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This unit makes use of manipulatives, pictures and number lines to help your students with common core addition skills such as: counting on, addition doubles, solving for missing addends and word problems. The variety of resources in this unit is meant to give your students the concrete support they need to build addition concepts before working with addition in a purely abstract way. Here’s what you’ll find in this product: Storyboards with Word Problems: Have you ever used storyboards with your students? They are great! Story boards provide a way for students to act out word problems so that they see what is actually happening in the word problem. In this section you will find story problem cards and answer sheets which can be used along with the storyboards (see preview). Students read the problem, and then act it out using the storyboard. Then students fill out the answer sheet. The word problems include the adding to, putting together and adding with unknowns in every position types noted in the common core. Some make use of three addends. Storyboards work whole group, but they are excellent for small groups. They can also be used as a modification for students who aren’t quite ready to be successful with word problems in an abstract sense. ‘Counting On’ Materials: Part of the common core for addition is using the strategy of ‘counting on’ to increase addition fluency. The provided number strips along with counters can be used as kinesthetic manipulatives for this skill. The three front and back ‘counting on’ practice sheets include number lines to provide a pictorial representation of counting on. Learning addition ‘doubles’ is another way to increase addition fluency. In this section you find two pages of pictorial representations of doubles that can be glued into a math journal or used as introductory practice. The five (front and back) doubles practice sheets included make use of pictures and number lines. The last practice sheets include no pictorial representations, and can help students gain fluency through repeated practice. ‘Missing Addend’ Materials: The storyboard word problems include ‘missing addend’ problems, but this section offers additional practice using number lines. The first practice sheet asks students to identify addends and sums to get them used to the vocabulary. The others have students find the missing addend using a number line. I hope you and your students find this product useful!

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Addition Practice 2 This resource also includes: - Answer Key - Join to access all included materials In this addition practice worksheet, students use their math skills to solve 22 problems that require them to add 1 digit numbers with 3 addends. 3 Views 3 Downloads Solve Addition Problems: Using Complements of 10 In a base ten number system, knowing the complements of ten is a huge help when learning addition with larger numbers. The third video is this series models how these special pairs of numbers can be used along with expanded notation to... 5 mins 2nd - 4th Math CCSS: Designed Solve Addition Problems: Using Key Vocabulary Being able to identify key words can make all the difference when solving word problems. The first video in this series on problem solving models how to locate specific words that indicate the solution to a question that involves... 4 mins 2nd - 4th Math CCSS: Designed

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This engaging, varied, and informative scheme of learning is designed to help students gain a valuable understanding of Mary Shelley's horror classic 'Frankenstein.' The lessons enable students to gain a comprehensive understanding of the key features of plot, character, context, and language, in addition to considering the key themes and ideas running throughout the text. All of the resources that you need are included in the bundle: informative and engaging whole lesson PowerPoints, worksheets, activities, and lesson plans. The bundle is made up of a wide-range of interesting and exciting lessons, including: - The Context of Frankenstein; - Victor Frankenstein - The Tragic Hero; - Shifting Narrative Viewpoints: - Shelley's Description of the Monster; - The Monster's Murders - Justified? - The Frankenstein Pointless Game. Stimulating, visual, and easily adaptable, these lessons provide suggested learning objectives and outcomes for students of a wide-range of abilities - The vast majority of tasks are differentiated to allow for different abilities and needs in your classroom. Each lesson loosely follows this logical learning journey to ensure that students learn in bite-size steps: - Defining/ Understanding - Analysing/ Creating - Peer or self evaluating. All of the lessons are interactive, employ a variety of different teaching and learning methods and styles, and are visually-engaging.

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Students explore multiplication and division problems using exponents. Students examine positive, negative and zero powers. They relate powers to geometric sequences. Students devise strategies and discover rules of exponents. 17 Views 39 Downloads Integer Exponents, Scientific Notation and Volume A one-stop resource for exponents, square and cube roots, scientific notation, and volume formulas guides learners through properties of exponents. As they learn to apply these properties to operations with scientific notation,... 7th - 10th Math CCSS: Designed New Review Extending Patterns with Exponents Don't think negatively about exponents. Young mathematicians dissect a fictional conversation between pupils trying to evaluate an expression with a negative exponent. This allows them to understand the meaning of negative exponents. 8th - 9th Math CCSS: Designed Zero, Negative, And Fractional Exponents The equations get a little more complicated in this video, where Sal works through several problems involving negative and fractional exponents, as well as integers to the zero power. Though the problems look tough, Sal demonstrates the... 4 mins 7th - 11th Math

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In 2009, the United Nations declared July 18th “Mandela Day”, an international day of honor for former South African President Nelson Mandela. Also his birthday, Mandela Day invites everyone, particularly young people, to take action to promote peace and combat social injustice. According to the official Mandela Day website, Mandela Day “was inspired by a call Nelson Mandela made [in 2008], for the next generation to take on the burden of leadership in addressing the world’s social injustices when he said that ‘it is in your hands now’.” Familiarize students with Mandela’s life and legacy by reading aloud Kadir Nelson’s Coretta Scott King Honor book, Nelson Mandela. Share the illustrations and stop frequently for questions and discussion of Mandela’s early life, determination to change social conditions in apartheid-era South Africa, and eventual presidency. Fill in any gaps with resources from the biographical websites found here. Then explain the purpose and mission of Mandela Day before inspiring students to brainstorm their call to social action by sharing this page from the Mandela Day website. There, students will see examples of service projects around the key themes of awareness building, food security, literacy and education, service and volunteerism, and shelter and infrastructure. Finally, invite students, as a class or in small groups, to determine a project they can undertake to plan and publicize their contribution to a more just world. How do you plan to recognize this day?

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On April 16, 1862, slavery came to an end in the nation’s capital. President Abraham Lincoln signed a bill passed by the U.S. Congress abolishing slavery in Washington, D.C. Many members of Congress wanted to do more, but felt limited by 1857’s Dred Scott decision of the U.S. Supreme Court, which largely ended Congress’ ability to legislate about slavery. In his majority opinion in Dred Scott v. Sanford, Chief Justice Roger Taney had written, “The Constitution of the United States recognises slaves as property, and pledges the Federal Government to protect it. And Congress cannot exercise any more authority over property of that description than it may constitutionally exercise over property of any other kind.” During the Civil War, members of Congress from the abolitionist “Radical” wing of the Republican Party looked for ways legislatively to abolish slavery nationwide, despite the Dred Scott decision, but most members of Congress believed that slavery only could be ended legally by constitutional amendment. A constitutional amendment would take time, especially as the U.S. Constitution had not been amended since 1804, and by the time of the Civil War some Americans considered it sacrosanct. It would not be until late 1863 that Congress would begin to act on what became the 13th Amendment. But one matter of agreement in Congress by late 1861 was its absolute authority over the District of Columbia, including slavery there, even with the Dred Scott decision. So when Congress convened in December 1861, the Radicals judged the time was ripe for slavery to be abolished in Washington, D.C. Senator Henry Wilson of Massachusetts, introduced a bill to do just that on December 4, 1861. From that date the bill worked its way through the congressional committee process receiving final passage in April 1862. About the same time it passed the D.C. emancipation bill, Congress threw its support behind President Lincoln’s proposal to offer federal financial help to any slave state that enacted gradual compensated emancipation. The D.C. emancipation bill followed the spirit, if not all the particulars of Lincoln’s proposal. The main similarities were it compensated financially loyal slaveholders for their lost property and promoted the emigration of former slaves in Washington, D.C., by paying them $100 if they agreed to leave the United States. The main difference was that the “Compensated Emancipation Act,” as it later came to be known (since no other American slaveholders would receive compensation for emancipation), provided for the immediate instead of gradual emancipation of slaves in the District of Columbia. While Abraham Lincoln in Spring 1862 preferred gradual to immediate emancipation, as he admitted in a letter to Horace Greeley dated March 24, 1862, seeing it as less socially disruptive (which was the same reason he preferred the emigration of ex-slaves), he could hardly veto the Compensated Emancipation Act since during his single term in Congress in the late 1840s, Lincoln had introduced a bill to end slavery in Washington, D.C. Lincoln did not explicitly address those concerns in a message to Congress and the American people on April 16, 1862, announcing his signature of the D.C. emancipation bill, opting instead to criticize the ninety-day time limit placed on compensation claims. His message read: I have never doubted the constitutional authority of Congress to abolish slavery in this District, and I have ever desired to see the national capital freed from the institution in some satisfactory way. Hence there has never been in my mind any question upon the subject except the one of expediency, arising in view of all the circumstances. If there be matters within and about this act which might have taken a course or shape more satisfactory to my judgment, I do not attempt to specify them. I am gratified that the two principles of compensation and colonization are both recognized and practically applied in the act. In the matter of compensation, it is provided that claims may be presented within ninety days from the passage of the act, “but not thereafter;” and there is no saving for minors, femes covert, insane or absent persons. I presume this is an omission by mere oversight, and I recommend that it be supplied by an amendatory or supplemental act. There was more that both Lincoln and Congress could do to end slavery in the United States, but the Compensated Emancipation Act struck a major blow against the peculiar institution. It signaled both legislative and executive branches were serious about freeing the slaves, and that from then on any disagreements between them about emancipation would not be whether that aim was proper, but about the most efficacious means to achieve it. Sources: 1) http://en.wikisource.org/wiki/Dred_Scott_v._Sandford; 2) http://memory.loc.gov/cgi-bin/ampage?collId=llcg&fileName=058/llcg058.db&recNum=75; 3) http://www.archives.gov/exhibits/featured_documents/dc_emancipation_act/transcription.html; 4) http://quod.lib.umich.edu/cgi/t/text/text-idx?c=lincoln;rgn=div1;view=text;idno=lincoln5;node=lincoln5%3A364; http://www.presidency.ucsb.edu/ws/index.php?pid=70146&st=&st1=#axzz1phpUC7yU.

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Below are some of the methods we have been using in class to work out different elements of our maths curriculum. -Recognise the place value of each digit in a two-digit number (tens and ones) -Compare and order numbers to 100 use < > and = sign -Read and write numbers in words and numerals to 100 -Use place value and number facts to solve problems We have worked on partitioning (splitting) two digit numbers into tens and ones using different methods and equipment. -To be able to recall multiplication facts for the 2, 5 and 10 times tables. -Show that multiplication of two numbers can be done in any order. -Solve multiplication problems using equipment, arrays, repeated addition and mental methods. We started by counting in 2s, 5s and 10s. We used numicon as a visual prompt at first. We also use the 2s, 5s and 10s numberline we have on our class wall. We then wrote the repeated addition sentence under the numicon to show that multiplication is adding the same number over again. We then moved onto using arrays for multiplication. We also discussed how the numbers can be multiplied in different order and you still get the same answer e.g. 2 x 5 = 10 5 x 2 = 10 Once the children were confident with the above methods we moved onto problem solving. They had to read the question. Underline the important information. Then write the calculation and work out the answer. -Calculate division facts for dividing by 2s, 5s and 10s. Link to know multiplication times tables. -Understand that division can not be done in any order like multiplication. -Solve division problems using equipment, jotting methods and mental methods. We focused on the sharing method for division. We started off by practically sharing objects between different amounts of people. We talk about that the objects have to be shared equally. We then focused on a written jotting to help them work out calculations. Some children linked moved onto representing the division calculations using arrays.

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“There needs to be a lot more emphasis on what a child can do instead of what he cannot do.” Dr. Temple Grandin. In light of these words uttered by Dr. Temple Grandin, the concept of inclusion comes to mind if we are to place more emphasis on what children can do instead of what they cannot. With that being the case we cannot separate our disabled children from the general education classrooms, they must be included so that they can enjoy the benefits that are to be had. Inclusion is referred to as, the educational practice of educating children with disabilities in classrooms with children without disabilities. The concept of inclusion takes on two general models, namely; “Push in” and “full inclusion”. The concept of inclusion, works in tandem with mainstreaming. Subsequently, advocates of mainstreaming did not want to see students with disabilities placed in special classrooms for an entire day. Rather, they developed the belief that more exposure to the general education classroom would be beneficial to everyone. Similarly, inclusion speaks to children with disabilities being included in the general setting under the responsibility of the general classroom teacher. Inclusion is considered to be flexible because students with disabilities can receive their instruction in another setting such as a resource room with additional support been provided by “paraprofessionals ”. (this is special-education worker who is not licensed to teach, but performs many duties both individually with students and organizationally in the classroom). When considering inclusion, there are characteristics that must be observed and these include; all students been welcomed in the general classroom regardless of their disability or the severity, the proportion of students with and without disabilities are proportional to each other, students are educated with peers in the same age grouping available to those without disability labels, and students with varying characteristics and abilities participate in shared educational experiences. As mentioned earlier, inclusion has two main models: “Push in” and “full inclusion”. “Push In” recommends that the special education teacher enter the classroom to provide instruction and support to the children. The “push in” teacher will bring materials into the classroom. The teacher may work with the child on math during the math period, or perhaps reading during the literacy block. The push in teacher also often provides instructional support to the general education teacher, perhaps helping with differentiation of instruction. On the other hand, full inclusion refers to the practice of serving students with disabilities and other special needs entirely within the general classroom. Consequently, all students with disabilities are served the entire day in the general classroom, although special education teachers and other personnel may also be present in the general classroom. (Knowlton, 2004 ). Is the concept of inclusion applicable within the Jamaican context? In response to that question, we ought to consider the benefits that can be procured from the inclusion of students with disabilities in the general education classroom. The benefits for students include; a greater emphasis on students strength as opposed to shortfalls and limitations, students with disabilities demonstrate higher level of academic performance in inclusive setting, and students with disabilities have a greater opportunity the develop social skills from other students. Inclusion is applicable in the Jamaican context because there are students in our Jamaican society that are diagnosed with disabilities of one kind or another and we want then to be able to enjoy the benefits that were outlined earlier. In an article published in The Gleaner dated May 2, 2013, the author is quoted as saying “PEOPLE with disabilities (PWD) represent one of the most vulnerable and marginalized groups of people in Jamaica. They are often uneducated, live in extreme poverty and hunger, and are often at serious risk of discrimination and violence.” Consequently, it is applicable and wise to promote inclusion in the Jamaican context. UNICEF (2004) (as sited in the The Gleanre may 2013), disabled children have little opportunity to enjoy their right to an education, as stipulated in the Child Care and Protection Act as well as the Charter of Fundamental Rights and Freedoms, because less than 15 per cent of these persons are enrolled in government operated schools. In addition, Susan B. Rifkin and Pat Pridmore (2001) (as sited in The Gleaner may 2013), argues that “education is a powerful tool for the economic empowerment of people with disabilities because people who lack education/information often lack power and lack choices about how to improve their lives.” This is goes to show why inclusion is applicable in the Jamaican context. It is heartwarming to know that in Jamaica the national disability policy stipulates that no child shall be denied access to any public education institution on the basis of a disability. Davis, G., & Rimm, S. (2004). Education of the gifted and talented (5th ed.). Boston: Allyn and Bacon. Davis, K. (2004 ). What’s in a Name: Our Only Label Should Be Our Name: Avoiding the Stereotypes. http://www.iidc.indiana.edu/?pageId=364 Retrieved April 28, 2014. David W. Dillard (). Differentiated instruction challenges. wvde.state.wv.us/…/PD/Differentiated%20Instruction%20Challenges.ppt. Retrieved April 20, 2014. Geralis,E (editor). Children With Cerebral Palsy: A Parents’ Guide. MD: Woodbine House, 1998. Hall, T(2009). Differentiated Instruction and Implications for UDL Implementation. http://aim.cast.org/learn/historyarchive/backgroundpapers/differentiated_instruction_udl#.U1VMoPldVvl. Retrieved April 20, 2014. Jaevion Nelson(2013). What About Children With Disabilities?. The Gleaner. Jerry Webster(2014) .Inclusion – – What is Inclusion. http://specialed.about.com/od/integration/a/Inclusion-What-Is-Inclusion.htm. Retrieved April 20, 2014. Mavropoulos,Y.(2000). Inclucive Education. http://www.uvm.edu/~cdci/prlc/unit2_slide/sld005.htm Retrieved April 20, 2014. Minnesota Association for Children’s Mental Health().Children’s Mental Health Disorder Fact Sheet for the Classroom. http://www.schoolmentalhealth.org/Resources/Educ/MACMH/PTSD.pdf. Retrieved April 16, 2014. Pace center(2006). What Is An Emotional or Behavioral Disorder?. http://www.pacer.org/parent/php/php-c81.pdf. Retrieved April 20, 2014. Price, G(2013). Dyscalculia: Characteristics, Causes, and Treatments. Numeracy advancing education in quantitative literacy, 6,1, p3-6. P4 Smith,M, Segal,J (2014). Post-Traumatic Stress Disorder (PTSD). http://www.helpguide.org/mental/post_traumatic_stress_disorder_symptoms_treatment.htm. Retrieved April 20, 2014. Tomlinson, C. A. (1999). The differentiated classroom: Responding to the needs of all learners. Alexandria, VA: Association for Supervision and Curriculum Development. W.L.Heward(2006). Labeling and Eligibility for Special Education. http://www.education.com/reference/article/labeling-eligibility-special-education/

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A force is a push or a pull on an object. It is measured in Newtons, N. This push or pull is the result of an interaction between bodies, such as someone pushing the object, tension in a rope, friction with the ground, gravitational force, air resistance and many more. Forces have a direction and a magnitude. This makes them vector quantities. A way of representing this is having the F in bold, F, underlined, F, or with an arrow over it. All the forces on an object can be drawn on a free-body diagram. This is useful for working out the overall force on the object. Each force on the object is represented as an arrow in the direction of a force. Here are some examples: For a box resting on the ground, the weight of the box is commonly represented as the mass times the acceleration due to Earth’s gravity, g, so mg overall. Because the box is stationary, there must be a reaction force, or normal force, N, equal and opposite to mg. If there is then a force applied horizontally, the box will accelerate, since F = ma. In the next case, the applied force provides a force upwards, equal to Fsinθ and a force horizontally, equal to Fcosθ (these are obtained by resolving the force given). The horizontal force causes acceleration, while the vertical force means that N decreases. All forces which aren’t perpendicular to each other have to be resolved so that they are: Back to Contents: Physics: Mechanics

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In her popular grammar textbook geared to English language teachers, Jane Straus explicates the form and function of a ‘pronoun’. Definition. A pronoun is a word that takes the place of a noun. Pronouns can be in one of three cases: Subject, Object, or Possessive. Rule 1. Subject pronouns are used when the pronoun is the subject of the sentence. You can remember subject pronouns easily by filling in the blank subject space for a simple sentence. Example:________ did the job. I, you, he, she, it, we, and they all fit into the blank and are, therefore, subject pronouns. Rule 2, Subject pronouns are also used if they rename the subject. They will follow to be verbs such as is, are, was, were, am, and will be. Examples: It is he. This is she speaking. It is we who are responsible for the decision to downsize. In spoken English, most people tend to follow to be verbs with object pronouns. Many English teachers support (or at least have given in to) this distinction between written and spoken English. Example: It could have been them. Better: It could have been they. Example: It is just me at the door. Better: It is just I at the door. Rule 3. Object pronouns are used everywhere else (direct object, indirect object, object of the preposition). Object pronouns are me, you, him, her, it, us, and them. Examples: Jean talked to him. Are you talking to me? » To be able to choose pronouns correctly, you must learn to identify clauses. A clause is a group of words containing a verb and subject. Rule 4a. A strong clause can stand on its own. Examples: She is hungry. I am feeling well today. Rule 4b. A weak clause begins with words such as although, since, if, when, and because. Weak clauses cannot stand on their own. Examples: Although she is hungry… If she is hungry… Since I am feeling well… Rule 4c. If a sentence contains more than one clause, isolate the clauses so that you can decide which pronoun is correct. Examples: Weak Strong [Although she is hungry,] [she will give him some of her food.] [Although this gift is for him,] [I would like you to have it too.] Rule 5. To decide whether to use the Subject or Object pronoun after the words than or as, mentally complete the sentence. Examples: Tranh is as smart as she/her. If we mentally complete the sentence, we would say, Tranh is as smart as she is. Therefore, she is the correct Zoe is taller than I/me. Mentally completing the sentence, we have, Zoe is taller than I am. Daniel would rather talk to her than I/me. We can mentally complete this sentence in two ways: Daniel would rather talk to her than to me. OR Daniel would rather talk to her than I would. As you can see, the meaning will change depending on the pronoun Rule 6. Possessive pronouns show ownership and never need apostrophes. Possessive pronouns: mine, yours, his, hers, its, ours, and theirs The only time it’s has an apostrophe is when it is a contraction for it is or it has. Examples: It’s a cold morning. The thermometer reached its highest reading. Rule 7. Reflexive pronouns—myself, himself, herself, itself, themselves, ourselves, yourself, yourselves—should be used only when they refer back to another word in the sentence. Correct: I worked myself to the bone. Incorrect: My brother and myself did it. The word myself does not refer back to another word. Correct: My brother and I did it. Incorrect: Please give it to John or myself. Correct: Please give it to John or me. Straus, Jane, 2001. The Blue Book of Grammar and Punctuation: The Mysteries of Grammar and Punctuation Revealed. Mill Valley, CA: Bare Bones Training & Consulting Co. pp. 6-8. || Amazon || WorldCat

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Learning how to solve a math problem in different ways has many benefits. 1. It helps students understand the underlying principles of a math topic. 2. It leads students to think about which approach is the fastest or most efficient way to solve a math problem. 3. It also leads students to understand that math questions can be posed in a variety of ways just like math problems can be solved in a variety of ways. Let us begin with the third benefit. Some students can solve a math problem when it is presented in one way. When the same idea is presented in a different way, they are completely lost. Not only would this be a nightmare on the day of state assessments, this misunderstanding undermines the entire point of a math lesson. This chart shows the different ways that multiplication can be presented. Many students just know of multiplication as being represented as "groups". Each example shows multiplication in a different context. It is important for students to understand the different ways that a math topic can be presented. It is also just as important for students to know that a math problem can be solved in a number of ways. I can remember walking past a student that had not memorized his multiplication facts. He drew tiny circles on the corner of his paper to find the answer to a math problem. This leads to point two on our list. Using multiple approaches to solve a math problem helps students determine which one is the most efficient as well as fastest. There is a place for drawing tiny circles to determine the answer to a problem. Using this method is not the most efficient because it takes so much time. Showing how to solve the same math problem in multiple ways helps the student determine the best approach to solve a math problem. Use the four box or two box approach. The math problem is written in the center of the page. The larger box can be divided into two or four parts. Each part can show a different way to solve the math problem. To Access Math Task Cards That Teach And Review A Variety Of Math Concepts Click Here and Scroll Down

