tenfold increase in specific impulse over chemical propulsion systems. A trip to Mars could take as little as three months, could carry a much larger payload, would minimize the negative effects of weightlessness and exposure to radiation on the crew, and cost far less. The concept behind nuclear thermal propulsion is simple. Fission in the reactor core produces energy. That energy heats the propellant. The propellent proceeds to exit the vehicle, and Newton's Second Law of Motion kicks in. The design, however, is tricky. Inside the core, a vortex is created, allowing the propellant to pass through while isolating the hot uranium plasma. Liquid hydrogen is the most likely candidate for the propellant, since it has a low molecular mass, and does not become radioactive. The intricacies of creating the vortex, injecting the uranium and increasing the efficiency of the system are still being worked out.

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This activity is intended to supplement Algebra I, Chapter 12, Lesson 6. Problem 1 – Introduction Press and enter the two functions Also, for the second expression, move the cursor to the left of and press ENTER until a circle appears. This will place a large circle in front of the graph as it is graphed on the handheld. To view the graphs, press ZOOM and select ZStandard. 1. How do the graphs of the two given equations compare? 2. What do the graphic results tell us about the two functions? Functions can often be expressed in several different ways. The second representation splits the initial rational function into fractional parts and is referred to as the sum of partial fractions. 3. How are the denominators in , the partial fractions, related to the denominator of the original expression ? So, to begin understanding how these partial fractions are developed, begin by writing two fractions using the factors of the denominator of . Let and represent the numerators yet to be determined. 4. What is the LCD (least common denominator) for ? 5. What is the result of multiplying both sides of by the LCD? 6. Substitute in a convenient number for and solve for . What value did you obtain for ? 7. Similarly substitute in a convenient number for and solve for . What value did you obtain for ? 8. Now substitute the values you found for both and into the equation shown in Question 4 to show the equivalent rational function and sum of partial fractions. 9. How do your results for Question 8 support your answer to the Question 2 regarding what the graphs of the functions and tell us about the two functions? Problem 2 – Practice 10. Express the rational function, , as a sum of partial fractions. 11. Graph the initial function and your sum of partial fractions using the graphing calculator as outlined in Problem 1. How does this verify your results? Explain your reasoning. Problem 3 – The Next Level 12. Express the rational function, , as a sum of partial fractions. 13. Graph the initial function and your sum of partial fractions using the graphing calculator. How does this verify your results? Explain you reasoning. Additional Practice Problems Represent each of the following rational functions as a sum of partial fractions. Verify your results graphically.

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Suppose that we have an election with three candidates: A, B, and C. On a standard ballot (like those used in most elections around the world) the three candidates would be listed and each voter would have to choose one. While the voter in this situation has only three choices, there are really six possible preferences that the voter can have. For example, the preference "A>B>C" means that the voter prefers A to B and B to C. In this case the voter would select "A" on the ballot. However, this voter would be unable to distinguish herself from a voter whose preference is "A>C>B." Why does it matter that voters in these situations cannot express their full preferences? It is especially important in elections where no candidate receives a majority of the votes. For example, in the 1998 Minnesota gubernatorial election, Reform Party candidate Jesse Ventura received 37% of the votes, with the candidates from the other two parties getting 34% and 28%. Even though no candidate received a majority, Ventura received a plurality -- more votes than any other candidate -- and was declared the winner. Should Ventura have won the election? It can be argued that most of the people who did not vote for Ventura would have had him as their third choice. If that were really true, then as many as 63% of the voters had Ventura as their last-place choice. Perhaps if voters in this election had been able to express their full preference, the outcome would have been different. When we want to describe how many voters have each of the six possible preference orders, we use a diagram developed by Donald Saari called the representation triangle. Each vertex of the triangle is labeled by a candidate, and the six regions of the triangle each represent one of the six preference orders. For example, the region labeled "A>B>C" is the region of points that are closest to A, second-closest to B, and farthest from C. A good way to remember this is that "closer is better": the regions closest to A represent the voters that have A as their top choice, and the regions second-closest to A represent the voters whose second choice is A. Let's illustrate how the triangle works using an example from . Suppose that the children in a class are trying to decide what kind of drinks they should have during lunch: soda, milk, or juice. The teacher asks the students to rank their preferences in order, and the results are as follows: |6||Milk > Soda > Juice| |5||Soda > Juice > Milk| |4||Juice > Soda > Milk| This voter profile would be represented by the diagram below. We put a zero in a region whenever the corresponding preference is held by zero voters. In this example, only 3 of the 6 possible preference orders were actually expressed by the students. The most common method for determining the winner of an election is the one we have already discussed: the plurality method. Voters simply cast a vote for their top preference. The candidate, if any, who receives more votes than any other is the winner. In the diagram below, the plurality totals can be determined by adding up the numbers in the regions corresponding to each candidate. The red regions correspond to A, the blue regions to B, and the green regions to C. In the interactive mathlet below, you can explore the plurality method by adding and subtracting voters from each of the six regions. In all of the interactive diagrams, left-clicking adds voters and right-clicking subtracts voters. To see one of the disadvantages of the plurality method, consider the "milk, soda, juice" example above. Milk is the plurality winner because it receives 6 votes, more than any other candidate. But while milk is top-ranked by more children than any other candidate, it is bottom-ranked by all other children. If 9 out of the 15 voters (a clear majority) ranked milk last, should it really be the winner? Perhaps we need a new way to determine the winner in situations like this.

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According to the revised Virginia Standards of Learning for 2009, students in Grade One will explore basic geometry in the form of shapes. They will focus on identifying and tracing, describing, and sorting plane geometric figures (triangle, square, rectangle, and circle) according the number of sides, vertices, and right angles; and will also construct, model, and describe objects in the environment as geometric shapes. Below is a list of five exceptional books to read with students while studying this topic. - Emberley, E. (1961). The Wing on a Flea. Canada: Little, Brown & Co. In poetic form Ed Emberley writes about triangles, rectangles, and circles in a descriptive way that helps children think about shapes in the environment. Teachers can utilize this book to provoke children to describe shapes in their own words, create shapes poems, and identity shapes around the school and classroom. - Grover, M. (1996). Circles and Squares Everywhere! Singapore: Harcourt Brace & Co. This book is a good resource to use when students are first beginning to compare and describe different shapes. Teachers can explain that a circle is different from a square in that a square has sides and is a polygon, while a circle has no sides and is a plane geometric shape. - Hoban, T. (1974). Circles, Triangle and Squares. New York: Macmillan Publishing Co., inc. This black and white photography book is filled with shapes that students have to search for. Since this is a picture book, the teacher may use it to ask questions about different shapes, have students identify shapes using vocabulary, and describe objects in the environment as geometric shapes. Murphy, S. J. (1998) Circus Shapes. Illus. Edward Miller. USA: Harper Collins Publishers. This book is an excellent resource to have children examine, identify, and describe plan geometric figures. Four shapes are featured in the circus-circles, triangles, rectangles, and squares- and all are described according to their attributes. - Thong, R. (2000) Round is a Mooncake. Illus. Grace Lin. San Fransisco: Chronicle Books. This book asks children thoughtful questions at the end of each description of a shape, and promotes cultural awareness as it highlights Chinese culture. Below is a list of helpful web sites for kids to explore while learning this topic. - From the web site Principles and Standards for School Mathematics, created by the National Council of Teachers of Mathematics, students can use an interactive geoboard to create rectangles, squares, and triangles. They can compose shapes in different sizes and positions to see that while the new shape may look different, it remains the same shape. - This interactive web site from Primary Resources introduces children to different characteristics of each shape and asks them to identify a shape’s sides, angles, and vertices. Since this site is from the U.K., it is a good idea to explain to children that in the U.K. they call a rectangle an oblong. - This simple shape sorter from Primary Resources asks children to classify shapes into different groups: right angles or no right angles, four sides or more or less than four sides, and quadrilateral or triangles. - The web site Illuminations allows children to explore numerous shapes, form patterns and objects with different shapes, and cut a shape into several different shapes. - This site from Primary Games is a simple memory game that asks children to match different shapes. It is a basic tool that will help children identify shapes and explain attributes of different shapes. Below is a list of helpful additional resources to support instruction for this topic. - Beacon Learning Center offers an insightful student web lesson for teachers to do with their students. This story about Mr. Mumble, an eager little mouse, explains to children the angles, sides, surfaces, and vertices of two-dimensional polygons and asks them to describe these shapes in their own words. - This is a PDF printable worksheet from About.com: Math that describes different shapes. Students have to answer questions based on their understanding of attributes of shapes. - This is a resource for parents from the Elementary Mathematics Office, Howard County Public School System (2008,2009). It lists objectives, vocabulary, and activities for parents to do with their First Grade students during geometry lessons. - Geometry Ideas by elementary school teacher, Linda Longpre, gives teachers numerous ideas for student activities for Grade One geometry. She gives whole class, partner and individual hands-on activities and also lists several books for this topic.

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