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Areas of Focus: The derivative of a function is a measure of how the function changes as a result of a change in the value of its argument. Given the function f(x), the derivative of f with respect to x is written as or as , and is defined by As shown in the figure, the derivative of the function f(x) at point x gives the slope of the function at x in terms of the ratio of the rise divided by the run for the line AB that is tangent to the curve at point x. The derivative of the function f(x) is also sometimes written as f ' (x). As shown in the figure, one can also write the definition of the derivative as The basic rules of differentiation are The derivative of commonly used functions: The following is a list of the derivatives of some of the more commonly used functions. The product rule for derivatives: Consider a function such as f(x)=g(x)h(x) that is the product of two functions. The product rule can be used to calculate the derivative of f with respect to x. The product rule states that For example, To take the derivative of f(x)=(2x+3)(4x+5)2 one can follow these steps The chain rule for derivatives: Consider the function f(U), where U is a function of x. One can calculate the derivative of f with respect to x by using the chain rule given by For example, to calculate the derivative of f(U) = Un with respect to x, where U = x2+a, one can follow these steps A point on a smooth function where the derivative is zero is a local maximum, a local minimum, or an inflection point of the function. This can be clearly seen in the figure, where the function has three points at which the tangent to the curve is horizontal (the slope is zero). This function has a local maximum at A, a local minimum at B, and an inflection point at C. One can determine whether a point with zero derivative is a local maximum, a local minimum, or an inflection point by evaluating the value of the second derivative at that point. Given a smooth function f(x), one can find the local maximums, local minimums, and inflections points by solving the equation to get all points x that have a derivative of zero. One can then check the second derivative for each point to get the specific character of the function at each point. Global maximum and minimum: The global maximum or minimum of a smooth function in a specific interval of its argument occurs either at the limits of the interval or at a point inside the interval where the function has a derivative of zero. As can be seen in the figure, the function shown has a global maximum at point A on the left boundary of the interval under consideration, a global minimum at B, a local maximum at C, and a local minimum at D. The derivative of a function of several variable with respect to only one of its variables is called a partial derivative. Given a function f(x,y), its partial derivative with respect to its first argument is denoted by and defined by Since all other variables are kept constant during the partial derivative, it represents the slope of the curve one obtains when varying only the designated argument of the function. For example, the partial derivative of the function with respect to x is evaluated by treating y as a constant so that one gets The chain rule: Consider a function f[U(x), V(x)] of two arguments U and V, each a function of x. The chain rule can be used to find the derivative of f with respect to x by the rule For example, consider the function f = UV2 where U =2x+3 and V=4x2. The derivative of f with respect to x is given by The integral of a function f(x) over an interval from x1 to x2 yields the area under the curve of the function over this same interval. Let F denote the integral of f(x) over the interval from x1 to x2. This is written as and is called a definite integral since the limits of integration are prescribed. The area under the curve in the following figure can be approximated by adding together the vertical strips of area . Therefore, the integral is approximated by This approximation approaches the value of the integral as the width of the strips approaches zero. A function F(x) is the indefinite integral of the function f(x) if The indefinite integral is also know as the anti-derivative. Since the derivative of a constant is zero, the indefinite integral of a function can only be evaluated up to the addition of a constant. Therefore, given a function F(x) to be an anti-derivative of f(x), the function F(x) + C, where C is any constant, is also an anti-derivative of f(x). This constant is known as the constant of integration and may be determined only if one has additional information about the integral. Normally, a known value of the integral at a specified point is used to calculate the constant of integration. The basic rules of integration are The indefinite integral of commonly used functions: The following is a list of indefinite integrals of commonly used functions, up to a constant of integration : Note: Remember to add a constant of integration. You evaluate the constant of integration by selecting the constant of integration such that the integral passes through a known point. Relating definite and indefinite integrals: To obtain the value of the definite integral knowing the value of the indefinite integral of the function, one can subtract the value of the definite integral evaluated at the lower limit of integration from its value at the upper limit of integration. For example, if you have the indefinite integral Note that C, the constant of integration, cancels in the subtraction and need not be included. It is common to sometimes use the notation Change of variables: Given a function U(x), one can use to change the variable of integration from x to U . The change of variables results in the rule For example, given the function we can write this function as where U = ax+b and . Therefore, the integral of f can be evaluated by using the following steps. Change of variables for a definite integral is similar with an additional change in the limits of integration. The resulting equation is For example, given the function , we can write this function as where U = ax and . Therefore, the integral of f can be evaluated by using the following steps. Integration by parts: Given the functions U(x) and V(x), one can use integration by parts to integrate the following integral using the relation For example, to evaluate the integral one can take and so that and . Using integration by parts we get The integral F of function f(s) over line AB, that is defined by s = 0 to s = l, is written as When either the domain of integration or the function is described in terms of another variable, such as x in the figure, one can evaluate F by a change of variables to get Depending on the format the information is provided in, it might be necessary to use the Pythagorean Theorem to relate the differential line element along the arc of the curve to the x and y coordinates. For example, in the figure shown we can see that The sign of the root must be selected based on the specifics of the problem under consideration. For example, consider integrating the function f(x,y) =xy2 over the straight line defined in the figure from point A to point B. Direct integration, using the relations The double integral of function f(x,y) first integrating over x and then integrating over y is given by The notation implies that the inner integral over x is done first, treating y as a constant. Once the inner integral is completed and the limits of integration for x are substituted into the expression, the outer integral is evaluated and the limits for y are substituted into the resulting expression. The rules of integration are the same as used for single integration for both the integration over x and the integration over y. To integrate over y first and then over x, the integration would be written as One can also write the integral limits without specifying the variable (i.e., without using "x=" and "y="). The order dxdy or dydx clearly specifies what variable a specific limit is associated with. Consider the following example of double integration of the function f(x,y) =xy2. Unlike the example, the limits of integration need not be constants. There will be no problem as long as the inner integral is conducted fist and the limits are substituted into the resulting expression before the outer integral is evaluated. For example, consider the following integral. The double integral F of the function over the area A is written as This integral is the sum of fdA over the area A. Each fdA is the volume of the column with base dA and height f. Thus, the integral gives the volume under the surface . To accomplish the summation that is represented by the integral, one needs to section the domain of integration A into small parts (i.e., into many small dAs). As shown in the figure, the domain of integration can be sections into rectangular sections, each with an area . At the limit of small element sizes, the sum of these area elements adds up to the original domain of integration. The differential element of area dA in a rectangular x-y coordinate system is given by either dA=dxdy or dA=dydx. The difference between the two is the order of integration. If done correctly, the value of the integration does not depend on this selection, yet the ease of integration may strongly depend on the choice for dA. If dA=dxdy is selected, then for each value of y an integration over x is conducted from the left limit of the domain to its right limit. This process fills the domain with differential elements of area and is shown in the figure. As can be seen from the figure, the limits of integration of x depend on the value of y so that the integral is written as On the other hand, if one takes dA=dydx, the order of integration changes. In this case, for each x between x1 and x2, the argument is integrated over y from the lower limit of area to its upper limit. This is shown in the figure. In this case the integral can be written as For example, consider the integral of f(x,y) =xy over the domain shown in the figure. The integral can be defined as Alternately, one can get the integral from As can be seen, the result of the integration does not change based on the selection of the order of integration, yet the setup of the integrals does change. The differential element of area in polar coordinates is given by This is a result of fact that the circumferential sides of the differential element of area have a length of , as shown in the figure. Otherwise the integration process is similar to rectangular coordinates. The centroid of an area is the area weighted average location of the given area. For example, consider a shape that is a composite of n individual segments, each segment having an area Ai and coordinates of its centroid as xi and yi. The coordinates of the centroid of this composite shape is given by As can be seen, the location of each segment is weighted by the area of the segment and after addition divided by the total area of the shape. As such, the centroid represents the area weighted average location of the body. For a continuous shape the summations are replaced by integrations to get where A is the total area. Centroid of common shapes: The following figures show the centroid of some common objects, each indicated by a C. Differential equations are relations that are in terms of a function and its derivatives. There are some methods for solving these equations to find an explicit form of the function. Some of the simplest differential equations are of the form The variables in such equations can be separated to get and then integrated to get where C is the constant of integration. A slightly more complicated differential equation is one of the form The variables in such equations can be separated to get and then integrated to get In general, if one can separate the variables, as was done in the two above examples, then one can use the methods of integration to integrate the differential equation. For example, consider the differential equation The variables in this equation can be separated to give The result of integrating this expression is where the constant of integration can be found knowing a point (xo, yo) that the function must pass through. For this case and the complete solution can be written as If the variables cannot be separated directly, then other methods must be used to solve the equation.

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Ribonucleic acid (RNA) is similar to DNA in that it is also a chain (or polymer) of nucleotides with the same 5' to 3' direction of its strands. However, the ribose sugar component of RNA is slightly different chemically than that of DNA. RNA has a 2' oxygen atom that is not present in DNA. Other fundamental structural differences exist. For example, uracil takes the place of the thymine nucleotide found in DNA, and RNA is, for the most part, a single-stranded molecule. DNA directs the synthesis of a variety of RNA molecules, each with a unique role in cellular function. For example, all genes that code for proteins are first made into an RNA strand in the nucleus called a messenger RNA (mRNA). The mRNA carries the information encoded in DNA out of the nucleus to the protein assembly machinery, called the ribosome, in the cytoplasm. The ribosome complex uses mRNA as a template to synthesize the exact protein coded for by the gene. Ribonucleic Acid is made up of a pentose group, which is a five carbon sugar, a phosphoric acid and a organic base. The structure of RNA is very similar to DNA. RNA is a linear polymer. However it does not have a linear structure. It has many regions in its polynucleotide chain where it folds in on itself creating structures that are called hairpin loops. This results in the formation of a helical structure like DNA in certain portions of its chain. Nucleotides such as ATP, GTP, CTP or UTP attach to the molecule by phosphodiester bridges (bonds). These bonds attach to either that 3' carbon or the 5' carbon in the sugar group ribose. In its chemical structure each nucleotide that makes of RNA has only one subtle difference from its DNA counterpart. It has one extra OH group. As DNA changes into RNA an OH group is added and TTP switches out with UTP. DNA's double helix structure is broken into two as it becomes RNA. RNA has a single helical structure. There are four types of RNA. There is the messenger RNA (mRNA), transfer-RNA (tRNA), ribosomal-RNA (rRNA), and catalytic-RNAs.(Purves 236-39) Messenger ribonucleic acid (mRNA) is a single-stranded RNA copy of a gene that is made during a process called transcription. After its synthesis, the mRNA is transported out of the nucleus to the cytoplasm where it binds to an organelle called a ribosome. The ribosome moves along the mRNA, reads the nucleotide sequence, and translates the "genetic code" into corresponding amino acids. The resulting chain of amino acids will eventually become a protein. Transfer ribonucleic acid (tRNA) is a small RNA molecule that participates in protein synthesis. Each tRNA molecule has two important areas: a trinucleotide region called the anticodon and a region for attaching a specific amino acid. During translation, each time an amino acid is added to the growing chain, a tRNA molecule forms base pairs with its complementary sequence on the messenger RNA (mRNA) molecule, ensuring that the appropriate amino acid is inserted into the protein. Ribosomal ribonucleic acid (rRNA) Over 50% of the ribosome is made up of rRNA and is required for the proteins to be properly made.(Purves 236-39) Role in Gene Expression - Main Article: Gene expression Proteins in the body are made from the instructional code found in DNA. The DNA however stays in the nucleus and is not accessible to the ribosomes that catalyze the polymerization of amino acids. RNA is instead created as a "message" (called messenger RNA) to be sent to the ribosome with instructions for assembling a protein. This messenger RNA is a transcript or copy of DNA that is almost, but not 100% identical. In particular, DNA is a deoxy form of the molecule (one fewer OH group per nucleotide). Also, in the process of making RNA, one of the nucleotides is substituted - TTP (Thymidine Triphosphate) is replaced for UTP (Uridine Triphosphate). Transcription is the process whereby DNA is copied to a single-stranded RNA. This process is catalyzed by the enzyme RNA polymerase. This enzyme attaches itself to a portion of the DNA strand and replicates it sending out mRNA or rRNA. During transcription there needs to be a promoter. A promoter is a certain sequence of DNA which RNA polymerase can bind to. It creates a very tight bond with the promoter. There are at least one promoter for every gene in the genome. Promoters do three specific jobs. They tell RNA, 1. Where to start transcription, 2. Which strand of DNA to read, and 3. The direction to take from the start. After the specific promoter has been chosen by the RNA polymerase a process called elongation begins. This process is where the polymerase adds nucleotides (A, U, C, G) to a section of DNA of about 20 amino acids and replicates it. However it is created antiparallel to DNA. DNA is 5' to 3' and RNA transcribes as 3' to 5'. The elongation process will continue until it reaches a certain termination site in the DNA. There is also a specific initiation site the tells where the transcription is to start taking place.(Purves 236-39) Electron micrograph of Ribosomal RNA transcription units of Chironomus thummi (Diptera). Magnification - 40.000x. - What is a Genome? by the National Center for Biotechnology Information - Messenger RNA (mRNA) Talking Glossary of Genetics Terms, National Human Genome Research Institute. Accessed September 25, 2010. - Transfer RNA (tRNA) Talking Glossary of Genetics Terms, National Human Genome Research Institute. Accessed September 25, 2010. - Molecular Biology more info - Purves, William K. et al. Life: The Science of Biology. Gordensville, VA. 2004.

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The three major basic properties of numbers in mathematics are the commutative, associative and distributive properties. Other important number properties include the properties of zero and the identity property of multiplication.Continue Reading The commutative property applies to addition and multiplication of numbers and basically states that the order of addition or multiplication does not affect the answer. For example, 15 + 14 = 29, and 14 + 15 = 29. Likewise, 10 x 12 = 120, and 12 x 10 = 120. The same principle holds true no matter how many numbers are added or multiplied together. The associative property also applies to addition and multiplication. This property states that it does not matter which numbers are grouped together in an addition or multiplication problem containing three or more addends or factors. For example, (10 + 11) + 12 = 33, and 10 + (11 + 12) = 33. Similarly, (2 x 3) x 4 = 24, and 2 x (3 x 4) = 24. The distributive property of numbers helps explain problems dealing with both addition and multiplication. For example, a relevant mathematical problem may ask, "If Bob makes $100 a day and Don makes $200 dollars a day, how much do they both make in two days?" The problem can be set up as follows: 2($100) + 2($200) = 2($100 + $200). Together they make $600. The properties of zero state that zero added to any number equals that number, and any number multiplied by zero equals zero. Any number added to its negative also equals zero. The identity property of multiplication states that multiplying any number by one does not change the number.Learn more about Arithmetic

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A part of North American history is known as Bacon’s Rebellion, and indeed it is one of the most intriguing parts of Jamestown’s immigration history. This was a power struggle between two individuals who were no less than stubborn and selfish. The two main individuals who played a part in Bacon’s Rebellion were the governor of Jamestown, Sir William Berkeley, and his cousin through marriage, Nathaniel Bacon, Jr. Governor Berkeley was an English Civil Wars veteran, a fighter of Native Americans, and during his first term as Governor, the King’s favorite. He had also made a name for himself as a playwright and a scholar. His name was deeply respected, as was his name as Governor of Virginia. Bacon was a total opposite of Berkeley in character. He was intelligent, to be sure, but he was also a troublemaker and schemer. In fact, his father had sent him to Virginia in the hopes that he would mature. When he arrived, his cousin Berkeley treated him with respect and extended him friendship, giving him land and even allowing him a seat on the council. Over time, however, Virginians, including Bacon, began to feel frustrated. There were economic difficulties, issues caused by weather, and other problems that led the colonists to feel the need to place blame on someone for the misfortunes they were suffering. This scapegoat took form in the local Native Americans. Issues between the Native Americans and the colonists did not make anything any easier for all parties involved. The colonists began to demand much of Berkeley regarding their safety, and feeling that their demands were being ignored, an uprising began. Over one thousand Virginians rose up to bring the confrontation to their governor, and they were led by none other than Nathaniel Bacon, Jr. They attacked Native Americans and chased Governor Berkeley from Jamestown before they ultimately set fire to the capital. Before aid could arrive sent from England, Bacon perished from dysentery. After his death, Bacon’s Rebellion soon lost steam. The governor, then aged 71 years, returned to power and put to death the remaining leaders of the rebellion. He also moved to seize rebel property without the benefit of trial. A later investigation completed by a committee sent from England resulted in Berkeley being removed as governor and returned to England, where he died in 1677. Bacon’s Rebellion was a power struggle between two individuals with two larger than life personalities. Between the two of them, they nearly destroyed Jamestown.

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This week in Geometry, students explored the concept of infinity. The unit we are in is about polygons, so we extended our understandings of polygons to ask if a circle should be considered a polygon. To help students construct an argument for this question, they were first asked to observe certain trends. The first observation was to note that as we add more and more sides to a regular polygon, these polygons start to look like a circle. Then from there, students were asked questions such as whether they think a circle has no straight sides, or an infinite number of them. To build on this dialogue, we also did a close read on how scientists have struggled with the concept of infinity as it applies to our universe. Is the universe infinite or finite? Is it growing or static in size? These are the questions we read about and tried to answer for ourselves in conjunction with our conversation on polygons and circles. During these discussions, students had brilliant insights, such as questioning what happens at the border between the finite and the infinite. Where is infinity minus one? Even if a pattern closely approaches a certain outcome, does it ever actually reach that outcome? How do we represent this concept of infinity when applying something that is infinite to an equation? Students were encouraged to have meaningful dialogue to help them form an opinion on these questions, and were told to explore the possible answers without fear of being wrong. Students took well to this challenge, despite never being given any direct answers to their questions, and in contrast, only receiving more questions to think about! To start getting more concreate answers, students were told to stay tuned for our next unit…circles!

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What are the Common Core State Standards? The Common Core State Standards are guidelines—not a set curriculum—to help teachers ensure their students have the 21st century skills and knowledge they need to be successful by providing clear student learning goals for Math and Language Arts. Forty-five states have adopted the new voluntary Standards that promote equity by ensuring all students, no matter where they live, are well prepared with the skills and knowledge necessary to collaborate and compete with their peers in the United States and abroad. Common Core State Standards Adoption The Common Core State Standards for Math (CCSSM) and the Standards of Mathematical Practice Like the Common Core Language Arts standards, the CCSSM define what students should understand and be able to do. The Common Core State Standards for Mathematics call for student understanding on a conceptual level, to grasp the foundational concepts behind math procedures and to continually engage in critical mathematical practices. - Standards define what students should understand and be able to do. - Clusters summarize groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject. - Domains are larger groups of related standards. Standards from different domains may sometimes be closely related. The Standards for Mathematical Practice describe the attributes of mathematically proficient students, and how they engage with and learn mathematics. The Standards for Mathematical Practice stay the same from the earliest grades through high school: 1) Counting and Cardinality, 2) Comparing, Operations and Algebraic Thinking, 3) Number and Operations in Base Ten, and 4) Number and Operations in Fractions. Click here for a printable download of the CCSSM. What are the major goals of the CCSSM? - Focus. Narrowing the scope of content covered in each grade allows students to more deeply understand material, and build a solid foundation for future work. - Coherence. Standards, educational materials and teachers’ instructions are consistent to form a unified message that makes sense to students. For math, it is about make connections between mathematical topics so there is a smooth progression across grade levels. - Rigor. ‘Rigor ‘means three things: conceptual understanding, procedural skill and fluency, and applications. Transitioning and implementing the Common Core State Standards Watch a webinar about transitioning and implementing the Common Core. The Common Core State Standards for Mathematics call for student understanding on a conceptual level, to grasp the foundational concepts behind math procedures and to continually engage in critical mathematical practices. Transitioning to teaching this mathematical way of thinking requires new tools and methods. One way to make the transition smoother is to formulate an overall plan and provide an online portal or wikispace for feedback, as well as a support system, online tools, and resources for teachers and administrators. Read a white paper about how to successfully plan for CCSS for math. A Common Core math standard example An example of how a Common Core math standard is structured can be seen in the very first one set for kindergarten: CCSS.math.Coten. K.C.C.A. 1) Count to 1000 by ones and by tens. It is alignment and is a building block for the Standards for Mathematical Practice 1) Counting and Cardinality. As the student advances through the curriculum, what changes is the way the Standards look as students engage with and master new and more advanced mathematical ideas that build upon and integrate with each other. So, standards and practice must be taught in tandem for the highest level of effectiveness. Aligning with the new standards Because the CCSSM are guidelines and not a national curriculum, the task of ensuring proper alignment is up to teachers and school administrators. While this gives educators freedom to implement the standards in a way that will be most beneficial for their own students, it also means that they need to develop or find new CCSS aligned educational materials. The Partnership for 21st Century Skills has suggestions to help educators, with sample math lessons, and a framework for aligning curricula and assessments: - Use backward-design principles (such as Understanding by Design, 1) to design curriculum that encourages inquiry-based learning and enables embedded, performance-based assessments. - Develop interdisciplinary performance tasks and or project-based learning units that integrate the full P21 Framework in alignment with CCSS, consider capstone performance such as senior portfolios. - Create curricula-embedded assessment to enable assessment as and for learning. - Collect and share exemplary student work that demonstrates mastery of college and career ready knowledge and skills. - Provide meaningful opportunities for educators to collaboratively review curricula, student work and student performance data in order to refine the curricula and assessments over time. Take advantage of the Partnership for 21st Century Skills free Common Core toolkit. The Common Core is designed to build understanding and to help the student realize that conceptual learning is a way of thinking and a skill. That means that the teacher acts as a guide, and creates an experiential environment to help students approach procedurally and conceptually, rather than teaching by rote. This means that the teacher or parents need to rethink their own approach to support re-engagement with math. Stanford University offers online courses for educators, including free Common Core classes. Here are some additional resources from DreamBox that cover Common Core-aligned lesson plans and lessons by grade. How technology helps implement the Common Core Technology—both devices and software—can be invaluable tools in teaching to new math standards and to support blended learning. Lessons can available 24/7 to students so work can continue in and out of school. Online lessons step students through material, allow for review of challenging material, and for the teacher to access progress reporting. One of the most valuable technologies to teach Common Core subjects is adaptive learning technology. It is software that learns and alters itself based on the student’s responses. Adaptive technology, particularly intelligent adaptive learning technology, supports competency based learning because it adjusts the student’s learning path and pace within and between lessons, and advances the student based on comprehension. It also provides formative and summative data in Common Core-aligned progress reports to the student’s teacher, so instruction can be tailored to individual needs, understandings, and interest. Read a recent Fraser Institute white paper about technology and education. Wiggins, .G.P.,& McTighe,J.(2005).Understanding by design.Alexandria,VA:Association for Supervision and Curriculum Development

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Negatives vs. Positives Prior to beginning algebra, most students have not had much practice with negative numbers. They are often not accustomed to taking a number’s sign into consideration. To help draw students’ attention to this important factor, ask them to highlight positive numbers in one color and negative numbers in another. -12 + 4 = Color-coding is a great strategy for helping algebra neophytes understand the idea of like terms. When adding or subtracting in expressions containing variables, ask students to highlight unattached numbers with one color and like terms with other colors before solving. Grouping blue terms with other blue terms will seem a lot more natural than grouping x’s with other x’s. Tip: Ask them to include the sign preceding each number in the highlight so that they will understand which numbers are positive and which are negative in tricky equations. When there is no sign, ask students to add in their own addition sign, then highlight it. 4n + 3x - 4 = 7x - 2n + 10 -> +4n + 3x - 4 = +7x - 2n + 10

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Logical operators are also called boolean operators. They operate with truth(boolean) values and the result is always a truth value (true or false). These operators are useful if you want to combine several conditions into a single statement. The new operators: &&(AND), ||(OR), ^(XOR), !(NOT). Before we analyze each of them, let’s recall what is a boolean data type. It holds a truth value. You can take a quick look in the Data Type lesson. Logical AND, also known as conjunction. It takes two operands. Returns “true” if both operands are true, otherwise returns “false”. For example we use three variables: bLeft, bRight, bResult: bResult = bLeft && bRight bResult will be “true” only if "bLeft" AND "bRight" are “true”. We can represent this in a truth table. Take your time and examine the table. Make sure you get the idea. Let’s put this into practice! Problem number 4 from your last homework(Previous lesson – math operators): ”Given are three numbers. Find if the second is the greatest.” Solution without conjunction: Solution, using the logical AND: See how we can combine 2 conditions in one block? Also note that it is always a good practice to use parenthesis to separate them. That improves code readability and prevents unexpected behavior. Logical OR, also known as “disjunction”. Accepts two arguments and returns “true” if at least one of them is “true”. bResult = bLeft || bRight bResult will be true, if "bLeft" OR "bRight" is true. Let’s create the truth table for this case: And one example.. The ^ operator is known with different names - Logical XOR, exclusive OR, sum by modulus of 2. Accepts two arguments and returns “true” if exactly one of them is “true”. bResult = bLeft ^ bRight bResult will be true, if bLeft is “true” and bRight is “false” or bLeft is “false” and bRight is “true”. Its truth table looks like this: Takes only one operand – right. The result is the opposite value of the operand. bResult = !bRight; bResult will be “true” if bRight is “false”. You can guess how this table looks like ;-) We can use this in many cases. In fact, it is the logical operator that I use the most. In this example we check if a certain file exists. If it doesn’t – we create it. We can combine NOT with the other logical operators: !(bLeft && bRight) This forms the logical NOT AND. In schematics this is used extremely often. They even have a separate element, called NOT AND (NAND). When you work with logical operators you could come across the De Morgan's laws. This is a little bit more advanced stuff. You may not find this very useful right now, or it could be difficult to understand. So don’t worry if you don’t get it on 100% ;-). The laws can be proved mathematically, but it is far out of our scope. Instead we want to focus on the logical operators and how they work. For exercise we will test the laws with example values. For this example we will use letters for the names of our variables. !( (A && B) || (C && D) ) = (!A || !B) && (!C || !D) Let’s give values to our variables and check if this is indeed correct. We accept: A= true, B = false, C = true, D = true. !( (true && false) || (true && true) ) =?= (!true || !false) && (!true || !true) !(false || true) =?= (false || true) && (false || false) !true =?= true && false false == false OK, in this case it works. I suggest you substitute the variables with another set of values and do the calculations on paper. This is a very good training. !( (A || B) && (C || D) ) = (!A && !B) || (!C && !D) There are many other laws in the world of logical operators, but they are out of our way. 1. Take a paper (or some text editor ;-) ) and answer the questions with few words. 2. Write an algorithm that takes the gender and age from the user. Check if it is a woman under 40 years. Use logical operators to do the check in a single block. Tip: (You can use a char or string variable to remember and compare the gender). 3. Test the second law of De Morgan, just like we did with the first law in the current lesson. 2)Software Development Process 4)Flow Chart Symbols 6)What is a variable

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Common Core asks our students to know common prefixes and suffixes. This activity lets your students learn the meanings of un, re, and dis. There is an informational poster and 20 different words using those prefixes. The students must match the sentence with the prefix in it to the meaning of that prefix. Teachers will copy, laminate, then cut apart the 4 rectangles on each page. Put them in an envelope with the direction sheet, recording sheet, and answer key. There is a cover page to put on the outside of your envelope or whatever storage system you use. This can be used in a small group setting, a reading center, or using your overhead document camera with the entire class. CCSS.ELA-Literacy.RF.2.3d Decode words with common prefixes and suffixes. This resource is NOT an open education resource and therefore may not be shared in part or whole as part of the US department of Education's go open campaign. Uploading it to a school server, county server, or other platform such as Amazon Inspire to be shared with other educators is against copyright terms.

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— [http://goo.gl/JMNr6i] Action research to improve student learning and_______________________Spanish pedagogy! This method of engaging students with comprehensible input, TPRS, is powerful. Storytelling is a revolutionary approach that makes so much sense in so many ways. Briefly, TPRS is based heavily on Stephen Krashen’s (and others’) research on second language acquisition and theories of the Natural Approach, or the theory that people learn second and more languages in much the same way they learned their first. The TPRS approach incorporates highly repetitive storytelling using the most frequently used words in a language, along with engaging reading materials, to deliver very comprehensible input to students. Experts document that within TPRS, students learn Spanish through stories, dramatic play, and body movements. Using TPRS, teachers provide instruction exclusively in the target language, foster a brain-body connection, and engage students in developmentally appropriate activities. There are a few key components of the method: 1. Comprehensible input: In order to acquire a language, you must understand what you hear. If you mostly understand what you hear (or read), it is comprehensible to you. Listening is so important!! 2. Stories: It is easier to learn new vocabulary and pick up grammatical structures naturally by listening (and understanding) stories that are short, funny, silly and involve emotions or surprises. Learning new vocabulary by studying flashcards or vocabulary lists is not very effective, but you probably already know that by now. 3. Question and answer lessons: Telling the story and answering lots of questions serves two functions. First, because the question and answer lesson is very repetitive, asking similar questions over and over again throughout the lesson, you get to hear the vocabulary and grammatical structures many, many times, which leads to better understanding and more retention. (This means you remember the words better!) Second, because the questions are simple and repetitive, you begin to understand quickly and answer quickly. Learning how to answer the questions quickly, without translating, without thinking will lead you to becoming a fluent English speaker.

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Visualization in Primary Mathematics Visualization activities fit well into the oral and mental starter for a lesson. Here is an example of one you might read slowly to a Year 6 class (or higher ability Year 5). Read through the visualization activity. Try to visualize the shape yourself. The children might benefit from sitting with their eyes closed, though some will prefer to keep their eyes open. Imagine a square-based pyramid made out of plasticine in the air in front of you. Ask yourself a few questions (but keep the answers to yourself). How many corners, or vertices, has the shape? How many edges? How many faces? Are the faces all the same shape? Now imagine a cube, with square faces the same size as the base of your pyramid, also floating in space. Slide your pyramid until it sits on top of the cube, with its base exactly in line with the top of the cube. Ask yourself some questions about the new solid: How many vertices has it? How many edges? How many faces? Are they all the same shape? Now imagine a sharp knife and use it to make a vertical cut through your solid. Examine one of the pieces you now have and look at the face created by your cut. Without saying anything, open your eyes and sketch the shape of this new face. Now compare your drawing with others. Check your solution using the illustrations on this page... You might think that visualization is just another word for fantasising. In a way, it is; only when we use visualization in mathematics, it's for a practical purpose. Visualizing shapes and spaces helps us to gain a very real idea of what is where! Once you get used to using such a method, you'll find that it has many everyday uses. For example... You park your bike in the shade when you arrive at school. The sun is on your left. Can you imagine where the sun might be by lunchtime? Or hometime? Perhaps it would be better to ensure that your bike is shaded in the middle of the day - the hottest time - even if this means parking it in direct sunlight when you get to school in the morning? Staying on the subject of shadows: can you imagine what shape shadow might be cast by different 3D solids? Try visualizing the shape of shadow cast by: a cube; a pyramid; a cylinder; a polyhedron. Try to imagine yourself on the telephone to a friend, describing the making of a paper plane. You will be imagining - visualizing - the making of it in your head, but you'll find it's a bit more difficult trying to get your friend to see what In pairs, describe a journey on foot within a neighbourhood you both know well. Use landmarks and map directions, as well as other instructions, to take your partner on an imaginary journey from A to B. Keep a score of how many times each of you ends up where the other visualized them doing so. As you can see, there are many uses for visualization methods not only in mathematics, but in day to day life too. You'll probably find that you can use the same methods in other school subjects - if you don't already do so. Try finding a use for visualization in each of your other curriculum subjects. And if you do, share your ideas with others! Wales, UK., November 2004.

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Game of Ten; More or Less? Lesson 13 of 16 Objective: SWBAT use a hundreds chart to add or subtract a ten within 100. Rev Them Up My class has been working hard on using mental math to add ten and subtract ten. I will review this concept and get their minds on math by using base ten blocks: (While holding up 3 base ten blocks and 4 ones units.) Students, what number do I have here? (34) I want to add ten, so I am going to put another base-ten block with it, what do I have now? (44) (If necessary, start with the 34 and point and count on the base ten block to add ten more) I am going to put one base-ten block down, what do I have now? (you have 34 again) What if I subtract ten from 34 and take one base ten away? (You have 24) (If necessary, start at 34 and count backwards while pointing at the sections on the base ten block.) If it is difficult for your students to see the tiny sections of the base-ten block, use unifix cubes instead. You could even snap together different colored cubes, so they can see each unit easily. I pick two more numbers and follow the same progression. Whole Group Interaction Students must develop a strong understanding of place value to use tens and ones to assist in addition and subtraction of 2-digit numbers. The Common Core Standards want first graders to be able to use their knowledge of place value as a strategy for completing addition and subtraction with 2-digit numbers. This requires being able to solve 2-digit addition problems by adding the ones to the ones and the tens to the tens. Today's lesson continues to help students understand how to figure out 10 more or 10 less without having to count (1.NBT.C.5). To do this, I want to help them identify the pattern that occurs on a 120 chart and show them how each column increases or decreases by ten as they move up and down. I want them to identify this pattern because it can help them internalize the connection between the value and the digit in the tens place as it changes by one (MP7). I am selecting the 120 chart as a tool for them to solve their problems, but my goal is for them to see this tool provides a strategic method to find their answer. To begin, I will ask a student to stand with a pointer and point out the numbers as the class helps me count down different columns. The patterns I want them to identify are: - As we go down a column the ones digit stays the same. - As we go down a column the amount of tens increases one set of ten for each row. I will have them practice by playing a game of I have, Who Has. To play this, cut the cards apart and pass them out. Have the 120 chart pulled up on the SmartBoard or have one posted in your class or on their desk for them to refer to. Find the student that has the beginning strip and start to play the game. My concrete learners have moved beyond using base-ten blocks to solve these problems and are relying on the more abstract too, the 120 chart, for support. I will have some students who need additional teacher support in using the chart correctly through the game for them to be successful. I will be walking around the room and assisting those that need it with their chart. It is very important to know your students' abilities and be ready to guide them towards an answer. For instance, some get lost in multiple step problems. I will assist by pointing out numbers on the 120 chart and helping them identify whether to move up or down to find their answer. I will do this by reminding them what it says on their play card: 10 more or 10 less. There are several different online sources to use for your students to practice this skill. No matter which sheet or online activity you select, make sure you point out to your students they need to pay attention to whether they are subtracting or adding. Because these problems are complex for first grader (they involve the application of both place value concepts and operations), students might miss the plus or minus signs. Here is an example of a student who used addition instead of subtraction. This is one student I will need to check in with next time to make sure the student sees the error. Below are several different practice pieces to access online: I have dry erase boards in my room that we can use for quick practice work. If you do not have these, you can put a sheet of paper inside a page protector and still use dry erase markers. It comes off just as easily. To close out our lesson I will pass out our dry erase boards and markers and provide a few problems for my students to solve involving adding or taking away 10 from a 2-digit number. I want them to write their answer and hold their board in the air for me to see. This way, I can quickly assess how my student have done with mastering today's material and plan future instruction.

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"Modern" eyes first appeared about 550 million years ago, having evolved through random mutations and natural selection from simple light-sensitive patches on the skin. Researchers at Lund University have calculated that the development of the camera-like eye from a light-sensitive patch might require roughly 1,829 steps (each involving no more than one percent change) and only 364,000 years. This is so fast that eyes could have evolved 1,500 times. Different eye types have emerged, but, generally, the process probably involved changes in the patch that created a depression, which deepened into a pit capable of sharpening sight that eventually narrowed, allowing light to enter through a pin-hole like aperture. With time, a layer of cells and pigment lined the back (retina), transparent tissue lined the front (lens), and liquids provided a curvature. Rollover the image to name the eyes portrayed. * A Pessimistic Estimate of the Time Required for an Eye to Evolve Nilsson, Dan-E.; Pelger, Susanne. Proceedings: Biological Sciences, Volume 256, Issue 1345, pp. 53-58

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Capital Letters (KS1) English Teaching Resources: Capital Letters (KS1) This resource teaches children about capital letters as required by the 2014 National Curriculum for England. It provides NC14 objectives, numerous examples of how to use capital letters and engaging consolidation activities to assess understanding. Capital Letters (KS1) is made up of an easy to understand 16 slide PowerPoint presentation (fully editable) and is accompanied by a four page PDF document which includes teacher notes and two worksheets. To preview English Teaching Resources: Capital Letters (KS1) in more detail please click on the PowerPoint images.

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We will learn about what is variation, direct variation, indirect variation and joint variation. In Mathematics, we usually deal with two types of quantities-Variable quantities ( or variables ) and Constant quantities ( or constants). If the value of a quantity remains unaltered under different situations, it is called a constant. On the contrary, if the value of a quantity changes under different situations, it is called a variable. For example: 4, 2.718, 22/7 etc. are constants while speed of a train, demand of a commodity, population of a town etc. are variables. In problems relating to two or more variables, it is seen that the value of a variable changes with the change in the value ( or values ) of the related variable (or variables). Suppose a train running at a uniform speed of v km./h. travels a distance of d km. in t hours. Obviously, if t remains unchanged then v increases or decreases according as d increases or decreases. But if d remains unchanged, then v decreases or increases according as t increases or decreases. This shows that the change in the value of a variable may be accompanied differently with the change in the values of related variables. Such relationship with regards to the change in the value of a variable when the values of the related variables change, is termed as variation. We will discuss about such variations, which are classified into three types: (1) Direct Variation (2) Inverse Variation and (3) Joint Variation. If two variables A and B are so related that when A increases ( or decreases ) in a given ratio, B also increases ( or, decreases ) in the same ratio, then A is said to vary directly as B ( or, A is said to vary as B ). This is symbolically written as, A ∝ B (read as, ‘A varies as B’ ). Suppose a train moving at a uniform speed travels d km. in t minutes. Now, consider the following table: A variable quantity A is said to vary inversely as another variable quantity B, when A varies as the reciprocal of B i.e., when A varies as 1/B Thus, if A varies inversely as B, we write A ∝ 1/B or, A = m ∙ (1/B) or, AB = m where’m (≠ 0) is the constant of variation. Hence, if one variable varies inversely as another, then the product of the corresponding values of the variables is constant. Conversely, if AB = k where A and B are variables and k is a constant, then A ∝ 1/B Hence, if the product of the corresponding values of two variables is constant, then one quantity varies inversely as another. Again, if A varies inversely as & then AB = constant ; but AB = constant implies that when A increases in a given ratio, B decreases in the same ratio and vice -- versa. Thus, if two variables are so related that an increase (or decrease ) in the value of one variable in a certain ratio corresponds to a decrease (or increase) in the same ratio in the value of the other variable then one variable varies inversely as another. Let a m. and b m. be the length and breadth r area 160 sq. m. Now, consider the following table: One variable quantity is said to vary jointly as a number of other variable quantities, when it varies directly as their product. If the variable A varies directly as the product of the variables B, C and D, i.e., if.A ∝ BCD or A = kBCD (k = constant ), then A varies jointly as B, C and D. We know, area of a triangle = ½ × base × altitude. Since ½ is a constant, hence area of a triangle varies oint1y as its base and altitude. A is said to vary directly as B and inversely as C if A ∝ B ∙ 1/C or A = m ∙ B ∙ 1/C (m = constant of variation) i.e., if A varies jointly as B and 1/C. If x men take y days to plough z acres of land, then x varies directly as z and inversely as y.

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|MadSci Network: Earth Sciences| Geothermal energy may be either in the form of heat or hot water. Deep in the planet's core, radioactive atoms such a uranium, potassium, and thorium have decayed for many billions of years. This has generated heat intense enough to melt solid rock. Because the earth's crust is a poor conductor of heat, this heat has largely remained deep underground near where it was produced. Like heat from a wood stove in a large room, the heat produced in the core gradually diminishes with distance. If you could stick a thermometer in the earth's core, the temperature may be as high as 6,600 degrees Celsius. If you stuck it into the mantle, the temperature might register between 3,700 and 1000 degrees Celsius. A few kilometers under the earth's surface the temperature ranges from a few dozen to several hundred degrees Celsius. The fault lines throughout the world create weak points in the crust that permits this geothermal energy to escape. The pressure that this energy creates causes movement in the magma, or molten rock, which tries to push the crust apart. However, the strength and weight of the crust does not allow the heat to emerge, except where the crust is weakest along the faults. For example, along the Pacific Rim there is a great concentration of geothermal activity. That's because they lie along the boundary of large, tectonic plates. Along the fault boundaries magma rises to the surface and forms geothermal vents such as volcanoes and lava flows. This heat and pressure also causes geothermal vents created by water. Over millions of years, water has trickled through the crust and collected in layers of porous rock called aquifers. The aquifers can be heated by geothermal energy to hundreds of degrees. At sea level the water would boil and turn to steam. Because of the enormous pressures several kilometers down, it cannot. Instead, it is pushed upward through channels and fissures, or cracks. It may bubble steadily out onto the surface; or it may rise into the air through geothermal vents as curling clouds of steam and condensed water vapor; or it may jet out of the ground as a geyser. Try the links in the MadSci Library for more information on Earth Sciences.

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All children are encouraged to read with fluency, accuracy, understanding and enjoyment and are taught to use a range of strategies to make sense of their reading materials. Reading goals include: * Phonemic awareness and phonic knowledge * Hear, identify, segment and blend phonemes in words * sound and name the letters of the alphabet * Link sound and letter patterns, exploring rhyme, and other sound patterns * Identify syllables in words * Recognize that the same sounds may have different spellings and that the same spellings may relate to different sounds * Word recognition and graphic knowledge * Read on sight high-frequency words and other familiar words * Recognize words with common spelling patterns * Recognize specific parts of words, including prefixes, suffixes, inflectional endings, plurals * Understand how word order affects meaning * Decipher new words, and confirm or check meaning * Work out the sense of a sentence by rereading or reading ahead Focus on meaning derived from the text as a whole Use their knowledge of book conventions, structure, sequence and presentational devices Draw on their background knowledge and understanding of the content. Reading for information * Children should be encourage to use the organizational features of non-fiction texts, including captions, illustrations, contents, index and chapters, to find information * Understand that texts about the same topic may contain different information or present similar information in different ways *Use reference materials for different purposes. * Children should be encouraged to develop their understanding of fiction, poetry and drama * They are taught to identify and describe characters, events and settings in fiction * Use their knowledge of sequence and story language when they are retelling stories and predicting events * Express preferences, giving reasons * Learn, recite and act out stories and poems * Identify patterns of rhythm, rhyme and sounds in poems and their effects * Respond imaginatively in different ways to what they read [for example, using the characters from a story in drama, writing poems based on ones they read, showing their understanding through art or music]. Language structure and variation Children are encouraged to read texts with greater accuracy and understanding, pupils should be taught about the characteristics of different types of text [for example, beginnings and endings in stories, use of captions]. During their primary years, children should be taught knowledge, skills and understanding through the following ranges of literature and non-fiction and non-literary texts. *The range should include stories and poems with familiar settings and those based on imaginary or fantasy worlds * Stories, plays and poems by significant children's authors * Traditional folk and fairy stories * Stories and poems from a range of cultures * Stories, plays and poems with patterned and predictable language * Stories and poems that are challenging in terms of length or vocabulary * Texts where the use of language benefits from being read aloud and reread. Non-fiction and non-literary texts The range should include information texts, including those with continuous text and relevant illustrations, dictionaries, encyclopedias and other reference materials. Anthropology Art Cooking skills Exercise skills Foreign languages Geography-History Language Mathematics Music Science Technology Who we Are HOME

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The 15th Amendment continues to affect the United States today because black men and women are voting as citizens throughout the nation. Black men and women are also entitled to more than the right to vote and are entitled to every right found in the U.S. Constitution, which is a result of the final success of the 15th Amendment.Continue Reading The 15th Amendment was enacted on February 3, 1870. Many states immediately created new laws, such as poll taxes and literacy tests in an effort to keep as many black American men from the voting booths as possible. It was not until 1965 when the Voting Rights Act was passed that black Americans were truly able to begin voting in large numbers. After this happened, the acceptance of black Americans grew and the general public began accepting that black Americans were to be given all of the basic rights granted to American citizens in the U.S. Constitution. The 15th Amendment was a historical win for black African-Americans, as was the Voting Rights Act signed into law by President Lyndon B. Johnson. When many Southern states attempted to ignore the new Voting Rights Act law, black Americans were able to appeal and challenge the restrictions so that they could vote. These laws were the start to a new America that was no longer racist or whose laws at the very least attempted to no longer be racially biased.Learn more about The Constitution

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Introducing Point of View One thing we will be focusing on was we begin to read the short fiction story "The Quinceañera Text" is explaining how the author develops the point of view of the narrator or speaker in the text. But what is point of view and how can we begin to determine the type of point of view a story is being told from? Let's watch the video below for an introduction. Guided Reading: "The Quinceañera Text" As we read the short story "The Quinceañera Text" (which can be found here) together, we will stop periodically to discuss the important literary elements and devices present in the story, including characters, point of view, setting, symbolism, and plot. You will make note of these using the document Literary Elements and Devices ("The Quinceañera Text") located in your Language Arts Google Classroom.

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Unit 3 - Atoms and the Periodic Table This unit looks at the ways elements are grouped together, what elements are made up of and the structure of an atom. Gathering Elements Together There are over 100 different elements. Some are shiny - like silver and gold - some are gases - like hydrogen and oxygen - and some are colour, like iodine and sulphur. When we are faced with a wide variety of things in common we often try to gather those which have something in common. This is called classification. An example of classification in the periodic table could be separating the elements apart depending on whether they are naturally occurring or made by scientists. Naturally Occurring: Titanium, Copper, Zinc, Hafnium and Niobium. Made by Scientists: Neptunium, Curium, Fermium and Nobelium. Another example of classification in the periodic table is the way in which the non-metals are on the right side and the metals are on the left side. The Physical State of a Substance The state of a substance whether solid, liquid or gas, can be determined using the following rules :- - Assume that room temperature is approximately 20'c. - If 20'c is below the Melting Point of the substance, it is a solid at room temperature ( Solid = Melting Point < Room Temperature). - If 20'c is between the Melting Point and Boiling Point of the substance, it is a liquid at room temperature ( Liquid = Melting Point <Room Temperature> Boiling Point ). - If 20'c is above the Boiling Point of the substance it is a gas at room temperature ( Gas = Room Temperature > Boiling Point). Families of Elements The name given to the modern-day arrangement of the elements is called the periodic table. The non-metals are found on the right side of the periodic table. The metals are found on the left side of the periodic table. The transition metals are metals in the centre of the periodic table. A 'group' in the periodic table is a vertical family of elements with similar properties. The group known as 'the alkali metals' are group 1 of the periodic table. The group known as 'the halogens' are group 7 of the periodic table. The group known as the 'noble gases' are group 8 of the periodic table. Examples of chemical and physical similarities of elements in Group 1 are: they are all soft metals which are shiny and silver, and they all react violently with water. Examples of chemical and physical similarities of elements in Group 2 are: they are all shiny and silver coloured, and they all react with acids and steam. Alkali metals are kept under oil, this is to prevent them from reacting with moisture in the air ( as alkali metals react violently with water). The noble gases are often referred to as the 'inert gases' as they are very unreactive. Some uses of the noble gases include: Helium - weather balloons, and neon lights. The similarity of the elements…

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New this week is a set of worksheets on finding fractions of lengths. Fractions is one of those subjects which can cause a lot of problems so it is important to get a sound early understanding. Children should come into Year 2 (age 6-7) being able to recognise halves and quarters and knowing that a half is one of two equal parts of an object, shape or quantity and a quarter is one of four equal parts. In Year 2 this knowledge is developed to include recognising one third, two thirds, two quarters and three quarters of shapes, sets of objects, quantities and lengths. Finding fractions of shapes can involve shading in or cutting out certain amounts of a shape e.g. shading two thirds of a rectangle. The important concept here is that the fractions must be of equal size. Finding fractions of sets of objects is usually done on a practical basis e.g. take 12 bricks and sort them into three equal piles – each pile is one third of the total number of bricks. This can also be done pictorially and strengthens the link between finding fractions and division. Finding fractions of quantities means finding a fraction of a number e.g. find a third of 6. This is a development from using shapes and objects and should only be done when children are confident with working with objects to find fractions. A key aspect of fractions is recognising equivalence. Put simply, this is the understanding that a half is equivalent to, or the same as two quarters, that four quarters is equivalent to one whole one etc. Another important aspect of work with fractions in Year 2 is counting in halves and quarters. By the end of the year children should be familiar with terms such as part, fraction, three quarters, one third and two thirds and be able to write these fractions in both words and numbers. Whilst we recommend that much of the fractions work in Year 2 should be practical in nature we have plenty of written material to reinforce the practical work. Why not take a look now? Once all this has been achieved children will be ready to move onto Year 3 work when much more is done on equivalent fractions, comparing fractions and even adding and subtracting simple fractions.

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Classroom functions are the purposes for which we use language in the classroom. These functions are many and varied, for example explaining and instructing. for each classroom function there are different exponents we can use. The choice of exponents depends on the learning context and purposes, the learners’ needs, their age and the level. When we choose language that is right for the situation and our audience, we say that we use language appropriately. In the exercises below you will find the next vocabulary: |Set a question||Stimulate discussion||Report back||–||–| LANGUAGE IN CLASSROOM.

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Why do this problem? When we use structured apparatus such as Cusenaire rods, dominoes, Numicom etc. we often assume that children understand more about the structure than perhaps they do. This activity encourages children to explore the structure in their own way - and you may be surprised at how many different ways there are. You could use this activity in one of two ways, depending on your children. The most obvious way is to focus on the different patterns that can be built up, but you could also use the activity to focus on the explanation or justification of the children's description or argument. You might like to have a go yourself before offering this activity to the children ... You will need several sets of dominoes (you could make laminated card sets from this print out ), one set between three or four children. If the dominoes are usually stored in a box, transfer them to a bag so that the children don't have a sense of a box being full. Ask the children to tip the dominoes out onto the table and have a look at them, perhaps having an opportunity to play with them and arrange them into different patterns if this is the first time they have seen them. Suggest that they may or may not be full sets and that before we can use them for a game we need to know if any are missing. Could they help you by finding out? Allow some time for this. When a group gives you a definitive answer ask them how they know and challenge them to arrange the dominoes on the table in some way to show you that they have/have not got a full set. Again allow some time for this. When, and if, appropriate you could suggest that the children move around the classroom to have a look at what other groups have done. You may then want to offer a little more time for those groups who haven't made much progress to have another go, having seen others' responses. Groups will respond in different ways. In increasing order of sophistication, groups may: - play a domino game where they match dominoes into a long train or loop, for example: - make piles or groups of dominoes with numbers in common, for example: - arrange the dominoes into a pattern or array, for example: In each case, ask how the pattern/structure they have chosen helps. The most sophisticated explanations will use the idea of all possible pairings of the numbers 0-6. The interactivity here may be helpful for whole class discussions of this activity. How many are there with blanks? Are there the same number of dominoes with ones? Tell me how you're arranging them. Why did you choose that way? Could you organise them in a different way? How does this show you that you have/haven't got them all? What if you had a set of 0-9 dominoes (download a set here ). How many do you think you would have? Do you need to make a set? How else could you record your ideas? The task Amy's Dominoes is a natural extension to this activity and can be solved using the dominoes as a resource, or without them by more confident children. Reducing the number of dominoes can make a pattern easier to spot. Offer a subset, say 0-4, and allow time to play and look for patterns before asking if they have a full set.

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Introduction to Logic |Unit level:||Level 2| |Teaching period(s):||Semester 2| |Offered by||School of Mathematics| |Available as a free choice unit?:||N The course unit unit aims to introduce the student to the idea of formalising arguments, both semantically and syntactically, and to the fundamental connection between these approaches. Logic is the study of arguments: what they are and what it means to say that they are sound. As such it is central to Mathematics, Philosophy and, to an increasing extent in recent years, Computer Science. Most of this course unit will deal with the most basic sort of logical argument (i.e., in everyday parlance, what we mean by 'A follows from B'), namely those which depend for their soundness simply on the commonly agreed interpretations of the logical connectives 'not', 'and', 'or' and 'implies'. That is referred to as propositional logic. We shall characterise the above notion of 'follows' in two fundamentally different ways, firstly in terms of preservation of truth (semantically), and secondly in terms of the formal rules it obeys (proof theoretically, or syntactically). The highlight of the course unit will be the Completeness Theorem for Propositional Logic, which tells us that these two quite different characterisations are equivalent. This is the younger sibling of the Completeness Theorem for Predicate Logic.That is a fundamental result for Mathematics which says that one can set up a notion of formal mathematical proof which is strong enough to capture mathematical truth: if something isn't formally provable then there must exist a counterexample. The propositional logic version of that theorem already allows us to introduce the key concepts and to see how a proof of such a general result can be achieved. In the final few lectures the student is introduced to some basic ideas about predicate logic. This deals with languages which allow the use of variables together with the quantifiers "for all..." and "there exists..." as well as functions, relations and constants. Such languages are of far greater expressive power than those of propositional logic and using them one can, in principle, formalise any mathematical argument. The Compactness Theorem for Predicate Logic will be stated and simple applications will be given. This part of the course unit serves as a brief introduction to these logics with quantifiers and to concepts which will be used in some level 3/4 units in Logi (for instance, the level 3 logic course contains a proof of the Compactness Theorem). On completion of this unit successful students will be able to: - formalise arguments in propositional logic both semantically and syntactically and understand how these are connected (via the Completeness Theorem); - in simple cases be able to determine whether 'A follows from B' is true, using a variety of methods; - be able to interpret formulas and sentences of predicate logic in mathematical structures and apply the compactness theorem in simple cases. Future topics requiring this course unit The course unit forms a coherent subject on its own, and provides necessary background knowledge for the third and fourth level Logic course units. - Other - 20% - Written exam - 80% Assessment Further Information - Two in-class tests; Weighting within unit 20% - 2 hours end of semester examination; Weighting within unit 80% 1. Motivation, syntax, propositional variables, connectives, propositional terms. 2. Valuations, logical consequence, logical equivalence, truth tables, satisfiability, disjunctive normal form, interpolation, adequate sets of connectives. 3. Rules of proof, formal proofs, the Soundness Theorem. 4. The Completeness and Compactness Theorems. 5. Languages for Predicate Logic, structures, interpretations, and the statement of the Compactness Theorem for Predicate Logic, with examples. Course unit notes will be provided. It will not be necessary to buy any books, but there a number of good books around which the student might enjoy (although they all tend to use substantially different notation, so that they are definitely not alternatives to the course unit notes), for example: H.B. Enderton, A Mathematical Introduction to Logic, (second edition) Academic Press 2001, ISBN 0122384520. E. Mendelson, Introduction to Mathematical Logic, Wadsworth and Brooks 1997, ISBN 0534066240. I. Chiswell and W. Hodges, Mathematical Logic, Oxford University Press 2007, ISBN 0199215626 (more elementary than the two above). W. Hodges, Logic, Penguin, 2nd revised edition 2001, ISBN 0141003146 (aimed at a more general readership; more about the relations with natural language and philosophy) Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding. In-class tests also provide an opportunity for students to receive feedback. Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour. - Lectures - 22 hours - Tutorials - 11 hours - Independent study hours - 67 hours

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New research has expanded on the discovery of a strange phenomenon called blackbody force, showing that the effect of radiation on particles surrounding massive objects can be magnified by the space that warps around them. The find could affect how we model the formation of stars and planets, and even help us finally detect a theoretical form of radiation that allows black holes to evaporate. In 2013, physicists announced radiation emitted from objects called ‘blackbodies’ could not only nudge small particles away, but tug them closer. What’s more, for hot-enough objects with only a small amount of mass, the pushing force could be stronger than their gravitational pull. If you’ve never come across the term, a blackbody is any opaque object that absorbs visible light, but doesn’t reflect or transmit it. Technically, blackbodies describe theoretically perfect objects that cannot reflect any light at all. Physical examples such as the carbon nanotube materials used to make the crazy-looking Vantablack coatings come pretty close. It’d be a mistake to think of all blackbodies as, well, black – they do emit radiation as their particles jiggle about, making them a useful way to describe an object’s thermal properties. Four years ago, a team of Austrian researchers figured out that the radiation emitted by a blackbody should have a rather curious effect on nearby atoms. To understand this effect, it helps to know that atoms can move and change direction when the photons they absorb cause a shift in their momentum. Given the right conditions, objects as large as a cell can be nudged around by a beam of light – a phenomenon commonly used in a form of technology called optical tweezers. Physicists have known for about a century that electromagnetic radiation can change the properties of nearby atoms through the Stark effect, which changes the positions of its electrons to sit in a lower energy state. This happens to make them more likely to move towards towards the brighter parts of a beam of light. The Austrian researchers put two and two together, showing how heat radiation could cause light to not only push particles away, but thanks to the Stark shift, they could also be pulled towards the object. “The interplay between these two forces – a typically attractive gradient force versus repulsive radiation pressure – is routinely considered in quantum optics laboratories, but it was overlooked that this also shows up with thermal light sources,” lead researcher Matthias Sonnleitner from the University of Innsbruck told Phys.org back in 2013. While force is incredibly weak, they also showed that the radiation’s net pulling power could actually be greater than the tiny amount of gravity produced by minuscule, hot objects, having implications for particles smaller than a dust grain. “These sub-micron-sized grains play an important role in the formation of planets and stars or in astro-chemistry,” said Sonnleitner. “Apparently, there are some open questions on how they interact with surrounding hydrogen gas or with each other. Right now, we are exploring how this additional attractive force affects the dynamics of atoms and dust.” Fast-forward to now, and another team of physicists has taken up where Sonnleitner and his colleagues left off, exploring the effect of both the blackbody’s shape and its effect on the curvature of surrounding spacetime on this optical attraction and repulsion. In particular, they calculated the warping of space – or topology – around a spherical and a cylindrical blackbody, and measured how the differences might affect the blackbody radiation forces. They found the curvature of the spherical blackbody and the topology of space surrounding it had a magnifying effect on the attractive force due to both the effect of gravity and the angle at which the radiation struck the particles. This wasn’t the case for the cylinder, with its flat surface and surrounding space, where the blackbody effect wasn’t magnified. While the effect wouldn’t be detectable in the laboratory, or even for objects the size of our Sun, for massive blackbody objects like neutron stars or more exotic forms of space-bending physics, this effect could make a significant difference. “We think that the intensification of the blackbody force due to the ultradense sources can influence in a detectable way the phenomena associated with them, such as the emission of very energetic particles, and the formation of accretion discs around black holes,” lead researcher Celio Muniz from Ceará State University, Brazil, explained to Phys.org. The team also applied the previous findings on the blackbody force to a concept called a global monopole – a theoretical point similar to an electric charge, which affects the shape of surrounding space without gravity – as well as another theoretical warping of space called a cosmic string. “This work puts the blackbody force discovered in 2013 in a wider context, which involves strong gravitational sources and exotic objects like cosmic strings as well as the more prosaic ones found in condensed matter,” Muniz said.

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|Objectives of this unit: The students will learn: Show the students the book "The Librarian Who Measured the Earth" by Kathryn Lasky (Little, Brown and Co., 1994). (You can find out more about the book at Amazon.com) As you tell them the story, show them the illustrations in the book. You can also coordinate your talk with the pages on this website. The suggested pages will be indicated below. Question: Do you think that people in 200 BC knew that the world was round? If you think yes, then what evidence did they have? After students have offered opinions, have them look at the first page of the story. As the librarian of the world renown library in Alexandria, Eratosthenes had access to the latest scientific knowledge of his day. He believed the earth was round. But how "round" was it? That was the question that stumped him. He may have imagined that the cross-section of the earth was like an orange sliced in half. You could see the sections of the orange. Also, if you walked along the edge of the orange your path would be circular. We know how to measure distances between two places on a flat surface. But how do you measure something round? Hold up a globe and ask the students how they might measure this globe. The suggestion may be to use a string, wrap it around the globe, and measure the wrap distance. Take a piece of string or rope, wrap it around the earth, mark the string, unwrap it, and measure the rope with a ruler.Have the students try it with the globe. Does it matter where the string is wrapped? (Yes, it should be at the widest possible place.) After the student comes up with an answer, ask the class if Eratosthenes might have done it this way. Walking around the world would be very difficult. Certainly, if he didn't get tired of walking he would not have managed the oceans. Sailing ships were not able to cross the oceans back then. So what other way might he have done this? How about option 2? What if Eratosthenes could drill a tunnel to the other side of the earth and measure that distance could he then figure out the circumference of the earth? The answer is yes. Eratosthenes knew this because he had studied some geometry. Now have the class do an experiment to help them discover the relationship between circumference and diameter. Here are two activities that the students can do. Hold up a circle and a diameter (i.e. a circular hoop and a stick with the same length as the diameter of the hoop.) Show them that the stick fits exactly across the widest part of the hoop. Question: If you know the length of the stick can you figure out the length of the hoop? Tell them that in the activity that follows they will have to come up with a conjecture about diameters and circumferences. Activity: Measuring "measurable" circles. In this activity students measure circles which unlike the earth can be measured directly. The students will discover that there is a relationship between the circumference and the diameter. (Do the Pi activity at http://mathforum.org/paths/measurement/disc.pi.html) Once they understand the relationship between circumference and diameter, have them click on this Javasketchpad applet (Pi Mystery) and explain why the "times number" doesn't change when the circle gets bigger or smaller. In this Javasketchpad sketch notice that the diameter is in pixels. If you multiple the diameter by the "times number" it will equal the circumference. On the Javasketchpad, drag the center of the circle to make it bigger (or smaller). Notice that the times number doesn't change much. Why not? What's another name for the "times number"? (pi) The important thing for students to understand is that the cirumference is always a little more than 3 times (pi) the diameter and it doesn't matter what the size of the circle is! Another way to say this is that the ratio of the circumference to the diameter stays the same as you change the length of the diameter. The proportionality of C / D holds! Since straight lines are usually easier to measure than round ones, it is easier to measure the diameter than the circumference. If Eratosthenes knew the earth's diameter all he would have to do is multiply the diameter by 3 1/7 or 3.14 (approximations for pi) to determine the circumference. Back to Teachers Guide

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Ice as we know it is pretty much the same whether it’s flowing as a Greenland glacier or covering one of Saturn’s icy moons, but it can behave very differently from one location to the next. The surface it’s sliding over, how much weight it’s carrying, chemicals in the environment, even the energy of the tides can affect its flow. To understand how quickly ice from glaciers and ice sheets can raise sea level or how moons far across the solar system evolved to hold vast, ice-covered oceans, we need to be able to measure those forces at work. Geophysicists Christine McCarthy, who studies ice, and Heather Savage, who works with rock mechanics, teamed up to develop a way to do just that at Columbia University’s Lamont-Doherty Earth Observatory. With engineer Ted Koczynski and former student Michael Nielson, they designed and built a new instrument that measures how ice responds under a wide range of conditions important to Earth and planetary science. At the heart of the new device is a small block of ice sandwiched between two rocks that simulate the texture of the rock bed beneath a glacier. The rocks are pushed together with a force that replicates the weight of the glacier overhead. Then a hydraulics-driven piston slowly pushes the ice down past the rocks—either steadily or in waves that imitate tidal changes—and sensors measure the forces at work. The scientists keep the whole thing at a constant temperature by circulating a water-methanol mixture through cooling blocks attached to the side of an aluminum cryostat that is chilled to match the temperature at the bottom of Earth’s glaciers, typically between 0°C and -20°C. To test conditions on much colder icy moons, the team is developing a second cryostat with fluid that circulates through a liquid nitrogen-cooled chamber to reach -90°C. The design borrows from a classic device called a biaxial deformation apparatus, which the Lamont Rock Mechanics Lab has used for years to study the behavior of faults and earthquakes. Other universities have tried to study ice deformation using large biaxial rock devices with some success. Lamont’s ice-specific version is designed with special temperature controls and sensors to explore three basic properties fundamental to the behavior of ice: friction, viscosity, and anelasticity, which is the ability to turn periodical mechanical energy, such as from tides, into heat. The team’s first experiments, described in the latest issue of the journal Review of Scientific Instruments, used a simple system of ice on rock to test out the instrument. A second paper currently in review explores the rate-state friction laws for the ice-on-rock system using two classic rock mechanics experiments. One experiment measured changes in friction by changing the speed that the ice was pushed between the rocks from a steady pace to a sudden jump in velocity. Another explored “frictional healing” by starting and stopping the movement, with increasing delays between movement. The team is now testing rough-up rock surfaces to more accurately mimic the till and the fine rock dust created on the glacial bed as glaciers scour the rock below. “One by one, you start adding complications, and that’s where you get to really contribute to the field,” McCarthy said. “You can say definitively, this affects this in this known way.” Models involving ice flow tend to treat the behavior of ice at the base of the glacier as either frozen and not moving or sliding away on melt, McCarthy said. “Our study has shown that there’s a continuum of sliding based on temperature,” she said. “We’re trying to provide more realistic values for models that try to predict how fast glaciers are moving over time. Particularly with changes in climate and other forcings, we want to know those long-term predictions.” NASA’s interest in the new cryogenic deformation apparatus goes far beyond Earth’s cryosphere to icy moons elsewhere in the solar system where temperatures are much colder. Studies of some of the moons orbiting Saturn and Jupiter have suggested that they are covered by ice, possibly with oceans underneath. On Saturn’s moon Enceladus, where temperatures reach an estimated -180°C, the Cassini spacecraft found geysers in the moon’s icy crust, raising more questions about ice behavior. It’s possible that chemicals present in the moon’s environment could significantly lower the melting point of ice, similar to how salt tossed on a sidewalk in winter prevents ice from forming, McCarthy said. Her team plans to incorporate small amounts of ammonia and sulfuric acid in future experiments to try to replicate that behavior at low temperatures and explore whether melt can be produced with small amounts of frictional heating, even at such low planetary temperatures. The project to design an apparatus to study forces on ice started with a $25,000 grant from the Lamont-Doherty Earth Observatory Innovation Fund, established by the Observatory’s Advisory Board. McCarthy’s team used that to start the design and secured larger grants from NASA, the National Science Foundation, and the Brinson Foundation. “The goal of the Innovation Fund is to give you the seed money, get started, and get some research funds to take it somewhere,” McCarthy said. “This is definitely a success story.”

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Trilobites are one the of earliest known arthropods. The are believed to have existed for about 270 million years and are considered to be one of the most successful early animals. Thanks to their hard exoskeletons, they where able to be fossilized in perfect condition, making them easier to study. Scientists consider trilobites to be the single most diverse class of extinct organisms. The smallest known trilobites are under a millimeter long, while the largest are over two feet long. All trilobites have a similar body with a head, thorax, and tail piece similar to insects. They also all have a central axial lobe that runs down the middle of their body like a spine, as well as a pleural lobe on either side. Beyond this basic body plan, there is incredible diversity among the different species. The majority of early trilobites are believed to be predators. They are believed to have eaten invertebrates such as worms. Evidence of this can be found in trace fossils which show trilobite trails suddenly stopping above worm burrows, suggesting that the trilobite was on the hunt for worms and stopped to catch one when they came across a burrow. This theory is further supported both by evidence of predatory trilobite ancestors and the fact that larger species of trilobites had larger digestive tracts, perfect for breaking down large chunks of prey. The earliest known trilobites were believed to have existed between 540 and 520 million years ago. Trilobites are thought to have originated from present-day Siberia and had radiated outward. They were believed to have originally had no eyes or facial structures, but evolved to have them later on. Trilobites developed one of the first sophisticated visual systems in prehistoric animals. There are currently three official types of eyes found in trilobites: holochroal, schizochroal, and abathochroal. The most common type for early trilobites to have was holochoral. As with the rest of the trilobite body, mutations were rampant among the animals, leading to many variations in eyes. Phacops trilobites had extremely well-developed eyes, giving them a perfect field of vision. Opipeuter trilobites had eyes that were so large, they covered a majority of the head. Several bottom-feeding trilobites had underdeveloped eyes or lost their eyes all together. The first time trilobites appear on the fossil record is during the pre-Cambrian era which was about 700 million years ago. At first, they appear to all be fairly uniform in shape and size, with little diversity or evolution. They seem to have existed in modern-day Siberia just before the breakup of the super continent Pannotia. After the breakup of Pannotia and the major shift in tectonic plates, trilobites were displaced from Siberia, which allowed them to migrate to different parts of the planet and to diversify. During the Cambrian era, which lasted for about 56 million years, trilobites rapidly diversified into their major orders: Redlichiida, Ptychopariida, Agnostida, and Corynexochida. In the middle of the Cambrian, trilobites had their first extinction crisis. The trilobites that survived developed different body shapes and thicker shells for defense against predators. There was a second, more intense, mass extinction event at the end of the Cambrian that is attributed to major environmental changes such as the loss of continental shelf area of the Laurentia continent, which makes up modern-day North America. This extinction event wiped out all Redlichiida as well as the majority of trilobites in the other orders. The Ordovician era lasted 41.2 million years and is marked by the movement of many brachiopods to new areas and many new appearances on the fossil record. Life flourished during this era, as it had done during the Cambrian era. Arthropods such as trilobites dominated the oceans.The Great Ordovician Biodiversification Event is credited with the rapid increase of diversification of all life on Earth. New forms of trilobites such as Phacopida, Trinucleioidea, and Agnostida took over where the Cambrian forms had gone extinct. Trilobites had evolved to live in new environments such as reefs and were continuing to evolve at an unusual rate. At the end of the Ordorvian, climate temperatures began to cool, with oceans going from 113 degrees fahrenheit to temperatures similar to modern oceans. Sea levels dropped as a result of glacial formations as well. While trilobites faired through the mass extinction better than many other organisms, they weren’t completely unscathed. Both Trinucleioidea and Agnostida went extinct as well as many other early-Ordovician animals. The Silurian era lasted 24.6 million years. The Silurian began just after the mass extinction of 60% of Ordovician marine life. Virtually no early Ordovician trilobites survived the mass extinction, but about 74% of the late Ordovician trilobites did, which accounted for all Silurian trilobite ancestors. One major evolutionary milestone of the Silurian was the evolution of jawed fish, a new predator for trilobites. The stable ocean temperature allowed trilobites to become very diverse and abundant. While the ocean temperature stabilized during the Silurian, the carbon cycle and weather didn’t. The silurian had a higher concentration of isotopic excursions than any other era. Thanks to rapid sea-level change occurring together with these isotopic excursions, trilobites were particularly impacted by bursts of mass extinction. The Devonian era lasted 60 million years and is characterized by the rapid evolution and migration of life on land. While other arthropods began to develop on land, trilobites remained in the seas and flourished. The sea levels remained high, which didn’t make it necessary for trilobites to move to land. Lichida and Phacopida were the dominating trilobite species. The end of the Devonian era marked the worst mass extinction of trilobites. The cause of the mass extinction is still being debated, but there is no doubt that marine life was the most severely-effected by it. Trilobites in particular were severely impacted, with three orders and all but five families becoming extinct. Only the order Proetida survived. The end of the trilobites came near the end of the Permian era. Proetida, the only surviving order of trilobites from the Devonian era, lacked diversity and halted future evolution. The Permian era ended with the largest mass extinction in Earth’s history. This extinction primarily effected marine life with calcium carbonate skeletons, as the trilobites had. It was during this extinction event that all trilobites became extinct. Today, isopods are the closest living things related to the ancient trilobites. They belong to the same phylum of hard-shelled, segmented, multi-legged animals called Arthropoda that trilobites did. These isopods exist both in the sea, as trilobites had, and on land.

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What are the steps of the order of operations? Why is it important that you follow the steps rather than solve the problem from left to right? Write an expression for your classmates to simplify using at least three of the following: o Groupings: Parenthesis, brackets, or braces o Multiplication or division o Addition or subtraction Consider participating in the discussion by simplifying a classmate’s expression, showing how the expression would be incorrectly simplified if computed from left to right, or challenging the class with a complicated expression. Respond to your initial post and provide your classmates with the answer to your expression. o What is the difference between an equation and an expression? Include an example of each. o Can you solve for a variable in an expression? Explain your answer. o Can you solve for a variable in an equation? Explain your answer. o Write a mathematical phrase or sentence for your classmates to translate. What resources are available to help you do well in this course? Which resources do you think will help you the most? Why? How do you plan to use the resources available to optimize your learning over the next 8 weeks? If the cost of a cell phone has decreased 400% during the past 10 years, does that correspond to a cost decrease of four times? Explain your answer as though you were talking to someone who has never taken algebra. What are the four steps for solving an equation? Should any other factors be accounted for when solving an equation? Should any factors be accounted for when explaining how to solve an equation? Explain your answer. How do you know if a value is a solution for an inequality? How is this different from determining if a value is a solution to an equation? If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution for both the equation and the inequality? Write an inequality and provide a value that is, or is not, a solution to the inequality. Respond to a classmate and determine whether or not the solution provided is a solution to the inequality. If the value he or she provides is a solution, provide a value that is not a solution. If the value is not a solution, provide a value that is a solution. Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Write an inequality for your classmates to solve. In your inequality, use both the multiplication and addition properties of inequalities. Describe in your own words how to solve a linear equation using the equality properties. Demonstrate the process with an example. Next, replace the equal sign in your example with an inequality by using the less than or greater than sign. Then solve the inequality. How do you know if a value is a solution for an inequality? How is this different from determining if a value is a solution to an equation? If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be solution to both the equation and the inequality? Write an inequality and provide a value that may or may not be a solution to the inequality. If a line has no y-intercept, what can you say about the line? What if a line has no x-intercept? Think of a real-life situation where a graph would have no x– or y-intercept. Will what you say about the line always be true in that situation? Provide an example of at least five ordered pairs that do not model a function. The domain will be any five integers between 0 and 20. The range will be any five integers between -10 and 10. Your example must not be the same as those of other students or the textbook. Why does your example not model a function? What similarities and differences do you see between functions and linear equations studied in Ch. 3? Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer. Create an equation of a nonlinear function and provide two inputs for your classmates to evaluate. Systems of equations can be solved by graphing, using substitution, or elimination. What are the pros and cons of each method? Which method do you like best? Why? What circumstances would cause you to use a different method? Respond to your classmates by indicating pros and cons they may not have considered. If you chose different methods, try to persuade them to see the value of the method you like best. Describe situations in which you might use their methods of solving equations. After taking this college algebra course, choose two of the following prompts (in two separate posts) to express your feelings or attitude about algebra: · Explain how you feel about mathematics now as compared to before you took this class. · My best kept secret about math is… · If math could be a color, shape, sound, etc., it would be…because… · When it comes to math, I find it difficult to… · I want to become better at math so that I… Has the content in this course allowed you to think of math as a useful tool? If so, how? What concepts investigated in this course can apply to your personal and professional life? In what ways did you use Adaptive Math Practice (AMP) for extra support?

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In this section we deal with plane mirrors. These are mirrors that are flat. In most cases the mirrors we see are pieces of glass with a silvered coating on the back, while in some cases the silvered coating may be on the front of the glass. Such a mirror is referred to as a front-surface mirror. Other objects behave like mirrors including smooth surfaces of lakes and ponds, windows, sides of aquariums, etc. What are the rules by which mirrors operate when light strikes them? That is our subject. When an ordinary object is placed in front of a plane mirror, it is sending light rays out from itself in all directions, either by emission or by reflection. This is shown here: Therefore the light rays that strike the mirror will be doing so from a wide variety of angles. What is the pattern for light's reflection and how does it depend on angle? In Reflection we picture a line perpendicular to the mirror at the point of reflection. This is called the Normal. (Remember when we used the normal to define the angles in Snell's Law.) The Law of Specular Reflection states that light reflecting from a plane mirror forms an angle to the NORMAL equal to the angle between the normal and the incident light. When an object is placed in front of a mirror, two different observers appear to see an image of the object in different places. The light, however, travels from the single object to the mirror and then to the respective observers. The manner in which it reflects must meet the conditions stated on the previously. Notice how the light reflects from the smooth surface of the mirror, creating congruent or equal angles to the normal at each place it strikes the mirror. The two observers only see light when it has been reflected from the mirror in the proper manner. It would appear that an infinite number of images is possible for a single object. Scientists believe, however, that there should only be a single image. What location could our two observers, or any other observers for that matter, agree upon? The observers' lines of sight can be extended back behind the mirror, to a place where the light rays both seem to originate. They can agree upon this one location, regardless of where they are standing. This is therefore the location of the image. What is the nature of the light at the image location? In fact, there is no light there. This is only the apparent source of the light so it is referred to as a virtual image. Virtual images are ones that are not formed by putting the light rays together, but only appear to exist as the apparent source of the light rays. What is the geometry of the plane mirror's image? In the next series of drawings we can follow the geometric proof of where the image is located. Use the vertical angle theorem to establish other angles congruent to the ones you had in the last drawing. And use the complementary angle theorem to establish two more sets of congruent angles. Now, using the logic of ASA, the two triangles formed, one on the object side of the mirror, the other one behind the mirror, can be proven congruent. Thus the triangle "behind" the mirror is the same size and shape as the triangle in front. The object and its virtual image can be joined by a line which is perpendicular to the mirror, forming altitudes for the two triangles. Now because the two perpendicular lines are altitudes for triangles that are exactly the same shape and size, their lengths must also be the same. This leads us to the following conclusion: The image formed by a plane mirror will be as far behind the mirror as the object is in front of it. A line joining the two will be perpendicular to the mirror. Now that we know where the image is located, we shift our attention to the size of the image. From our life experiences, we notice that our image appears to get smaller as we move away from a mirror. How else could an entire truck's image fit into the small rearview mirror on a car? Our object (shown on the left in the diagram below) has an image which is as far behind the mirror as the object is in front. Thus the lengths of the two perpendicular lines are equal. This equality of distance also applies at every point. In particular, we may wish to look at the line joining the "top" of the object and the "top" of the image. The line segments are equal in length and perpendicular to the mirror. The same holds true for the line segments joining the "bottom" of the object and image. Now we look at both lines, noticing that since they are both pependicular to the mirror, they must be parallel to each other. Thus the distance from top to bottom on the object is the same as from top to bottom on the image. They're the same size!! The image formed by a plane mirror is the same size as the object. Why does the image look smaller, then, the further we go from a mirror? It's a simple matter of perspective. Something the same size, but further away, takes up a smaller angle of our vision. Therefore it seems to be smaller. MORE ABOUT THE IMAGE: A final question for thought, how is the image related to the object? It's the same size and the same distance from the mirror. But something's not correct. If we stand before a mirror wearing a sweatshirt with STANFORD written on it, our image will be wearing a sweatshirt with on it. This brings up the nature of the image and how it's related to reality. Let's make some further observations. When we point up, does the image point up or down? It points Up, the same as we do. If the mirror is on the north wall or your room, and you point towards the east, which direction does your image point? East, also If you point towards the mirror (away from yourself), which direction does the image point? In the opposite direction, Towards You. Thus, the image is reversed from front to back, not left-to-right as we are used to thinking! Hint: The answer to the test question isn't that the image in a plane mirror is inverted, it's upright and reversed front-to-back. Even more fascinating things happen when we employ two or more plane mirrors in combination. Check out the section on Multiple Mirrors or simply go back to the Mirror Menu or to the Main Menu.

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Introduction to lesson: This lesson will introduce your students to basic addition facts from a totally different perspective. No need to memorize 100 addition facts, 30 to 35 are all you need to know. This lesson will give your students a visual and conceptual understanding of addition. Ten frames are a great tool to help students gain number sense, a conceptual and a visual understanding as to what addition really is. You may even wish to consider exploring other number frames to see how they could be used in the same manner to add in other number bases and how the same conceptual ideas hold true in all number base numeration systems. Materials included in this lesson: 1. A PowerPoint lesson containing 5 sections and 10 different activities to keep students involved in the lesson while they learn basic addition facts. This will give you freedom to walk around the classroom to observe student understanding while presenting the lesson. Be sure to run through the PowerPoint several times before using it in the classroom so you understand what is coming next with each click. 2. An activities worksheet to go along with each section of the PowerPoint. This will meet the needs of the kinesthetic learners, allow you to observe student participation in the lesson, and give students a reference for when they complete their homework. 3. A homework assignment geared to help students master the concept, not be overwhelmed with a large number of problems or copying each problem before applying the concept. 4. A note to parents to help them understand the reasons behind the lesson, what the lesson is on, and the expectations of the student. Remember, keeping the parents on board is crucial to enhancing students’ learning experience. 184 Slides and 10 Activities

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Maths 7-11 years Explaining numbers to children It is important that pupils have a clear understanding of numbers and how to use them. Younger children start establishing a clear understanding of units then they gradually progress to Tens. Visual aids such as conkers, beads, blocks or sometimes fingers can help establish the number concept As our number system is worked in BASE 10 each number has a place value. This means that its value depends on its position. In arithmetic the positions or columns are given names. This shows for example the number 965. For the number 9 6 5 we have: U = 5 units T = 6 groups of 10 = 60 H = 9 groups of 100 = 900 In these number examples the figures underlined have the following values: 3789 3 is 3000 (three thousand) 40327 40 is 40000 (forty thousand) 65891 8 is 800 (eight hundred) An even number is a number which can be exactly divided by 2 e.g 2 4 6 8 10. All other numbers are odd numbers e.g 1 3 5 7 9 11. A prime number is a number which can only be divided exactly by itself and by one. All prime numbers are odd numbers apart from 2. 1 is not a prime number 5 7 11 13 29 and 53 are examples of prime numbers. Square numbers are numbers whose dots can be arranged in the shape of a square. e.g. 16 Have fun with Numbers and Maths Please see the right side menu for the full range of maths topics covered.

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How big is that? Lesson 18 of 22 Objective: SWBAT to use scientific notation and the laws of exponents to compare the sizes of planets and stars How big are the planets in our solar system? How can we comprehend these volumes? Students start this class by reviewing a chart of our solar system and making notes in the margins. I ask them to write down any patterns they notice and make note of anything unexpected. This is the chart I give: Planet Mean Radii This is the wikipedia site I pulled it from: After we discuss their observations, I ask them a general question, "how do you find the number of times that one object will fit into another?" As we discuss this topic, I elaborate if students are stuck or unclear on what I mean, I ask, "what if you wanted to know how many times a ping pong ball would fit inside a basketball?" The goal is to get them to name the operation of division and why that is the perfect operation for the task. The second goal in this conversation is to review how we find the volume of a sphere. I like to bring up the connection to a cylinder (a sphere fills 2/3 of a cylinder with an equal base and height), but any interpretation of the formula will do. I like to review this process with a sample problem. For example, the volume of a ping pong ball with a radius of 40mm would be.... Before we calculate, I mention that I want all volumes today in km. I would ask them to consider if they want to convert before or after they calculate volume. Here I would advise students to convert before, because converting with cubic units can be tricky. On each table is a mystery bag. Inside students will find two images. They need to compare those images to an object in the solar system. The idea is to find out how many times bigger the volume of each object is than the one before it. For example, they might have a ping pong ball and the Star Sirius. If they choose to throw Earth into the mix, I want to know how many ping pong balls would fit into the volume of the Earth and how many would fit into the Star Sirius. I would also want to know how many times the volume of the Earth would fit into Sirius. Reversing the process, I also want to know what fraction of Sirius would fit into the Earth and what fraction of Sirius would fit into the ping pong ball. I would also want know what fraction of the Earth would fit into the ping pong ball. Essentially, I am asking students to make 6 multiplicative comparisons. If you have spherical objects with radii a, b and c where a < b < c, find: 1) the number of times the volume of a fits into b and c 2) the number of times the volume of b fits into c 3) the number of times the volume of c fits into a and b 4) the number of times the volume of b fits into a In the resources, I include photos of the objects that I use. I place one star and one non-star in each bag. Two important notes about the image resources: - The star files are named by star and the size of the radius of the star. For example, 883 R Antares.png is the file name for the Star Antares and 883 R is the radius of the star. The "R" stands for solar radius and is based off the size of the radius of our sun. Thus, students will also need: Solar Radius.png - The non-star objects are named appropriately, but the measurement that is given is the diameter. For example, 3.4 meters twine ball.jpg is the file name for the largest ball of twine with a diameter of 3.4 meters. This was initially done by accident, but ended up working really nicely as an opportunity to engage in mathematical practices. Students now have to discuss the terms radius and diameter in a lesson about scientific notation. The sizes of these stars are truly unbelievable. Each table has a different star but is perhaps unaware of how truly massive their star is. Unless they chose to compare it to the sun in our solar system, they might not have any reference for the incredible scale they are dealing with. I address with the summary by showing them this great image from wikipedia: Star-sizes.jpg As students share their findings, we extend the math by seeing if this image is correct. As a class we compare how many times larger each of the stars are to our sun. By constantly referencing our sun in the discussion, students get a sense of the massive size of these stars. Because this lesson is complex and deals with many aspects of scientific notation, I usually end with an exit ticket question, like how many times larger is this start than another. This is a good reference for me, because I like to follow up with a project. I need to know how well they handled this lesson in order to gauge how ready they are to start asking their own questions.

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Geometry for New Hampshire students enhanced with: visual, tactile and auditory. Identify and Describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. Correctly name shapes regardless of their orientations or overall size. Identify shapes as two-dimensional (lying in a plane, “flat”) or three dimensional (“solid”). analyze, compare, create, and compose shapes. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices's / “corners”) and other attributes (e.g., having sides of equal length). Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”

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In this unit, students will learn about the properties and rules they can use when working with shapes and angles. They will begin by classifying triangles and quadrilaterals, and will then learn how to calculate angles on a line, angles at a point, vertically opposite angles, angles in triangles and quadrilaterals, angles on parallel lines and exterior and interior angles of polygons. ABOUT THIS RESOURCE PACK: This pack is designed to provide teachers with complete lesson plans and classroom resources to teach excellent lessons. It is designed to both teach the mathematical content and draw students into deeper consideration of its implications, including mathematical reasoning and problem solving skills. THE PACK CONTAINS: 7 Lesson Plans: Full ready-to-use lesson plans on the following topics: - Classifying shapes - Angle rules - Angles in triangles - Angles in quadrilaterals - Angles on parallel lines - Exterior angles - Interior angles Lesson Resources: A variety of additional resources to accompany the lesson plans, including student worksheets and aids for students needing extra support. 2 Homework Activities: Further activities to give students to complete at home. Assessment: A series of questions to enable you to assess the progress of students in this unit of work.

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The parts of speech are the essential building blocks to teaching students good grammar. Understanding the parts of speech and how they fit together makes writing and reading make sense. Building Language Arts skills on the eight parts of speech can be a fun learning experience if taught creatively and with enthusiasm. Begin with nouns. A noun is a person, place, thing or idea. Get students to list as many nouns as they can. Put them in categories on an overhead or white board as they say them. Take the list of nouns students come up with (stop them before there are too many), and start asking for words that describe each one. List those in front of each word. These are adjectives. An adjective is a word that describes a noun. Ask students to look at each noun adjective pair and give it something to do. Example: Big dogs bark. Explain that this action word is a verb. List how the words do things. Example: Big dogs bark loudly. Tell students that how something does the action is an adverb. An adverb describes a verb, adjective or other adverb. Make another sentence to go with your first group. Ex: Look at the big dogs. They bark loudly. Explain to students that "they" in the second sentence refers to "big dogs" in the first. "They" takes the place of the noun "dogs" and is a pronoun. Add these words to the second sentence: around the neighborhood. "Around" is a preposition that implies a relationship. Where to they bark? Around the neighborhood. Identify or add the two final parts of speech, the conjunction and the interjection. "Look at the big and little dogs. Wow! They bark loudly around the neighborhood." The conjunction joins words, phrases and clauses and the interjection displays emotion and is usually followed by an exclamation point. - To reinforce grammar skills think about using the Grammar Rocks videos in your classroom. They address many grammar skills in a fun and memorable way.

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COMPLEMENTS INTRODUCTION: Basic binary digits are described as UNSIGNED values. This is because if you look at the string of bits (zeros and ones) there is no indicator whether or not this value is positive or negative. You must use an additional symbol "+" or "-" to indicate the sign of the number. There are some types of number systems where you can determine the sign of number without using an addition symbol. You can tell whether it is positive or negative by looking at the bits. Such representations are referred as SIGNED representations because you can determine the sign of the number from the number itself. In signed representations you the MOST SIGNIFICANT BIT (MSB) indicates the sign of the number. The MSB is the left most bit. If the MSB is equal to 0 then the number is positive. If the MSB is equal to 1 then the number is negative. e. g. 001111101 is positive ^ | The MSB is equal to zero e. g. 101101010 is negative ^ | The MSB is equal to one At this point you might ask yourself why bother with signed representations - we perform decimal based subtractions in every day life using base ten unsigned representations and we " re all happy and well adjusted people. The reason why it's important to learn about signed representations is because when the computer tries to subtract one number Y from another number X, it doesn't do so in the same way that we do: i. e X - Y Instead it uses a technique known as negating and adding: i. e. X + (-Y) which is still equal to X - Y CONVERSIONS (UNSIGNED BINARY TO SIGNED VALUES) This is summary of what you must do to convert an unsigned binary value to a complemented value. 1's complement 2's complement Binary value > = 0 No change No chang Binary value < 0 Swap the bits Swap the bits and add one to the result. Carry out Add it back in Ignore it Swapping the bits means we substitute 1's for 0's and 0's for 1's. DOING SUBTRACTIONS VIA COMPLEMENTS (ala Negate and Add) How do we do this with the negate and add First convert these numbers to binary: Base 10 Base 2 (must be signed! ) eg 4 0100 -6 -0110 = -2 I added one extra zero to the left hand side as an extra placeholder. When I convert these numbers to signed values, this digit it will represent the sign of the number. We cannot do a mathematical operation in the computer on minus six in this form. It must be converted to a SIGNED VALUE. You can use either a 2's complement representation or a 1's complement representation. But make sure that you keep straight which one you use (don't switch halfway thru a computation between a 1's and 2's complement representation or vice versa). e. g. Number to convert 1's complement 2's complement (flip bits) (flip bits + 1) -0110 1001 1010 Add the complemented values with to the original number above (negate and add remember). 1's complement way 2's complement way Number from above (4) 0100 0100 The complemented number 1001 1010 -- -- Summed Result 1101 1110 Convert to this value from a complemented form to regular binary -0010 -0010 Convert from binary -2 -2 to decimal Notice that there is no carry out so we con't have to worry about adding in the overflow or ignoring it. But this conversion only occurs for negative numbers. Look again at the circles that I drew in lab, a positive number is a positive number number matter what binary representation that you use. That means that if the MSB is equal to a zero, when we get to the second last step, when we try to find the equivalent unsigned binary value no conversions are necessary. A positive unsigned digit will look the same in signed (1's and 2's complement form). Here's another example on complements that does have an overflow bit (carry out): Done using 1's complement: Base 10 Base 2 10 1010 -3 -0011 Now here's comes the fun stage, molding the unsigned base two numbers into signed one's and two's complement representations. Base 2 Add zero to left Convert to 1's complement 1010 01010 01010 0011 00011 11100 Add the numbers 10 + (-3): 01010 +11100 -- Overflow = > 1 00110 Goes here -> +1 -- 000111.

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College PhysicsScience and Technology We can represent electric potentials (voltages) pictorially, just as we drew pictures to illustrate electric fields. Of course, the two are related. Consider [link], which shows an isolated positive point charge and its electric field lines. Electric field lines radiate out from a positive charge and terminate on negative charges. While we use blue arrows to represent the magnitude and direction of the electric field, we use green lines to represent places where the electric potential is constant. These are called equipotential lines in two dimensions, or equipotential surfaces in three dimensions. The term equipotential is also used as a noun, referring to an equipotential line or surface. The potential for a point charge is the same anywhere on an imaginary sphere of radius surrounding the charge. This is true since the potential for a point charge is given by and, thus, has the same value at any point that is a given distance from the charge. An equipotential sphere is a circle in the two-dimensional view of [link]. Since the electric field lines point radially away from the charge, they are perpendicular to the equipotential lines. It is important to note that equipotential lines are always perpendicular to electric field lines. No work is required to move a charge along an equipotential, since . Thus the work is Work is zero if force is perpendicular to motion. Force is in the same direction as , so that motion along an equipotential must be perpendicular to . More precisely, work is related to the electric field by Note that in the above equation, and symbolize the magnitudes of the electric field strength and force, respectively. Neither nor nor is zero, and so must be 0, meaning must be . In other words, motion along an equipotential is perpendicular to . One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor. This implies that a conductor is an equipotential surface in static situations. There can be no voltage difference across the surface of a conductor, or charges will flow. One of the uses of this fact is that a conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding. Grounding can be a useful safety tool. For example, grounding the metal case of an electrical appliance ensures that it is at zero volts relative to the earth. A conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding. Because a conductor is an equipotential, it can replace any equipotential surface. For example, in [link] a charged spherical conductor can replace the point charge, and the electric field and potential surfaces outside of it will be unchanged, confirming the contention that a spherical charge distribution is equivalent to a point charge at its center. [link] shows the electric field and equipotential lines for two equal and opposite charges. Given the electric field lines, the equipotential lines can be drawn simply by making them perpendicular to the electric field lines. Conversely, given the equipotential lines, as in [link](a), the electric field lines can be drawn by making them perpendicular to the equipotentials, as in [link](b). One of the most important cases is that of the familiar parallel conducting plates shown in [link]. Between the plates, the equipotentials are evenly spaced and parallel. The same field could be maintained by placing conducting plates at the equipotential lines at the potentials shown. An important application of electric fields and equipotential lines involves the heart. The heart relies on electrical signals to maintain its rhythm. The movement of electrical signals causes the chambers of the heart to contract and relax. When a person has a heart attack, the movement of these electrical signals may be disturbed. An artificial pacemaker and a defibrillator can be used to initiate the rhythm of electrical signals. The equipotential lines around the heart, the thoracic region, and the axis of the heart are useful ways of monitoring the structure and functions of the heart. An electrocardiogram (ECG) measures the small electric signals being generated during the activity of the heart. More about the relationship between electric fields and the heart is discussed in Energy Stored in Capacitors. Move point charges around on the playing field and then view the electric field, voltages, equipotential lines, and more. It's colorful, it's dynamic, it's free. - An equipotential line is a line along which the electric potential is constant. - An equipotential surface is a three-dimensional version of equipotential lines. - Equipotential lines are always perpendicular to electric field lines. - The process by which a conductor can be fixed at zero volts by connecting it to the earth with a good conductor is called grounding. What is an equipotential line? What is an equipotential surface? Explain in your own words why equipotential lines and surfaces must be perpendicular to electric field lines. Can different equipotential lines cross? Explain. Problems & Exercises (a) Sketch the equipotential lines near a point charge + . Indicate the direction of increasing potential. (b) Do the same for a point charge . Sketch the equipotential lines for the two equal positive charges shown in [link]. Indicate the direction of increasing potential. [link] shows the electric field lines near two charges and , the first having a magnitude four times that of the second. Sketch the equipotential lines for these two charges, and indicate the direction of increasing potential. Sketch the equipotential lines a long distance from the charges shown in [link]. Indicate the direction of increasing potential. Sketch the equipotential lines in the vicinity of two opposite charges, where the negative charge is three times as great in magnitude as the positive. See [link] for a similar situation. Indicate the direction of increasing potential. Sketch the equipotential lines in the vicinity of the negatively charged conductor in [link]. How will these equipotentials look a long distance from the object? Sketch the equipotential lines surrounding the two conducting plates shown in [link], given the top plate is positive and the bottom plate has an equal amount of negative charge. Be certain to indicate the distribution of charge on the plates. Is the field strongest where the plates are closest? Why should it be? (a) Sketch the electric field lines in the vicinity of the charged insulator in [link]. Note its non-uniform charge distribution. (b) Sketch equipotential lines surrounding the insulator. Indicate the direction of increasing potential. The naturally occurring charge on the ground on a fine day out in the open country is . (a) What is the electric field relative to ground at a height of 3.00 m? (b) Calculate the electric potential at this height. (c) Sketch electric field and equipotential lines for this scenario. The lesser electric ray (Narcine bancroftii) maintains an incredible charge on its head and a charge equal in magnitude but opposite in sign on its tail ([link]). (a) Sketch the equipotential lines surrounding the ray. (b) Sketch the equipotentials when the ray is near a ship with a conducting surface. (c) How could this charge distribution be of use to the ray? Tập tin đính kèm - College Physics - Introduction: The Nature of Science and Physics - Introduction to One-Dimensional Kinematics - Vectors, Scalars, and Coordinate Systems - Time, Velocity, and Speed - Motion Equations for Constant Acceleration in One Dimension - Problem-Solving Basics for One-Dimensional Kinematics - Falling Objects - Graphical Analysis of One-Dimensional Motion - Two-Dimensional Kinematics - Dynamics: Force and Newton's Laws of Motion - Introduction to Dynamics: Newton’s Laws of Motion - Development of Force Concept - Newton’s First Law of Motion: Inertia - Newton’s Second Law of Motion: Concept of a System - Newton’s Third Law of Motion: Symmetry in Forces - Normal, Tension, and Other Examples of Forces - Problem-Solving Strategies - Further Applications of Newton’s Laws of Motion - Extended Topic: The Four Basic Forces—An Introduction - Further Applications of Newton's Laws: Friction, Drag, and Elasticity - Uniform Circular Motion and Gravitation - Work, Energy, and Energy Resources - Linear Momentum and Collisions - Statics and Torque - Rotational Motion and Angular Momentum - Introduction to Rotational Motion and Angular Momentum - Angular Acceleration - Kinematics of Rotational Motion - Dynamics of Rotational Motion: Rotational Inertia - Rotational Kinetic Energy: Work and Energy Revisited - Angular Momentum and Its Conservation - Collisions of Extended Bodies in Two Dimensions - Gyroscopic Effects: Vector Aspects of Angular Momentum - Fluid Statics - Fluid Dynamics and Its Biological and Medical Applications - Introduction to Fluid Dynamics and Its Biological and Medical Applications - Flow Rate and Its Relation to Velocity - Bernoulli’s Equation - The Most General Applications of Bernoulli’s Equation - Viscosity and Laminar Flow; 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THE ROBINSON LIBRARY |The Robinson Library >> American History >> United States: Local History and Description >> Middle Atlantic States >> General History and Description| the line that supposedly divides North from South In 1632, King Charles I of England gave the first Lord Baltimore, George Calvert, the colony of Maryland. In 1682, King Charles II gave William Penn the territory to the north, which later became Pennsylvania. A year later, Charles II also gave Penn land on the Delmarva Peninsula. It was this last grant that led to what is now known as the Mason-Dixon Line (or Mason and Dixon's Line). According to the original charters, the boundary between Maryland and Pennsylvania was supposed to be along 40 degrees north, but that line had never been formally "drawn." The addition of what is now Delaware to Penn's colony added extra confusion to the boundary question, and the Calvert and Penn families asked the British court to resolve the issue. In 1750, England's chief justice declared that the boundary between Pennsylvania and Maryland ran west and south from a point 15 miles south of Philadelphia. Ten years later, the two families agreed on the compromise and to have the boundary surveyed. America had no surveyors capable of taking on this task, however, so the Calverts and Penns agreed to hire two men from England. Charles Mason and Jeremiah Dixon arrived in Philadelphia in November 1763. Mason was an astronomer who had worked at the Royal Observatory at Greenwich and Dixon was a renowned surveyor. They precisely established the point fifteen miles south of Philadelphia from which the boundary was to be drawn and erected a limestone benchmark. After establishing the line between Maryland and Delaware they began working their way west along the Maryland-Pennsylvania border. The men had been hired to "draw" the boundary for a distance of five degrees of longitude west from the Delaware River, but on October 9, 1767 their Iroquis guides refused to go any further because they had reached the border of their lands with the Lenape, with whom they were engaged in hostilities. The team made their final observations on October 11, 233 miles from its starting point, but 36 miles away from their intended end point. Their survey was officially received and accepted by the Penn and Calvert families on October 18. one of the original crownstones set by Mason and The line drawn by Mason and Dixon remained nothing more than the Pennsylvania-Maryland-Delaware boundary until 1820, when the Missouri Compromise established a boundary between the slave states of the south and the free states of the north. That boundary became referred to as the Mason-Dixon line because it began in the east along the Mason-Dixon line and headed westward to the Ohio River and along the Ohio to its mouth at the Mississippi River and then west along 36 degrees 30 minutes North. map of the Mason-Dixon Line Aside from its completion to the western border of Pennsylvania, the Mason-Dixon line has not been changed since its first drawing. The tools Mason and Dixon were crude compared to the surveying technology of today, but modern technology has found their line to be remarkably accurate. Although many of the original marker stones were removed by locals and souvenir hunters over the subsequent years, a great many still stand; many of the ones stolen in years past have also been recovered and placed back in their original locations. Library >> American History >> United States: Local History and Description >> Middle Atlantic States History and Description This page was last updated on October 18, 2017.

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In this tutorial we will learn about truth table. Introduction to Propositional Logic, types of propositions and the types of connectives are covered in the previous tutorial. Every proposition (simple or compound) will take one of the two values true or false and these values are called the truth values. We denote the value true as 1 and value false as 0. Truth value is defined as the truth or falsity of a proposition. All proposition will have a truth value (i.e., they are either true or false) Consider the following simple proposition. 2 is greater than 1 The truth value of the proposition is TRUE. Consider another simple proposition. The word Mango comes before the word Apple in Oxford Dictionary. The truth value of the proposition is FALSE this is because M comes after A. The truth value of a compound proposition can be figured out based on the truth values of its components. Consider the following compound proposition. October 21, 2012 was Sunday and Sunday is a holiday. The given compound proposition is made up of two simple propositions p = October 21, 2012 was Sunday q = Sunday is a holiday Remember! we can denote propositions using small letters like a,b,c... p,q,r... etc If we check 2012 calendar, 21st October was Sunday. So, truth value of the simple proposition p is TRUE. Sunday is a holiday. So, the truth value of the simple proposition q is TRUE. So, p = TRUE and q = TRUE. We started with the following compound proposition "October 21, 2012 was Sunday and Sunday is a holiday". Note the word and in the statement. It is joining the two simple propositions into a compound proposition. So, we can write x = p AND q where, x is the compound proposition created by joining the two simple proposition p and q using the conjunctive operator AND. The truth value of x will be TRUE only when both p and q are TRUE because we are using the conjunctive operator (also called AND). Note! if any one of them is FALSE then truth value of x will be FALSE. We know that the truth value of both the simple proposition p and q is TRUE. So, we can write x = p AND q = TRUE AND TRUE So, the truth value of the compound proposition x = TRUE. Therefore, the truth value of a compound proposition can be figured out based on the truth values of its components. A truth table is a complete list of possible truth values of a given proposition. So, if we have a proposition say p. Then its possible truth values are TRUE and FALSE because a proposition can either be TRUE or FALSE and nothing else. And we can draw the truth table for p as follows. Note! we can denote value TRUE using T and 1 and value FALSE using F and 0. There is a formula to calculate the total number of rows in the truth table for a given number of propositions for all possible truth values combination. We know that we can denote proposition using small letters like p, q, r, ... etc and we also know that a proposition (simple or compound) can either be TRUE or FALSE and nothing else. So, if we have 1 proposition (say p) then, total possible truth values of p = 2 i.e., 21 = 2 Similarly, if we have 2 propositions (say p and q). Then, all possible truth values = 22 = 4 Similarly, if we have 3 propositions (say p, q and r) Then, all possible truth values = 23 = 8 The negation operator simply inverse the truth value of a proposition. This is the only operator that works on a single proposition and hence is also called a unary connective (operator). If p is a proposition then its negation is denoted by ~p or p'. So, if p is true then, NOT p i.e., ~p = false. Similarly, if p is false then, ~p = true. Following is the truth table for the negation operator The OR connective (operator) works with two or more propositions. The disjunctive of p and q propositions is denoted by p + q p ∨ q And the result of p + q is true only when p is true, or q is true or both are true. Truth table for disjunctive (OR operator) for the two propositions Note! If one of the proposition is 1 (true) then output is 1 (true). The AND connective (operator) works with two or more propositions. The conjunctive of p and q propositions is denoted by p . q p ∧ q and the result of p . q is true only when both are true. Truth table for conjunctive (AND operator) for the two propositions Note! If both propositions are 1 (true) then output is 1 (true). The conditional operator is also called implication (If...Then). The conditional p ⇒ q is false when p is true and q is false and for all other input combination the output is true. The proposition p and q can themselves be simple and compound propositions. The first part p is called the antecedent and the second part q is called the consequent. The conditional p ⇒ q can be expressed as p ⇒ q = ~p + p Truth table for conditional p ⇒ q For conditional, if p is true and q is false then output is false and for all other input combination it is true. We can also express conditional p ⇒ q = ~p + q Lets check the truth table. We can see that the result p ⇒ q and ~p + q are same. The bi-conditional operator is also called equivalence (If and only If). The bi-conditional p ⇔ q is false when one proposition is true and the other is false and for all other input combination the output is true. The proposition p and q can themselves be simple and compound propositions. The bi-conditional can be expressed as p ⇔ q = (p . q) + (~p . ~q) Truth table for bi-conditional p ⇔ q For bi-conditional, if one proposition is true and the other is false then output is false. For all other input combination it is true. We can also express bi-conditional p ⇔ q = (p . q) + (~p . ~q) lets check the truth table We can see that the result p ⇔ q and (p . q) + (~p . ~q) are same. And this brings us to the end of this tutorial. Copyright © 2014 - 2018 DYclassroom. All rights reserved. rendered in 0.0442 sec

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Numbers to 5 In this unit students • learn the count sequence to 5, counting by ones; • connect counting to cardinality by pairing objects with a number name; • answer “how many?” questions; • count objects in sets; • compare numbers of objects; • write numbers. Although K.CC.A.1 calls for students to count to 100, the full intent of that standard is not met in this unit. In this unit, students practice counting by ones up to five. The teacher might lead students in choral counting. Students also start learning how to write numbers up to five. Students begin to develop an understanding of the relationship between numbers and quantities. They point to objects in sequence and match them to number names, and come to understand that the total number of objects in a set corresponds to the last number said in the sequence. They learn that that each successive number name refers to a quantity that is one larger than the last. They learn to make a one-to-one correspondence between numbers names and objects by working with “how many?” questions. They also compare the number of objects in sets of 5 or less. Although formal work with addition and subtraction has not yet begun, the counting work students do with numbers to 5 is foundational for building fluency in expressing 5 as a sum of two numbers in different ways. Comment on this unit here.

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Heat and Chemical Reactions Recall that Dalton’s atomic model properly stated that in chemical reactions atoms rearrange as the reaction proceeds. In more modern terms this means chemical bonds are broken and formed, broken to split a compound into smaller parts and formed as smaller parts stick together into a bigger compound. In terms of energy these changes are accompanied by a certain amount of heat gain or loss. Imagine a chunk of pure sodium lying around. In the pure elemental state there is no forming or breaking of bonds, but chemistry knowledge says that exposed sodium will not stay in elemental form for long. Any water it is exposed to, even the humidity in the air, will cause a reaction that gives off a very noticeable amount of heat. At this point a determination for the change in energy can be determined by determining the change in heat and work. What if the amount of heat for the reaction was desired before the reaction occurred? Determining this would be like determining the chemical potential energy for the sodium. This chemical potential energy is expressed in terms of heat, and is called enthalpy (H). Chemists have calculated and tabulated enthalpy of reactions. The same problem occurs with enthalpy as with heat - it is impossible to calculate an absolute value. The way chemists got around this problem is to say that the elements in their pure, elemental form have an enthalpy of zero, and then all the other measurements can be made relative to that value. Below is an example list of some enthalpies of formation (the change in enthalpy when the compound is formed from the pure elements). Why is the value for H2, F2, and Cl2 zero? Remember the results are compared to the elemental forms, which is diatomic for seven elements. Most of the enthalpies are negative, which means the system loses energy as the products are formed. The study of the change in heat (and energy in general) during a reaction is called thermodynamics. Thermodynamics has placed reactions into two broad categories: endothermic and exothermic. Endothermic reactions require energy as the reaction progresses, and this is most often accomplished by absorbing heat. (Think endo = enter and thermo = heat.) The surroundings must provide this energy to the system, and if your hand was the surroundings it would feel cool as the heat leaves your hand. Often chemists denote that heat is needed by writing it as reactant, and the same could be done with any form of energy. Sometimes heat is written over the arrow of an equation to mean heat is added as the reaction goes that direction. An endothermic reaction has a positive value for the enthalpy (established by "committee"), and so only one of the products listed in the table above would be labeled as an endothermic reaction. Common endothermic reactions include melting, evaporating, vaporizing (boiling), and decomposition. Some chemicals are stored in amber colored bottles because light energy is enough to get the chemical to decompose. Exothermic reactions are literally the reverse of endothermic reactions, in that they give off energy (usually in the form of heat) as the reaction progresses. (Think exo = exit.) Exothermic reactions would be warm to the touch (provided it is a safe enough to touch). Heat can be written as a product, and sometimes written with an arrow pointing away from the reaction to indicate heat is escaping. Exothermic reactions have a negative value for enthalpy, as energy is given off. Common exothermic reactions are freezing, condensing, most synthesis reactions and of course, combustions. Often chemists use a visual representation of the enthalpy of a reaction to get a general idea about the change in enthalpy that occurs as a reaction progresses. Enthalpy is the dependent variable and time is the independent variable (the one the experimenter controls). A diagram like this is helpful as the enthalpy could be likened to the potential energy of a ball traveling the same curve. Overall the ball would travel downhill and the ball’s potential energy is less than it had to begin with (-Ep). The same is said about the enthalpy of the reaction. The products have less enthalpy than the reactants, so the overall ∆H has a negative value (energy is given off). This reaction would be called an exothermic reaction. It may be surprising to see that the reactants have to go “uphill” or gain energy before they can form products, even in an exothermic reaction. This amount of energy is called the Energy of Activation (Ea). Most reactions, even exothermic ones, require some amount of energy to get started, just like it takes a match to get a log in a fireplace to burn. The actual amount of energy needed depends on the reaction and if necessary for calculations would have to be specified. Once the reactants reach the top of the “hill” the products can form spontaneously. Because the “downhill” side of the diagram is bigger than the “uphill” side, the overall reaction has the value of negative enthalpy (exothermic) as would be measured from the ∆H from the graph. What would the diagram look like for an endothermic reaction? Water can be separated into hydrogen and oxygen, but it takes energy (usually in the form of electricity). Now the reaction is endothermic because the products end up with more energy then the reactants started with. Notice the value for ∆H is not the entire height of the “hill”, but is only the difference between the products and the reactants. The energy of activation is the larger amount and will never be completely the same as the ∆H. Some of the energy of activation is returned as the products roll “downhill”. In both exothermic and endothermic reactions the ∆H = ΣHproducts - ΣHreactants. If ΣHproducts - ΣHreactants < 0, then the negative sign indicates it is an exothermic reaction. If ΣHproducts - ΣHreactants > 0, then the positive sign indicates it is an endothermic reaction. (Just like in math class, the symbol Σ (capital sigma) means the sum of.) For the purpose of comparison, chemists often determine a value for enthalpy under specific conditions. The standard temperature and pressure for the enthalpy of substances is 25 °C (298 K), 1 atmosphere of pressure, and a concentration of 1 M for solutions. Enthalpy is a state function, which means the value is only dependent on the initial and final enthalpies. There is no need to worry about how the enthalpy changes between those states, which is very convenient as the curves shown in the graphs shown above are idealized. For those reactions for which chemists have successfully completely figured out exactly what happens as the reactants form products there are often many peaks to the graph, not just one big one. In addition, most reactions happen at a rate that is too fast to determine what exactly is happening, so technically for these reactions there would be a known curve. As enthalpy is a state function none of this matters, and the enthalpy calculations are determined as easily as finding the initial and final enthalpies and subtracting.

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|PICTURES FROM THE PROVIDED POWER POINT| - Students need a blank sheet. - Students need to see the picture you/they describe at the end of the task Level: Some of the pictures provided might be difficult to describe. Use or find pictures that cover vocabulary seen in class. Whatever the level, students should know prepositions/expressions of location (to the left, underneath..) Remember, click Power Point if you want to use the provided options. First STEP: Model the task - Pre teach necessary" location" vocabulary (background, to the left, to the right, underneath …) and/or mime necessary vocabulary (wheelchair for first picture, for example) as you describe the pictures. - Describe any of the pictures in the Power Point (or any other from the text book). Students should not see the picture until the end of the task. - Show the picture - Students compare their pictures and decide if they missed something or misunderstood something Option A) Students can create a short text responding questions about the picture. Some possibilities are: What are the characters thinking/saying? Why are they there? What are they going to do next? Option B) Most students sit with their back to the board so that they don't see the projected picture. - One or two students, facing the board and watching the picture (from a print or the projector), describe a picture to his/her/their classmate(s) - Students compare their pictures and the projected picture. REMEMBER: The teacher can use one of the pictures included in the power point, a picture from the textbook or bring his/her own picture. By Maria Zabala

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Study the following for your test: Wordlist Unit 1 : know the words below. Don’t come up with something else, just study the words from your book to get full points! Sentences Unit 1 : please study the sentences carefully. You can get 2 points per sentence! Click on: Grammar in a Nutshell 1 to open the powerpoint presentation for more information on all the grammar topics for this unit. In Unit 1, you learn about: - Personal pronouns - Present simple More info about each of these can be found below. Countries & Nationalities: know the name of the country and what the people in that country are called. So someone who lives in Germany (Duitsland) is called German (Duitser). More about grammar! So: if you talk about something general, use ‘a’ or ‘an’ (in Dutch: ten). You use ‘an’ when the following words starts with a vowel-sound (klinkerklank). Use ‘the’ when you mean something specific, for example: the toxic apple that was given to Snow White. Check this explanation out as well… Above you can find the spelling rules to make plural nouns. Make sure you know them by heart. Of course there are always exceptions. They are called irregular (7 + 8). Please fill in the following worksheet! Click here to download. Click here for an online exercise. Click here for an explanation (in Dutch) and a couple of exercises to practice this part of your English grammar.

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Classifying and Sorting Solid Shapes In this geometry worksheet, 1st graders examine the ways they can sort solid shapes using faces, curved parts, or corners. They examine 7 black line pictures and sort them by the given rules. They apply rules such as finding the shapes with 6 faces or drawing a box around the shapes with one face. They find something in their kitchen that is a shape that rolls. They draw the item.

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What are arguments? In the previous article, we discussed what statements are. Statements are the kind of sentences that can be true or false. When someone is trying to persuade you to believe something, they will express this as a statement. But how do you know if what they are trying to persuade you of is true or false? Unless they just want you to take their word for it without further discussion—and you probably shouldn’t—they will give you reasons in support of their views. Those reasons will also be expressed as statements. Together, all those statements form what we call an argument. This course is all about developing skills to evaluate whether arguments are good or bad. We will talk about good and bad arguments later. Before that, we need to be clear on what arguments are, and how to recognise them. - Definition: An argument is a group of statements some of which, the premises, are offered in support of another statement, the conclusion. You can think of the premises of an argument as reasons that are given in support of a view, which is expressed in the conclusion of the argument. Let’s see a very simple example of an argument: Stan was driving his truck over the speed limit. He had no excuse for driving over the speed limit. Furthermore, he was intoxicated. Therefore, Stan was breaking the law. We can easily isolate the conclusion: - Stan was breaking the law. Notice that we do not include the word ‘therefore’ when we state the conclusion. The word ‘therefore’ is not part of the statement that forms the conclusion. All other statements are premises. We have: - Stan was driving his truck over the speed limit. - Stan had no excuse for driving over the speed limit. - Stan was intoxicated. The word ‘therefore’ is what we call a conclusion indicator. It is very common to use a conclusion indicator to stress the part of an argument that is being argued for. Arguments can also have premise indicators. Conclusion and premise indicators are words that are used to make clear which statements are premises and which statements are conclusions in arguments. Here’s a list of the most common ones. |Conclusion indicators||Premise indicators| Indicator words are not always present in arguments. You may have conclusions that are not accompanied by conclusion indicators. But typically, the rule of thumb is that if you have a conclusion indicator, then the statement to which it is attached is the conclusion of the argument. And likewise with premises. When arguments are given to you in the wild, they’re not always presented in such a clear way. We will show you lots of examples of arguments, and you will see that they quite often look very messy. This means that you will have to do some work to identify the conclusion and the premises. And this is generally far from easy. Because of that, we will represent arguments always in the same format, which we call the standard form of an argument. © Patrick Girard, University of Auckland

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Math and science were invented by humans to describe and understand the world around us. We observe that there are some quantities and processes in our world that depend on the direction in which they occur, and there are some quantities that do not depend Mathematicians and scientists call a quantity which depends on direction a vector quantity. A quantity which does not depend on direction is called a scalar quantity. has two characteristics, a magnitude and a direction. When two vector quantities of the same type, you have to compare both the magnitude and the direction. On this slide we describe the method for adding two vectors. Vector addition is one aspect of a larger vector algebra which we are not going to present at this web site. Vector addition is presented here because it occurs quite often in the study of rockets and because it demonstrates some fundamental differences between vectors and scalars. Vectors are usually denoted on figures by an arrow. The length of the arrow indicates the magnitude and the tip of the arrow indicates the direction. The vector is labeled with an alphabetical letter with a line over the top to distinguish it from a scalar. We will denote the magnitude of the vector by the symbol |a|. The direction will be measured by an angle phi relative to a coordinate axis x. The coordinate axis y is perpendicular to Note: The coordinate axes x and y are themselves vectors! They have a magnitude and a direction. You first encounter coordinates axes when you learn to graph. So, you have been using vectors for some time without even knowing it! If we construct a dashed line from the tip of the vector a running parallel to the x-axis, it cuts the y-axis at a location we label ay. Similarly, a line from the tip of the vector parallel to the y-axis cuts the x-axis at ax. The quanities ax and ay are called the of the vector and both are scalar quantites. To add two vectors, a and b, we first break each vector into its components, ax and ay, and bx and by, as shown on the figure. From the rules which govern the of vectors, the blue vector b is equal to the black vector b because it has equal equal length and equal direction. Now since the components of vector a and vector b are scalars, we can add the x-components to generate the x-component of new vector c: cx = ax + bx Similarly, we can add the y-components: cy = ay + by The new components, cx and cy, completely define the new vector c by specifying both the magnitude and the direction. Looking carefully at the diagram, we see that adding two vectors produces a new vector which is not in the direction of either of the original vectors, and whose magnitude is not equal to the sum of the magnitudes of the original vectors. Vector algebra is very different from scalar algebra because it must account for both magnitude and direction. Note: On this slide, for simplicity, we have developed the components in only two dimensions; there are two coordinate axes. In reality, there are three spatial dimensions and three components of all forces. This is important in our derivation of the general equations of for flight trajectories and for the Euler equations which describe the forces and resulting motion of fluids in the engine. We can break very complex, three-dimensional, vector problems into only three scalar equations. Beginner's Guide Home

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Last week, I featured the Zoozoo Animal World Series to teach different verb tenses in the classroom (read the article here). This week, I’ll be presenting ways to incorporate fictional narratives into discussions about time! Understanding different verb tenses is not only important for grammatical purposes—recognizing temporal word forms is integral to understanding any narrative. The Common Core Standards also expects first-grade students to “use verbs to convey a sense of past, present, and future (e.g., Yesterday I walked home; Today I walk home; Tomorrow I will walk home)” (CCSS.ELA-LITERACY.L.1.1.E). The Fables and the Real World Series showcases fictional fables that teach universal life lessons. The Milkmaid and Her Pail utilizes all three verb tenses—past, present, and future—in its story. Nevertheless, it remains at Guided Reading Level G and stays accessible to your students! - Introduce the book to your students. Do you think this book is fiction or nonfiction? Why do you think so? - Tell them that you’ll be focusing on time and the sequencing of events during today’s reading. - Discuss the opening phrase “once upon a time.” What is the meaning of this phrase? What does it tell us about when the story takes place? - Based on “once upon a time,” do we expect the story to be told in past, present, or future tense? Examine the verb in the sentence to confirm your students’ prediction. Page 5, 7, and 9: - Identify the two different verb tenses on the page. Why does the milkmaid speak in the future tense? (Because she is fantasizing about things that she can buy in the future.) Page 6 and 8: - Identify other words on this page that are related to time. (“Then,” “soon.”) - Identify the two different verb tenses on the page. Which word signals that the verb is in future tense? (“Will.”) - Return to the farmer’s dialogue on page 3, 15, and 16. - What tense does the farmer use when he speaks? (Present tense.) - Why does he speak in present tense? Explain that when the farmer was speaking, it was a “now” or a present in which the story was taking place. For your students, though, that “now” was “once upon a time,” and the story has already happened. The story is simply recording what the farmer said in that moment, so it is in present tense. [Note: the concept of relative temporal perceptions is quite abstract and related to “acknowledging differences in the points of view of characters” (CCSS.ELA-LITERACY.RL.2.6), so don’t worry about stressing this point.] - Examine the second sentence of dialogue on page 3. What tense does the farmer use and why? Familiarity with different verb tenses serves as a powerful tool for fiction reading. With a keen sensitivity to words that trigger time, students will develop greater comprehension of story timelines and event sequencing. Whether you’ve taught, teach, or will teach verb tenses to your students, The Milkmaid and Her Pail is a great addition to your classroom library! Click the image below to download an informational sheet about the Fables and the Real World Series, which includes the book featured in this blog post.

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Ninth graders find the height of every day objects using techniques learned through postulates that allow triangles in a problem to be similar. They calculate the length of a missing side and solve proportions. 3 Views 25 Downloads The Angle-Angle (AA) Criterion for Two Triangles to Be Similar What do you need to prove triangles are similar? Learners answer this question through a construction exploration. Once they establish the criteria, they use the congruence and proportionality properties of similar objects to find... 9th - 10th Math CCSS: Designed Mathematics Within: Slope and Triangles Learners discover a method for determining the slope of a line by creating and comparing similar triangles. They fold coordinate grids to make three similar triangles then measure the sides to compare the relationships between the... 8th - 10th Math CCSS: Adaptable New Review Inscribed Similar Triangles: Lesson Create similar triangles with a little altitude. A section of an extensive playlist on basic geometry discusses how an altitude of a right triangle creates similar triangles. Using the theorem, the presentation finds unknown side... 4 mins 6th - 12th Math CCSS: Adaptable Similar Triangles and Proportions Pupils investigate similar triangles and proportions as they make conjectures about the length of sides of similar triangles. For this lesson, have your class construct similar triangles using Cabri Jr so that they share a common vertex. 9th - 12th Math CCSS: Designed Identifying Similar Triangles Math whizzes work with angle sums and exterior angles to figure out the measure of other angles. This particular publication provides comprehensive support in the form of an anticipatory activity, questions designed to prompt discussion,... 7th - 9th Math CCSS: Designed

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The Constitution is the supreme law of the land in the United States. With a positive overtone, the preamble, articles, and amendments in this document protect the rights of all US citizens. Create a similar document for your class to ensure that everyone has a voice and rights that make them feel safe and comfortable expressing themselves. At the beginning of each year, most teachers clarify classroom rules and expectations, both academic and behavioral. You can use Constitution Day, September 17th, to not only talk about this important document, but begin discussions about rights and responsibilities. Involving your class in creating a class constitution makes them part of the process of government and give them a vested interest and responsibility in following and upholding the laws they have determined. Kick off this lesson with an exercise that gets students thinking about fairness. For example, open the class saying that your favorite color is green, so all students with green eyes will be exempt from homework for the week. You could also say something like, "Anyone wearing sneakers will get 5 extra minutes of recess, while those wearing other types of shoes will have to stay inside doing extra math work." Continue sharing ways that you will discriminate or bend the rules until someone points out that you are not being fair. Discuss what fair means and how it relates to equality. After discussing fairness, have students attempt to summarize their ideas with an acrostic poem they have written using the letters F-A-I-R. Next, introduce the students to the US Constitution. Focus on three areas of the document, the preamble, the articles, and a few amendments. Share the School House Rock video of the Preamble. Work as a whole class to write a preamble to your class constitution. You can follow the preamble format. For example: "We the students of _____ class, in Order to form a more perfect Union, establish _____ , insure _____, provide for ______, promote ______, and secure _____, do ordain and establish this Constitution for our classroom." The articles of the constitution outline the structure and function of the government. For this lesson, the first ten amendments to the Constitution, or Bill of Rights, will likely be more interesting to students. You can take this opportunity to study the entire Bill of Rights, but a focus on the first and fourth amendments are a great way to help students find ideas for classroom rights. Many students don't like working in teams. To help them think about classroom rights, you may also want to talk about norms for group work. They usually have lots of complaints and ideas! Work as a class to brainstorm a list of rights. You may want to add your own ideas for the rights of the teacher! Divide the class into small teams. Have each team choose 5 rights they think are most important. Each team should craft a clear and concise statement articulating each of these rights. Have them add these rights to a single page in Wixie. Next, have two teams meet together to discuss what they have written. Teams should then edit their list of rights to include new wording or even new rights. After class, log in to your Wixie account and use the import pages feature to combine all of their work into one file. When students return to class, project their ideas and read the articles on each page. As you move through the each page, discuss which rights are similar and which ones have the wording the class likes best. Create a new blank page and copy the rights you want to keep as a class. Make edits to the wording for a final version. Print the final constitution in large format or create a version using poster or chart paper so you can post it in the classroom for everyone to see. Make time for a formal reading of the preamble and articles. The Constitution was ratified by the states. To ratify your classroom constitution, have each student come to the front to sign, or add their "John Hancock," to the document. You may wish to invite a school administrator as witness to the process to lend an air of additional importance to the event. Print copies of the document for students to take home and share with their families. You can get a sense of student's understanding of essential social studies ideas like the importance of rules and rights vs. responsibilities. You can get a sense of their critical thinking skills as you discuss the idea of fairness. As students work to write the rules, you will be able to assess their ability to change a negative sentence (rule) into a positive sentence (right). This is also an opportunity to focus the importance of specific vocabulary and terminology for clear and concise writing. Since this is the beginning of the year, you may want to focus assessment on student behavior and teamwork. Jean Fritz.Shh! We're Writing the Constitution. ISBN: 0698116240 David Catrow.We the Kids. ISBN: 0142402761 Syl Sobel.The US Constitution and You. ISBN: 147920773X School House Rock - Preamble (Note: Ad at front) Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others' ideas and expressing their own clearly and persuasively. The Inquiry Arc 1. Developing Questions and Planning Investigations 2. Applying Disciplinary Concepts and Tools 3. Gathering, Evaluating, and Using Evidence 4. Working Collaboratively and Communicating Conclusions Dimension 2: Civics Explain the need for and purposes of rules in various settings inside and outside of school. Examine the origins and purposes of rules, laws, and key U.S. constitutional provisions. 6. Creative Communicator Students communicate clearly and express themselves creatively for a variety of purposes using the platforms, tools, styles, formats and digital media appropriate to their goals. Students: a. choose the appropriate platforms and tools for meeting the desired objectives of their creation or communication. b. create original works or responsibly repurpose or remix digital resources into new creations. d. publish or present content that customizes the message and medium for their intended audiences. Ideas for engaging elementary students in science as they explore the curriculum through creative projects. Get this FREE guide that includes: What can your students create? Create custom rubrics for your classroom. Graphic Organizer Maker Create custom graphic organizers for your classroom. A curated, copyright-friendly image library that is safe and free for education.

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Describe Prisms and Pyramids Using Algebra Lesson 15 of 37 Objective: SWBAT describe the relationship between the bases, faces, edges, and vertices of pyramids and prisms using algebraic expressions The first 10-15 minutes of this section are for students to build a prism and a pyramid. I will have nets ready to cut for prisms and pyramids from a triangular base up to an octagonal base. Before students start working, I will explain how to cut and fold the net for best results. It will help to set a timer so that this process, including cleanup, can be finished quickly. Once the shapes are made, students will complete a table to describe the attributes of each shape. I will give about 30 seconds per shape and then ask students to pass the shapes on. Once we’ve agreed on the attributes, I ask students to describe the various parts of an n-sided prism and pyramid (MP2, MP8). I’d like students to grapple with this independently before seeking help. I will ask: What is the relationship between the sides of the base and the lateral faces, vertices and edges? Students will then be asked to find any attribute of a solid when given another piece of information. Example: A certain prism has 12 vertices, how many sides does the base shape have? The lesson will conclude with an exit ticket. Students work independently.

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- Start with questions that lead to model sentences in which the grammatical rule is included. E.g. How long have you been learning English? How long have they been playing football? How long has she been cooking pizza? Etc. - Encouraging students to answer the questions in complete sentences using the grammatical rule and write the model sentences on the board. - Read the sentences focusing on the main features of the rule (highlight the form with different colour or by underlining them). - Tell students the function and the meaning of the grammatical rule, when to use it and how to apply it in communication. - Encourage students to do some different and various exercises on the rule to familiarize them with it. Check understanding and involve as many students as possible. - Elicit the form of the rule from students and write it on the board. - Ask students to give more meaningful examples of the rule. - Give more practice of the rule creating real-life situations for students to use the rule in.

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In this Section: In this section, we continue to learn about place value and our number system. We will learn how to write a number in expanded notation, also known as expanded form. This method of writing a number emphasizes the place value of each and every digit of the number. This will help us to visually understand how each digit in a number gains its value. To write a number in expanded notation, we form the sum of each digit multiplied by its corresponding place value (ones, tens, hundreds, thousands,…).

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For all students, it is important to see that researchers use a wide variety of definitions of individual bilingualism. There are very strict and very demanding psycholinguistic definitions, such as Bloomfield's (1933) claim that a bilingual should possess "native-like control of two or more languages". Others, such as Weinreich (1953) and Grosjean (1997) propose definitions that are based on language use rather than language competence. Before showing students the range of definitions of bilingualism, it can be very helpful to ask them to formulate their own definition in writing. Students can subsequently collect these definitions and discuss them in class. This often leads students to formulate very original views on the issue and it generates an interest in the definitions given by the experts in the field, which are to be presented and discussed subsequently. A bilingual individual, generally, is someone who speaks two languages. An ideal or balanced bilingual speaks each language as proficiently as an educated native speaker. This is often referred to as an ideal type since few people are regarded as being able to reach this standard. Otherwise, a bilingual may be anywhere on a continuum of skills. Literacy abilities may be an additional dimension to bilingualism, but they are often referred to separately as biliteracy, leaving bilingualism to carry the weight of oral language abilities. Bilingualism is a specific case of multilingualism, which has no ceiling on the number of languages a speaker may dominate. The timing and sequence in which one learns each of the languages has led to other distinctions between kinds of multilingualism. Much of the linguistics literature, for example, identifies native language or mother tongue as a first language, ignoring the possibility or diminishing the value of having more than one native language or mother tongue. Such a person is often referred to as a simultaneous bilingual, while someone who acquires the second language after the first one is often referred to as a sequential bilingual ("early" if between early childhood and puberty, and "late" if after puberty). The context of language acquisition leads naturally to distinguishing between "informal" bilinguals, who acquire their languages outside of formal settings like schools, imitating the natural processes of acquiring the mother tongue, and "formal" bilinguals, who generally learn the language in schools or similar settings. When these terms apply to groups, one speaks of bilingual or multilingual communities or nations. The aggregate enumeration of the speakers in these groups (also referred to as language diversity or demography) will often profile the number of monolingual and bilingual speakers of each language. For example, there may be a multilingual community in which speakers are monolingual in each of three languages. This would be rare, and the language groups would probably be isolated from each other. More often than not, a multilingual community or nation has multilingual individuals. If the situation involves social or political power, then a language group may be referred to as a language minority (minority-language) group or a language majority (majority-language) group, reflecting the power relationship to other groups in the society or political unit.

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Writing Complete Sentences First, let's take a look at the vocabulary, or important words, that you need to know for this lesson. noun - this is a part of speech. A noun is a person, place, thing, or idea. Examples: Ms. Sarno (person), Pennsylvania (place), chair (thing), love (idea) verb - this is also a part of speech. A verb can express an action, or a state of being or condition. Examples: run, or running (actions); is, seemed (state of being) sentence - a group of words that form a complete thought. Example: Ms. Sarno teaches Language Arts at PALCS. subject - who or what the sentence is mainly about, or who or what is doing the main action in the sentence. The subject is almost always a noun (person, place, or thing). Example: in the sentence Ms. Sarno teaches Language Arts at PALCS., Ms. Sarno is the subject. predicate - in a sentence, the predicate tells what the subject is doing, or tells something about the subject. A complete predicate includes the verb and all of the words that complete the thought in the sentence. Example: in the sentence Ms. Sarno teaches Language Arts at PALCS., the word teaches is the verb, and the phrase teaches Language Arts at PALCS is the complete predicate. fragment - an incomplete sentence, or a sentence that does not include a complete thought, or does not include both a subject and a predicate. Example: Teaches Language Arts at PALCS. This is not a complete sentence, because there is no subject - just a predicate!

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The appeal to states' rights is of the most potent symbols of the American Civil War, but confusion abounds as to the historical and present meaning of this federalist principle. The concept of states' rights had been an old idea by 1860. The original thirteen colonies in America in the 1700s, separated from the mother country in Europe by a vast ocean, were use to making many of their own decisions and ignoring quite a few of the rules imposed on them from abroad. During the American Revolution, the founding fathers were forced to compromise with the states to ensure ratification of the Constitution and the establishment of a united country. In fact, the original Constitution banned slavery, but Virginia would not accept it; and Massachusetts would not ratify the document without a Bill of Rights. South Carolinians crowd into the streets of Charleston in 1860 to hear speeches promoting secession. The debate over which powers rightly belonged to the states and which to the Federal Government became heated again in the 1820s and 1830s fueled by the divisive issue of whether slavery would be allowed in the new territories forming as the nation expanded westward. The Missouri Compromise in 1820 tried to solve the problem but succeeded only temporarily. (It established lands west of the Mississippi and below latitude 36º30' as slave and north of the line—except Missouri—as free.) Abolitionist groups sprang up in the North, making Southerners feel that their way of life was under attack. A violent slave revolt in 1831 in Virginia, Nat Turner’s Rebellion, forced the South to close ranks against criticism out of fear for their lives. They began to argue that slavery was not only necessary, but in fact, it was a positive good. As the North and the South became more and more different, their goals and desires also separated. Arguments over national policy grew even fiercer. The North’s economic progress as the Southern economy began to stall fueled the fires of resentment. By the 1840s and 1850s, North and South had each evolved extreme positions that had as much to do with serving their own political interests as with the morality of slavery. As long as there were an equal number of slave-holding states in the South as non-slave-holding states in the North, the two regions had even representation in the Senate and neither could dictate to the other. However, each new territory that applied for statehood threatened to upset this balance of power. Southerners consistently argued for states rights and a weak federal government but it was not until the 1850s that they raised the issue of secession. Southerners argued that, having ratified the Constitution and having agreed to join the new nation in the late 1780s, they retained the power to cancel the agreement and they threatened to do just that unless, as South Carolinian John C. Calhoun put it, the Senate passed a constitutional amendment to give back to the South “the power she possessed of protecting herself before the equilibrium of the two sections was destroyed.” Controversial—but peaceful—attempts at a solution included legal compromises, arguments, and debates such as the Wilmot Proviso in 1846, Senator Lewis Cass’ idea of popular sovereignty in the late 1840s, the Compromise of 1850, the Kansas-Nebraska Act in 1854, and the Lincoln-Douglas Debates in 1858. However well-meaning, Southerners felt that the laws favored the Northern economy and were designed to slowly stifle the South out of existence. The Fugitive Slave Law of 1850 was one of the only pieces of legislation clearly in favor of the South. It meant that Northerners in free states were obligated, regardless of their feelings towards slavery, to turn escaped slaves who had made it North back over to their Southern masters. Northerners strongly resented the law and it was one of the inspirations for the publishing of Harriet Beecher Stowe’s Uncle Tom’s Cabin in 1852. Non-violent attempts at resolution culminated in violence in 1859 when Northern abolitionist John Brown abandoned discussion and took direct action in a raid on the arsenal at Harpers Ferry, Virginia. Though unsuccessful, the raid confirmed Southern fears of a Northern conspiracy to end slavery. When anti-slavery Republican Abraham Lincoln won the presidential election in 1860, Southerners were sure that the North meant to take away their right to govern themselves, abolish slavery, and destroy the Southern economy. Having exhausted their legal and political options, they felt that the only way to protect themselves from this Northern assault was to no longer be a part of the United States of America. Although the Southern states seceded separately, without intending to form a new nation, they soon banded together in a loose coalition. Northerners, however, led by Abraham Lincoln, viewed secession as an illegal act. The Confederate States of America was not a new country, they felt, but a group of treasonous rebels.

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Many uniformitarian scientists believe that about five major periods, and several short periods, of glaciation have occurred on Earth.1 In the evolutionary time scale, these ice age periods sometimes lasted several hundred million years and extended back 2–3 billion years ago. These supposed ice ages have been interpreted from till-like rocks2 and other apparent glacial signatures observed within sedimentary rocks around the world. One such ice age is called the Neoproterozoic, or Late Precambrian, and thought to have started about 950 million years ago and ended about 520 million years ago.3 During this 430 million-year period, according to evolutionary time, there were several long ‘glacial’ and ‘interglacial’ periods. ‘Snowball Earth’ hypothesis Based on early paleomagnetic studies, evolutionists deduced that most Precambrian ‘ice ages’, including the one about 2.5–2.2 billion years ago extended as far south as the equator.4 This radical proposal caused many scientists to question the paleomagnetic results, mainly because it is easy to remagnetize rocks. After many paleomagnetic measurements and several decades (i.e. Sohl, Christie-Blick and Kent5), the idea of an equatorial ice sheet, implying a completely glaciated Earth, has become widely accepted. Kerr writes: ‘And last year, most researchers agreed that one part of the sweeping hypothesis—the claim that glaciers once flowed into ice-covered tropical seas—is correct … .’6 This is the ‘snowball Earth’ hypothesis. John Crowell, one of the chief investigators of supposed ancient ice ages, had been skeptical of the paleomagnetic measurements for several decades, but now has accepted the measurements. There are several major problems with the idea that ice sheets reached the tropics at low elevation. One problem is that, once ice and snow covered the entire Earth, a frozen Earth would maintain itself indefinitely by ice-albedo positive feedback. Ice and snow have a high albedo, which causes most of the solar radiation to be reflected back to space. Without atmospheric warming, the temperature of the Earth would plummet far below freezing and the frozen condition would become very stable. So, a catastrophic climatic event would be required to melt a ‘snowball Earth’. How could life have survived? The Cambrian period and its supposed ‘explosion’ of life occurred around 550 million years ago.7 This means that the worldwide Neoproterozoic ice age was raging during, or just at the end of, the time when multicellular life exploded over the Earth. The origin of multicellular life would have occurred earlier, at the beginning of the supposed ice age, since some metazoan life occurs between 1,000 and 700 million years ago according to their time scale.8 The origin of life itself has already been pushed back to over 3 billion years ago. So, it seems that evolutionists now have a serious problem with the supposed evolution of multicellular life. Kerr asks: ‘How could life have survived … in a world in which the average surface temperature would have hovered around –50°C, not to mention the all-encompassing sea ice that would average a kilometer thick compared to the Arctic Ocean’s few metres?’6 In a later article, he asks: ‘How could early life have weathered such a horrendous environmental catastrophe without suffering a mass extinction? … How could algae and perhaps even early animals have survived 10 million years sealed off by globe-girdling ice?’9 Hyde et al. reinforce this concern: ‘But this period was a critical time in the evolution of multicellular animals, posing the question of how early life survived under such environmental stress.’8 It seems like evolutionists are caught in a bind. The problem of the cap carbonates Now that most geologists have accepted that the Earth was covered with snow and ice while multicellular life was evolving, another perplexing problem needs to be explained. This is the problem of the cap carbonates, which have a high amount of dolomite. The cap carbonates are interpreted as warm-water rocks because dolomite requires hot water to precipitate from solution. These rocks are very common directly above the Neoproterozoic ‘ice age’ deposits, sometimes with a knife-sharp contact.10 The textures of the cap carbonates often indicate rapid precipitation from warm seas saturated with carbonate.11 Hoffman and Schrag state the significance of such an abrupt transition to the cap carbonates: ‘But the transition from glacial deposits to these “cap” carbonates is abrupt and lacks evidence that significant time passed between when the glaciers dropped their last loads and when the carbonates formed.’12 ‘Snowball Earth’ followed by a rapid hothouse is considered doubly bizarre to some geologists.11 Even more strange is the fact that the hothouse existed before and during the ‘ice ages’ based on the distribution of other carbonates associated with the ‘ice age’ deposits. Carbonates are located below Late Precambrian ‘ice age’ deposits, and in Scotland carbonates, including dolomite, are interlayered within ‘glacial’ deposits.13 Carbon isotope ratios in the cap carbonates also appear to reinforce the idea that practically all life died out during the ‘ice age’.14 Uniformitarian scientists used to say that the carbonates associated with ‘glacial’ deposits were ‘cold-water’ carbonates, citing evidence from patches of biogenetic carbonate that form in cold water today.15 This was obviously a dodge. Now, they are simply accepting the temperature implications of these cap carbonates at face value and postulating a ‘hothouse’ immediately after the ‘glaciation’. The freeze-fry model Evolutionists are back to the drawing board in trying to explain how life supposedly blossomed while such overpowering catastrophes were taking place. Hoffman and Schrag12 have proposed a radical hypothesis that they believe explains the oscillating freeze-fry climate, as well as the mystery of the origin and evolution of multicellular life. Hoffman and Schrag agree that ‘snowball Earth’ would have been an ice age catastrophe of monumental proportions: ‘Dramatic as it may seem, this extreme climate change [Late Cenozoic ice age] pales in comparison to the catastrophic events that some of our earliest microscopic ancestors endured around 600 million years ago. Just before the appearance of recognizable animal life, in a time period known as the Neoproterozoic, an ice age prevailed with such intensity that even the tropics froze over.’16 They say only geothermal heat kept the oceans from freezing clear to the bottom, leaving all but a tiny fraction of the planet’s microscopic organisms to die. The heat near hydrothermal vents kept only patches of life going. Hoffman and Schrag grudgingly agree to the necessity of a hothouse immediately following this catastrophe: ‘To confound matters, rocks known to form in warm water seem to have accumulated just after the glaciers receded.’17 They then propose an hypothesis that produces the ‘snowball Earth’ followed by its rapid reversal to a hothouse. It is this hothouse that subsequently caused the rapid diversification of multicellular life. Suddenly, the bizarre sequence of events is now ‘expected’.18 This is just one example out of hundreds of the incredible plasticity and unfalsifiability of the evolutionary/uniformitarian paradigm. How does Earth transform from a snowball into a steam bath? In storytelling suspense, typical of evolutionary scenarios, Hoffman and Schrag12 explain that volcanoes popped through the ice and belched life-saving carbon dioxide. The extra carbon dioxide in the atmosphere supposedly caused a super greenhouse effect. But, another problem arises, as the hothouse is also precarious to life: ‘Any creatures that survived the icehouse must now endure a hothouse’.16 If one such freeze-fry episode seems fantastic, this scenario supposedly repeated itself four times during the Late Precambrian and at least once during the Mid Precambrian.4 Origin of banded-iron formations The freeze-fry model is also supposed to solve another great mystery of geology—the origin of banded-iron formations.11,19 In the freeze-fry story, millions of years of ice cover would deprive the oceans of oxygen, causing iron from hydrothermal vents to become soluble in the ocean water. Once the ice melted, oxygen would mix into the ocean and cause the iron to precipitate. However, if the oceans lost their oxygen, how could life survive around those deep-sea vents? Another problem with attempting to solve this puzzle is that banded-iron formations not only follow ‘ice ages’, as predicted by the theory, but are also mixed down into the ‘glacial’ deposits.13 Complicating the issue even more, there are no banded-iron formations after the Late Precambrian ‘ice age’. Expanding their theory, Hoffman and Schrag apply the freeze-fry model to future climates by predicting dire consequences of global warming that is assumed to result from increased carbon dioxide today: ‘Certainly during the next several hundred years, we will be more concerned with humanity’s effects on climate as the earth heats up in response to carbon dioxide emissions … but could a frozen world be in our more distant future?’20 Climate modellers used to pay no attention to the snowball Earth hypothesis. However, now that they believe it is ‘proved’, they have attempted to model it by computer climate simulations. Interestingly, many of the modelling efforts are having problems coming up with a totally glaciated Earth.9 For instance, the model of Hyde et al. failed to produce a ‘snowball Earth’.8 However, their model does provide hope for multicellular life in another way—by keeping areas of open water at the equator. However, Scrag and Hoffman21 do not believe that the ‘slushball earth’ model of Hyde et al. agrees with the geologic and paleontologic data. The geological record supposedly indicates that the oceans were completely sealed off or close to it, say the proponents of ‘snowball Earth’.9 Neither do Hyde et al. agree with ‘snowball’ Earth, pointing out many serious problems.22 One difficulty computer modellers encounter is to generate enough carbon dioxide to melt the ice as demonstrated by Hoffman and Schrag.14 In order to reverse the ‘snowball Earth’, the concentration of carbon dioxide in the atmosphere would need to be 350 times the current atmospheric concentration.23 This is a tough challenge for volcanoes, which are more likely to cause cooling by volcanic ash and aerosols than warming by carbon dioxide.24 Models of course are imperfect,9 so proponents of ‘snowball Earth’ believe the models are wrong and need to be adjusted. Kirschvink et al.25 claim some models do predict runaway glaciation with pack ice becoming 500–1,500 m thick, at least for the supposed ice age that occurred about 2.4 billion years ago. They also believe the melting of the ice in the Late Precambrian supplied the ‘trigger’ for evolution of multicellular organisms.26 Painted into a corner It seems as though evolutionists have painted themselves into a corner with their ‘snowball Earth’ hypothesis. They have several near-impossible problems to solve—all at a time when supposedly multicellular life was exploding just before or during the Cambrian explosion. This time, they have two catastrophes to work into their scenario. But evolutionists always seem to have another hypothesis to add when boxed into a corner. If they only realized that the solution to the crazy freeze-fry idea is to challenge the glacial interpretation of the particular rocks. However, mainstream scientists have been unable to abandon their ancient ice age story, so they are stuck with their ‘weird and bizarre’ freeze-fry world, terms used by Kerr.6 For creationists, the rocks and their associated ‘glacial diagnostic features’ can be explained very easily. They are the result of gigantic submarine landslides in a warm ocean that was precipitating carbonates in the early part of the Genesis Flood.15

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This Modeling Division of Fractions lesson plan also includes: - Join to access all included materials Provide a meaningful context for learning about the division of fractions with this upper-elementary math lesson. Presented with a simple, real-world problem, young mathematicians work in small groups to develop visual models that help them to find a solution. - Add this lesson to an upper-elementary or middle school math unit on fractions - Create a worksheet that students can use to record their solutions to the guided practice problems - If possible, give learners the option of using fraction manipulatives to model the math problems in this lesson - Lesson provides suggestions for extending learning and differentiating instruction - Offers writing prompts that students can respond to in their math journals

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Standard: CCSS ELA. L3.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. This unit plan outlines desired outcomes, acceptable evidence, and learning activities for a 3rd grade reading unit for ELL students about prefixes and suffixes. CCSS ELA. L3.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. Prefixes and suffixes can be attached to words to change meaning. Prefixes and suffixes have their own meanings that change the definitions of words in a similar way. Students will know common prefixes and suffixes and their meanings. Students will know that not all prefixes and suffixes can be added to create real words. Students will be able to infer the meaning of a word based on its root and prefix or suffix. Students will be able to explain how a prefix or suffix changes the meaning of a word. Weekly affix quiz: Students match five definitions to their corresponding words with an affix attached. Daily Homework: Worksheet with a new root/base word with proper and improper prefixes and suffixes Group Discussion: As a class, discuss words that are used to describe people, such as artistic, poetic, excitable, memorable, unhappy, unafraid, etc. Point out the base words in each (art, music, poem, etc.). Prompt students to talk about people they know with these qualities, and how the words are similar/different from the base words. Digital Flashcards: In pairs, students use a tablet to play a word game called Rooty and His Word Hunt. The game presents a root word and its meaning and then attaches a prefix or suffix. Partners will test each other on identifying the meanings of words with an affix. Word Builder: On their tablets, students build words using the Word Builder app. The app allows students to build new words by attaching prefixes and/or suffixes to a base word. The app tells the students if the words they create are Standard English words or not. Students record as many accepted words as possible and add them to the classroom Word Wall. Writing Activity: Using new words from the Word Wall, students write an original story correctly using at least five words containing a prefix or suffix. Students then type their stories in a word processing application. Illustrations: Using SketchPads, an online art program, students illustrate their stories. For each of the five words chosen as examples of prefixes and suffixes, students will create a drawing to depict the meaning of the word. Students can choose to read their stories or display their illustrations to a classmate or the group.

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These lessons are for Valentine's Day and teach students figurative language. The students define assonance, consonance, and hyperbole. They then annotate on the poem to analyze how the author uses this figurative language in the poem. This then asks further questions leading them into an analysis on how the author's word choice affects the tone of the poem. There are two poems that the students compare to see how word choice affects the overall tone of a poem. The students then write their own 8 line poem using assonance, consonance, and a hyperbole along with an illustration. Students love this activity for Valentine's Day and it is engaging and aligned with Common Core.

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Activities for Teaching Vocabulary: How Can You Teach (or Learn) New Words? First of all, when using activities for teaching vocabulary there are two key points we must Click Here for Step-by-Step Rules, Stories and Exercises to Practice All English Tenses - The student has to actually USE the new words. He or she must understand the new word's meaning and then practice - Each word has several aspects to it. The first and most important is the word's meaning. After that you have: pictures, word's usage, pronunciation and spelling. For each of those aspects you can use different activities. Let's say you teach (or learn) the word "exhilaration". First you clearly define its meaning: "excitement and happiness". You can use a good and simple English dictionary for the meanings of words. Then you can show one or more pictures that express "exhilaration". It can really help understanding. And it is definitely much more interesting that way! Funny pictures take it one step further, since they are usually more fun. Next: how is this word used? Make some example sentences: - "After winning the lottery she felt - "Climbing that mountain was really hard, but in the end we all felt - "The bride and groom left the church with great Have the students make up sentences of their own. Of course, merely reading the word is not enough. You need to know how to pronounce it properly too! Teach the correct pronunciation of the word. How come it is pronounced that way? For example, the word "cake" is pronounced with a sound because of the silent E at the end. (English pronunciation may appear disorganized at times, but actually, there are some helpful rules on the subject. Visit the English section for more information on the sounds Finally, you can't really claim you know a word, if you cannot use it in writing. Therefore you must know its spelling. Dictations can be used to make the students memorize the new words' spelling. The problem with a dictation is that after it is over, it is very easy to forget all about it… So it is in no way a replacement for the actual and repeated usage of the word in reading and writing. So here is an example lesson plan to teach some - Make a list of the new words you want to teach. Make sure they are right for your students' level: not too difficult, not too easy. - Prepare for yourself the words' meanings as well as some - Prepare some games with the new words (see - Go over the new words with your students, and see that they get - Play some games with the new words. For example: flashcards, playing cards, etc. You can use or invent whatever games you like. - Read a story/stories with the new words. The more those words repeat in the text, the better. Make sure the stories do not contain hard words that the students do not know yet. - After that, make some more activities. exercises, questions, and so forth, to further practice the new words. - On the next lesson, study some new words, but don't forget the "old" ones! They do require repeating. Activities for Teaching Vocabulary – Final Words For more data on the subject please read the Building Vocabulary and Some Common Mistakes And no matter which activity you use, keep this key question in front of you: Does it make the students USE and REPEAT the new words? The next main thing is to make it fun Make a game out of it. Involve some points, some winners, etc. Learning new words doesn't have to be boring. When done nicely, it can be a lot of fun! Visit the Vocabulary section to improve your vocabulary!

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Introduction to Viruses How Do Viruses Reproduce? Although details of the mechanisms vary widely among different virus groups, all viruses must follow three basic steps to reproduce. First, they must gain entrance and deliver their genomes into cells. Bacteriophages attach to cells and inject their DNA into the host bacteria cell. Other viruses bind to specific receptors (protein molecules) on the surface of host cells. Binding of the virus can trigger the cellular process of endocytosis, essentially tricking the cell into letting the virus inside. Enveloped viruses (viruses surrounded by a lipid bilayer) use the glycoproteins, contained in the envelope, to bind to a cellular receptor. Next, the envelope fuses with the plasma membrane of the cell and the viral contents are released inside the cell. If the viral genome is still surrounded by a layer of protein after it enters the cell, the virus undergoes an “uncoating” step to make the genetic material accessible. Second, the virus commandeers the machinery of the host cell so that it can make copies of its viral genome and synthesize viral proteins. In addition to the manufacturing machinery, the virus needs building blocks for its nucleic acid and proteins. It utilizes the host cell’s nucleotides to make copies of its genetic material and the cell’s amino acids to make proteins. At the most basic level, all viruses need to replicate their genome and produce capsid proteins. Many viruses encode additional proteins, that enhance their abilities to take over a cell, replicate to higher levels, or to evade host immune responses. RNA viruses often provide their own enzyme, a polymerase, to replicate their genome, because the host cell does not provide some the necessary enzymes. Virus-encoded polymerases are especially important for RNA viruses that need to make a DNA copy of their genome or for (-) strand RNA viruses to synthesize a (+) strand that can be translated. DNA viruses usually use the host cell DNA polymerase, which normally copies cellular DNA. Viruses use the transcription and translation machinery of the cell to manufacture virus proteins. Some viruses produce proteins that modify the cellular transcription and translation apparatus to ensure preferential synthesis of viral proteins over cellular ones, and some viruses even can completely shut down the synthesis of host cell proteins or destroy the host cell’s DNA. Finally, the nucleic acid and protein components are synthesized, the virus particle is assembled with the protein capsid surrounding the genome. There are various mechanisms by which a virus can exit a cell. Some viruses lyse, or burst open cells to release the virus particles. This process immediately destroys the host cell. Other viruses will bud out of the cell through the plasma membrane and acquire an envelope. In any case, hundreds or thousands of infectious virus particles are released from an infected cell. These newly made virus particles then go on to infect new host cells and continue the cycle of virus reproduction. It is constructive to keep in mind that unlike a cell, which duplicates its DNA and reproduces from a preexisting cell by dividing to form two daughter cells, a virus can use a single nucleic acid template to make hundreds or more copies of its genome. A useful analogy is that a virus genome can be reproduced multiple times from a single copy, much like a piece of paper can be reproduced numerous times in a copy machine. Note: The relative sizes of the virus particles and the cell in the diagram are not to scale. The viruses actually are much smaller, relative to cells, than indicated. - Campbell, N.E., & Reece, J.B. (2002). Biology (6th ed.). San Francisco: Benjamin Cummings. - Flint, S.J., Enquist, L.W., Krug, R.M., Racaniello, V.R., and Skalka, A.M. (2000). Principles of Virology: Molecular Biology, Pathogenesis, and Control. ASM Press. - Herrmann, C. (2006). Virus replication. Your slide tray is being processed. Funded by the following grant(s) Video and transcript courtesy of Wah Chiu, PhD, National Center for Macromolecular Imaging at Baylor College of Medicine. Funding for the video provided by NCMI, NIH.

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- Each atom has a charged sub-structure consisting of a nucleus, which is made of protons and neutrons, surrounded by electrons. - The periodic table orders elements horizontally by the number of protons in the atom’s nucleus and places those with similar chemical properties in columns. The repeating patterns of this table reflect patterns of outer electron states. - Do Now– Get out your science notebook and add to the Table of Contents- “Periodic Table p.73” (Right Side) and Head page 73 properly with “Periodic Table-Notes-4/18/17” - Demonstration– Balloon and Stream of Water video- Share out to class your observations of what happened when the charged balloon was held near a stream of water and explain why it happens. - Driving Question Summary Table– Complete the Summary Table on pages 68-69 for the Protons, Neutrons, & Electrons Activities on pages 70-71.

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Copyright © University of Cambridge. All rights reserved. Why do this activity? This activity provides a meaningful task for practising rounding three-digit numbers to the nearest multiple of 100. It encourages children to record their results, notice patterns and make predictions. A possible starting point is using a number line to remind the class what is meant by rounding. The interactive dice can be used to model the activity on an interactive whiteboard or can be used by the children as they engage with the task. You may also find that individual dice are useful. As the task is being modelled, the results should be recorded in a table, perhaps like the one below: This organisation of results will support the children to notice patterns and conjecture about when numbers will round to different multiples of 100. Some children may move onto the extension tasks (below). Which numbers can we make? What will they round to? Will they round up or down? Why? Do they round to the same multiple of 100? Why? When will this happen? Does it make a difference if the digits rolled are unique? : Did the class find examples where some of the three-digit numbers round to the same multiple of 100? Can they then come up with a rule about when this will happen? When will two round to the same? Or three? Or four? Or five? Or all six? : Did the class find examples where each of the three-digit numbers round to a different multiple of 100? Why? Why not? : Having completed the original task, ask the children to add a column to the right hand side of their table to note when numbers round up or down. Can they predict from the initial dice roll, how many of the three-digit numbers made will round up or down? : What if you change the numbers on the faces of the dice? Can you pick numbers so that all of the six three-digit numbers round to the same multiple of 100? Can you pick numbers so that all of the six three-digit numbers round to a different multiple of 100? : What happens if you round to the nearest multiple of 10 instead of the nearest multiple of 100? Extension 6: Have a go at the activity Round the Four Dice and practise rounding numbers to the nearest multiple of 1000. Copies of the table to write straight into would be handy. A number line might also be useful to support children in reasoning about which multiple of 100 is closest to a given number. Children may like to try Round the Two Dice before tackling this task.

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The surface of the Earth is made of interlocking tectonic plates. The tectonic plates are always moving in relation to each other. When two plates pull away from each other, the seafloor spreads along the boundary of the two plates. At the same time, it contracts in another area. The Continental Drift Theory Until 1912, most scientists accepted the contraction theory about the origins of the continents. According to this theory, the continents were formed by the cracking of the Earth's surface as it cooled from its original molten state. The weakness in this theory was that the Earth's mountains should all have formed at about the same time. This was not the case, so there was clearly something missing from the theory. In 1912, scientist Alfred Wegener proposed that the continents actually rested on huge plates that drifted over time, pulling away from each other or colliding together. Wegener's opinions were controversial at first, but later evidence confirmed this theory of continental drift. When molten rock, or magma, rises up from far below the surface of the Earth, it can split a continental plate in two. This process is called "rifting." The short-term result of rifting is volcanic and earthquake activity, with magma pouring out to the surface along the fault line. The long-term result is that the plate breaks up into two plates, which begin to drift apart from each other as the magma cools and creates new ground. As the two plates push away from each other, a "rift valley" is formed. Spreading of the Seafloor Wegener's hypothesis of continental drift was not embraced when he first proposed it because he was unable to explain what caused the process. In the 1960s, a geologist named Harry Hess was able to show how the seafloor spread when magma rose to the surface. He demonstrated that the ridges in the middle of the great oceans were the result of magma breaking through, creating a "divergent boundary" where the seafloor spread apart. Magma builds up along the edges of the boundary and forms the ocean ridges. The force that pushes the magma to the surface of the Earth is called convection. Radiation decaying below the surface releases heat. Because heat rises, the hot molten rock below the crust of the Earth tends to rise to the top. Convection forms into currents that drive the tectonic plates either together or apart. The seafloor spreads along diverging boundaries, but it also contracts along the converging boundaries as seafloor is pushed below the surface by two plates in collision with each other. Seafloor is constantly being built in some places and destroyed in others.

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Download free 90-day trial versions of the most popular TI software and handheld emulators. Check out TI Rover activities that put math, science and coding in motion. Customize your summit experience with sessions on math, STEM, coding and more. March 13, 2011 Students investigate ordered pairs by graphically exploring the coordinates of a point on a Cartesian plane and identifying characteristics of a point corresponding to the coordinate. In this short activity, students explore an ordered pair on the coordinate plane. They will enter a given point into lists and then graph as a scatter plot. Students will determine in which quadrant the ordered pair is located. Students will identify characteristics of points in the four quadrants. They will move the cursor around the graph screen to determine in which quadrants the x- and y-values of coordinates are negative and positive. In the second part of the activity, students will identify ordered pairs of data for a given function for the cost of ordering pears. They will enter ordered pairs into lists and observe the pattern as the ordered pairs appear in a scatter plot. Then students will identify a line of fit and compare the slope to the given function. © Copyright 1995-2018 Texas Instruments Incorporated. All rights reserved.

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Running an empire demanded more than a treaty. The US labored for decades before and after the Spanish-American War to lay the groundwork and administrative systems that supported its new borders. This section explores how America officially annexed Puerto Rico, the Philippines, and Hawaii. Beginning in the fifteenth century, Puerto Rico was a stronghold of Spain's Caribbean empire. With the outbreak of the Spanish-American War, the US quickly set its sights on San Juan. American troops invaded and occupied Puerto Rico in July 1898 and met little resistance. Puerto Ricans welcomed the US as a liberator. They interpreted American collaboration as a chance for economic reform and eventual freedom. By October, Spain surrendered Puerto Rico to American troops, yet with peace came new tension. Puerto Ricans lobbied for independence. Politicians in Washington, DC questioned where exactly Puerto Rico—and the other new territories—stood in relation to mainland politics. Debate came to a head with a series of Supreme Court rulings known as the "insular cases." These determined that the Constitutional rights allotted to states and citizens did not apply to Puerto Rico or its people, even though the territory was subject to taxes, legislation, and other obligations dictated by Congress. According to the Supreme Court, Puerto Rico would be "foreign in a domestic sense."

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AP Government Chapter 12 Notes: The Congress * Members of the public hold the institution in relatively low regard while expressing satisfaction with their individual representatives. * If the Federal bureaucracy makes a mistake, the senator’s or representative’s office tries to resolve the issue. What most Americans see of Congress, therefore, is the work of their own representatives in their home states. * Why Was Congress Created? * Congress was created to work not just for local constituents but also for the nation as a whole. * The Founders of the American republic believed that the bulk of the power that would be exercised by a national government should be in the hands of the legislature. * The leading role envisioned for Congress in the new government is apparent from its primacy in the Constitution. * Article I deals with the structure, the powers, and the operation of Congress. * Bicameral legislature – Senate and House of Representatives * The two chambers of Congress reflected the social class biases of the founders. * They wished to balance the interests and the numerical superiority of the common citizens with the property interests of the less numerous landowners, bankers, and merchants. * This goal was achieved by providing in Sections 2 and 3 of Article I that members of the House of Representatives should be elected directly by “the people,” whereas members of the Senate were to be chosen by the elected representatives sitting in the state legislatures, who were more likely to be members of the elite. * With the passage of the 17th amendment in 1913, the Senators are also to be elected directly by the people. * The logic of separate constituencies and separate interests underlying the bicameral Congress was reinforced by differences in length of tenure. * Members of the House of Representatives are required to face the electorate every two years. * Senators could serve for a much more secure term of six years – even longer than the four-year term provided for the President. * Terms are staggered so that only 1/3 of the senators would face the electorate every two years, along with all of the House members. * The Powers of Congress * The Constitution is both highly specific and extremely vague about the powers that Congress may exercise. * The first 17 clauses of Article I, Section 8, specify most of the enumerated powers of Congress – that is, powers expressly given to that body. * The right to impose taxes and import tariffs (one of the most important of the domestic powers) * Borrow money * Regulate interstate commerce and international trade (one of he most important of the domestic powers) * Establish procedures for naturalizing citizens * Make laws regulating bankruptcies * Coin and print money and regulate its value * Establish standards of weights and measures * Punish counterfeiters * Establish post routes * Regulate copyrights and patents * Establish the federal court system * Punish pirates and other committing illegal acts on the high seas * Declare war (most important foreign policy power) * Raise and regulate an army and a navy * Call up and regulate the state militias to enforce laws, to suppress insurrections, and to repel invasions * Govern the District of Columbia * Congress is also able to establish rules for its own members, to regulate the electoral college, and to override a presidential veto. * Some functions are restricted to only one chamber. * Under Article II, Section2, the Senate must advise on, and consent to, the ratification of treaties and must accept or reject presidential nominations of ambassadors, Supreme Court justices, and “all other... Please join StudyMode to read the full document

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Objectives of the remodelled lesson The students will: Students examine pictures of models of atoms, are provided with materials, and are asked to make their own models of oxygen, carbon, or sodium atoms. They are asked if they can make the electrons revolve. [From Concepts in Science: 6th Grade by Paul F. Brandwein, Elizabeth K. Cooper, Paul E. Blackwood, Elizabeth B. Hone. p. 293.] This lesson fragment offers an opportunity for students to discuss the purposes of models in general and the specific benefits of making models of atoms. Students can also practice assessing models, in light of those purposes. By examining their models at length and in great detail, students can develop their clarity of thought and expression, and review what they know about atoms. Strategies used to remodel The class could begin by discussing models in general and analyzing the concept. "What does 'model' mean? What models have you seen or made? Did they help you understand what they modeled? How? Why? How can you tell a good model from a poor model? What's an example of a good model? Why? A poor one? Why? S-15 What differences were there between models you have seen and the things they modeled? (Ask this of several of the examples previously given.) Why make models? What purpose do they serve?" S-14 Tell students that they are going to make models of atoms. Have students discuss what they know about atoms, and ask, "How could models of atoms help us? How could we make a model of an atom?" You might ask them what parts they would need, and how they could put them together. S-1 Students could make and evaluate various models of atoms and engage in an extended process of designing, making, discussing, and improving models of atoms. S-8 Students could be led in a discussion of the strengths and weaknesses of various models, with questions like the following: (Of each proposed model ask,) What parts does it have? What parts do atoms have? Does the model have any extra parts? Does it leave out parts? How is each part of this model like the part of the atom? (Continue for each part, including the connecters.) Unlike? (Encourage multiple responses.) Could this model be improved? How? How do these models help us? How could they mislead us? How can we avoid being misled? S-10 Do these models help you understand atoms? How, or why not? Do any of these models suggest questions about atoms? What? Do the models help you find answers to those questions? Why or why not? Are the differences between the model and the atom relevant to the question you asked? Why or why not? S-31 How could this model be improved? Why would that improve it? The teacher could use the idea of models to clarify the concept 'analogy'. Have students recall analogies. Have them compare models and analogies. (A model is a thing, analogies are words. Both have similarities and differences to the originals. Both can be evaluated in terms of their purposes and whether relevant features are similar or different.) S-23

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Please complete the following before our next class: Pg. 164 – Exercise C Pg. 165-6 – Reading 1 Vocabulary Pg. 166-167 – Read “Cultural Differences in Counting” Pg. 168-9 – Main Ideas and Details Also, prepare to answer the following discussion questions in class: - Do you like doing math? Why or why not? - Do you think math is important? - What are examples of how you use math in life? (Ex. adding up purchases when shopping) - What are examples of how math makes modern life possible? (Ex. Math is used when designing buildings.) Questions to guide your reading: Cultural Differences in Counting - Are numbers and math the same all over the world? - How do people in the United States count on their fingers? - What’s the opposite way of counting with one’s fingers? - How do people in China count with their hands? - How do cultures and languages differ when it comes to numbers? - How do we know cultures and languages differ in this way? - How did scientists test the aboriginal children? - Why were their findings significant? - Where else was a similar study done? With whom? - What did researchers learn about the Pirahã? - How do the Pirahã express quantities? - Do the Pirahã use numbers at all? - Why do some languages have number words while others don’t?

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In 1974, just a couple years after the launch of the first Landsat satellite, scientists noticed something odd in the Weddell Sea near Antarctica. There was a large ice-free area, called a polynya, in the middle of the ice pack. The polynya, which covered an area as large as New Zealand, reappeared in the winters of 1975 and 1976 but has not been seen since. Scientists interpreted the polynya’s disappearance as a sign that its formation was a naturally rare event. But researchers reporting in Nature Climate Change disagree, saying that the polynya’s appearance used to be far more common and that climate change is now suppressing its formation. What’s more, the polynya’s absence could have implications for the vast conveyor belt of ocean currents that move heat around the globe. Surface seawater around the poles tends to be relatively fresh due to precipitation and the fact that sea ice melts into it, which makes it very cold. As a result, below the surface is a layer of slightly warmer and more saline water not infiltrated by melting ice and precipitation. This higher salinity makes it denser than water at the surface. Scientists think that the Weddell polynya can form when ocean currents push these denser subsurface waters against an underwater mountain chain known as the Maud Rise. This forces the water up to the surface, where it mixes with and warms colder surface waters. While it doesn’t warm the top layer of water enough for a person to comfortably bathe in, it's enough to prevent ice from forming. But at a cost—the heat from the upwelling subsurface water dissipates into the atmosphere soon after it reaches the surface This loss of heat forces the now-cool but still dense water to sink some 3,000 meters to feed a huge, super-cold underwater ocean current known as Antarctic Bottom Water. Antarctic Bottom Water spreads across the global oceans at depths of 3,000 meters and more, delivering oxygen into these deep places. It’s also one of the drivers of global thermohaline circulation, the great ocean conveyor belt that moves heat from the equator towards the poles. But for the mixing to occur in the Weddell Sea, the top layer of ocean water must become denser than the layer below it so that the waters can sink. To find out what has been going on in the Weddell Sea, Casimir de Lavergne of McGill University in Montreal and colleagues began by analyzing temperature and salinity measurements collected by ships and robotic floats in this region since 1956—tens of thousands of data points. The researchers could see that the surface layer of water at the site of the Weddell polynya has been getting less salty since the 1950s. Freshwater is less dense than saltwater, and it acts as a lid on the Weddell system, trapping the subsurface warm waters and preventing them from reaching the surface. That in turn, stops the mixing that produces Antarctic Bottom Water at that site. That increase in freshwater is coming from two sources: Climate change has amplified the global water cycle, increasing both evaporation and precipitation. And Antarctic glaciers have been calving and melting at a greater rate. Both of these sources end up contributing more freshwater to the Weddell Sea than what the area experienced in the past, the researchers note. To look at what the future might hold for this system, de Lavergne and colleagues turned to a set of 36 climate models. Those models, which predict that dry places of the world generally get drier and wet places get wetter, show that this area of the Southern Ocean should see even more precipitation in the future. The models don’t include melting glaciers, but those are expected to add more freshwater, which could make the lid on the system even stronger, according to the researchers. A weakening of the mixing of water in the Weddell Sea could explain, at least in part, a shrinking in Antarctic Bottom Waters reported in 2012. “Reduced convection would reduce the rate of Antarctic Bottom Water formation,” says de Lavergne. That “could cause a weakening in the lower branch of the thermohaline circulation.” That lower branch is the cousin to a similar process of convection happening in the Labrador Sea of the North Atlantic, where cold water from the Arctic sinks and drives deep currents south. If this source of deep water were shut off, perhaps because of an influx of freshwater, scientists have said that the results could be disastrous, particularly for Europe, which is kept warm by this movement of heat and water. Climate researchers consider this scenario highly unlikely but not out of the realm of possibility. And even a weakened system can have effects on climate and weather around the world. More immediately, though, a weakening of the mixing in the Weddell Sea could be contributing to some of climate trends observed in Antarctica and the Southern Ocean. By keep warmer ocean waters trapped, the weakening may explain a slowdown in surface warming and expansion in the sea ice, the researchers note. The weakening of the Weddell Sea mixing has also kept trapped all the heat and carbon stored in those deeper layers of ocean water. If another giant polynya were to form, which is unlikely but possible, the researchers warn, it could release a pulse of warming on the planet.

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Earth & Space Science Students learn how groundwater collects. Students explore the relationship between porosity, permeability, groundwater, and the water table. After completing this tutorial, you will be able to complete the following: Water below the Earth's surface is called groundwater. After a rainfall or snow melt, some of the water soaks into the soil and becomes groundwater. Groundwater occupies open spaces, called pores, between grains of soil. The ratio of open pore space to solid material in the soil (or another material) is called the porosity. A layer of gravel or sand can actually be as much as 40 percent open pore space. Solid igneous rock, on the other hand, can have essentially no open pore space. In order for water to get into the pores, though, there needs to be connections between the pores. In other words, there needs to be an unbroken pathway for the water to follow. This leads to the idea of permeability. Permeability is defined as the rate at which water flows through a material. Permeability depends on porosity, since a rock with no open space will not allow water to flow through, but it also depends on the connections between those pores. The permeability of different materials is generally measured experimentally. Groundwater collects in permeable layers underground, called aquifers. Aquifers represent an important source of water around the world. The Ogallala Aquifer, for example, underlies parts of eight states in the western United States, with a total ground area of approximately 450,000 square kilometers. Water from the Ogallala Aquifer has been estimated to support close to 20 percent of the wheat, corn, cotton, and cattle produced in the United States. Occasionally, especially in areas where layers within the Earth have been tilted, permeable layers may be exposed at the Earth's surface in one location, but deep underground somewhere else. If covered by an impermeable layer, water that soaks into the permeable layer where it reaches the Earth's surface may flow down the tilted layer, becoming pressurized by the weight of the water above it. A well drilled into the pressurized layer is called an artesian well. Because of the pressure, groundwater rises in an artesian well without pumping. In some cases, the water may even shoot out of the ground in a fountain. |Approximate Time||20 Minutes| |Pre-requisite Concepts||Students should be familiar with the properties of materials and with soil types.| |Course||Earth & Space Science| |Type of Tutorial||Concept Development| |Key Vocabulary||clay, drill, drought|

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What is it called when we cut a shape or object into two equal parts? What is it called when we cut a shape or object into four equal parts? What might it be called when we cut a shape or object into three equal parts? Use slides 12-44 of the Introduction to Fractions PowerPoint to revise halves, quarters, thirds, fifths and eighths. Revise the function of the numerator (the number of pieces of the whole you have) and the denominator (the number of pieces that make up the whole). For each fraction, reiterate how many pieces are needed to create a whole. Provide each student with either a label or a circle segment from the Fraction Wheels (there are 29 pieces altogether; it may be necessary to select an appropriate number of pieces, according to the number of students in the class). Allow the students to walk around the classroom so they can find all of the matching parts to make a whole circle. They should also find the appropriate label for their fraction. Once the students have found their group, ask them to sit down and make the whole circle together, using the fraction pieces. Ask each group: Which fraction does your piece represent? How many of these pieces were needed to make the whole circle? Provide each student with a copy of the Fraction Flags Worksheet. Monitor and support the students as they complete the worksheet. Once completed, these could be added to the classroom fractions display.

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SummaryStudents download the software needed to create Arduino programs and make sure their Arduino microcontrollers work correctly. Then, they connect an LED to the Arduino and type up and upload programs to the Arduino board to 1) make the LED blink on and off and 2) make the LED fade (brighten and then dim). Throughout, students reflect on what they've accomplished by answering questions and modifying the original programs and circuits in order to achieve new outcomes. A design challenge gives students a chance to demonstrate their understanding of actuators and Arduinos; they design a functioning system using an Arduino, at least three actuators and either a buzzer or toy motor. For their designs, students sketch, create and turn in a user's manual for the system (text description, commented program, detailed hardware diagram). Numerous worksheets and handouts are provided. In order to design and create new interactive devices, engineers must have a basic understanding of circuits, microcontrollers, computer programming and actuators. Many electronic devices that we interact with daily, such as cell phones, cameras, digital thermometers and blenders, possess microcontrollers that control the devices' functions. Actuators, including LEDs, speakers and motors, are essential components of robotic system. These components are incorporated into circuits that can be controlled using microcontrollers. Like computer and electrical engineers, students are challenged in the final assessment to design their own programs to perform certain tasks using Arduinos and circuits they have built. Students should be familiar with circuits and the basics of programming, including: - Voltage, current, resistance, series and parallel circuits; - Wires, batteries, resistors and breadboards; - Light bulbs, LEDs and piezo buzzers; and - Variables and mathematical operations, control structures (if/else statements, for loops, and while loops), functions and simple serial communication. After this activity, students should be able to: - Construct viable circuits using Arduinos and simple actuators. - Develop programs for the Arduino using the functions pinMode(), digitalWrite(), analogWrite(), and delay() to control actuators through digital pins. More Curriculum Like This Students learn how to connect Arduino microcontroller boards to computers and write basic code to blink LEDs. Provided steps guide students through the connection process, troubleshooting common pitfalls and writing their first Arduino programs. Then they independently write their own code to blink ... Students learn how to set up pre-programmed microcontroller units like the Arduino LilyPad and use them to enhance a product’s functionality and personality. They do this by making plush toys in monster shapes (template provided) with microcontrollers and LEDs sewn into the felt fabric with conducti... Students gain practice in Arduino fundamentals as they design their own small-sized prototype light sculptures to light up a hypothetical courtyard. They program Arduino microcontrollers to control the lighting behavior of at least three light-emitting diodes (LEDs) to create imaginative light displ... Students are introduced to several key concepts of electronic circuits. They learn about some of the physics behind circuits, the key components in a circuit and their pervasiveness in our homes and everyday lives. Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc. Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc. Each student pair needs: - 2 computers or laptops, ready to receive a download of the free Arduino IDE software - 1 Arduino, such as an assembled Arduino Uno R3 for $25 - 1 USB cable - 12 or more wires/jumper wires - 2 or more alligator leads/wires - 1 breadboard, such as a half-size breadboard for $5 - 5 LEDs - 2 or more 220-ohm resistors - 1 piezo speaker or buzzer, such as a piezo buzzer (PS1240) for $1.50 - 1 DC motor with a less than 9V rating, such as a "130 size" DC toy/hobby motor with two soldered wires for $2 - Arduino Overview Handout, one per person - Activity 1: Getting Started Handout, one per person - Activity 2: Making an LED Blink Worksheet, one per person - Activity 3: Making an LED Fade Worksheet, one per person - Arduino Design Challenge #1 Overview Handout, one per person - Homework Handout, one per person - Example Student Progress Tracking System Handout (optional, for teacher) - Common Functions for Arduinos Reference Sheet, as needed - Activity 4: Using a Photo-Resistor Handout, one per person (optional, extension) To share with the entire class: - capability to project an image of the Arduino on the classroom board (such as the Arduino Overview Handout) - (optional) access to the Internet for research and email, plus Word® or Google documents (optional: If you have a cell phone, or if students have cell phones handy, bring them out to look at during this discussion.) You've all used cell phones, right? If you want to call someone, what do you do? You press on the "phone" icon and then scroll through your list of contacts, and then select the person you want to call. Simple enough. But how does the phone make this happen? Think about it—what is inside this device that tells it what colors to display? How does it figure out where your finger is pushing? Well, inside is a tiny computer called a microcontroller. That little device controls the sensors, lights and other electronic components in your phone, which all work together to make an impressive, powerful interactive system. What if you wanted to create your own phone or some other electronic device? What would you need to learn or figure out? (Possible answers: Identify necessary electrical elements that you could use, learn how to connect these elements to a microcontroller in a viable circuit and program the microcontroller.) Great! But before we can tackle something as advanced as a cell phone, let's start by building some very simple systems—such as a system made of one microcontroller and one LED. How do we program a microcontroller to make an LED do different things? Well, that's what we're going to figure out today! actuator: A device that affects (or does) something. Examples: LEDs, speakers and motors. input : Signals or information received by a system. LED: Acronym for light-emitting diode. An electronic device that emits light when current flows through it. Note that, since it is a diode, current can only flow in one direction through the LED. microcontroller: A small computer on a single chip. output: Signals or information sent by a system. physical computing: The process of designing devices to interact with the world around them. sensor: A device that measures a physical quantity. Often, it is an electrical device whose resistance depends on the physical quantity it measures. Examples: photoresistors, temperature sensors and keyboards. serial communication: A process for communicating with a computer in which data is sent one bit at a time. Necessary Prior Knowledge Before starting this activity, students should have a conceptual understanding of current, voltage and resistance, and be able to identify and create series and parallel circuits. An excellent refresher resource can be found at the Physics Classroom. Students must also be capable of simple programming, ideally in C or C++ (the basis for the Arduino programming language). Specifically, students must understand what variables are, how to declare them, and how to perform mathematical operations with them, as well as use control structures like if/else statements, for loops and while loops. Cplusplus has a tutorial for brushing up on these concepts (see the bullets under "Basics of C++" and "Program structure"). While four 60-minute periods work well to conduct the described activities, some activities may span across multiple periods. Throughout the Procedure section, suggested time allotments are provided. Through these series of activities, students engage in physical computing, which is the process of using electronic components to design devices that interact with humans and the world around them. To do this, students learn how to use simple actuators. Think of actuators as the inverse of sensors: they are devices that convert electrical signals into "physical actions" in order to affect their surroundings. LEDs and piezo speakers are small and inexpensive actuators that are easy for beginners to work with. An LED (light-emitting diode) is a device that releases light when current runs through it. Similarly, a piezo speaker ("buzzer") is a device that produces sound waves when current flows through it. Small DC motors are also great actuators for beginners, but be sure to use motors with small voltage ratings. If you want to use a computer to control LEDs, you'll quickly realize that they have no way to be directly connected to the computer. This is where the Arduino comes in. An Arduino is a microcontroller that is conveniently designed to enable physical computing. It is compatible with many different sensors and actuators, easily programmable using a language similar to C/C++, and is inexpensive (less than $30). The Arduino Uno board can be powered using an external power source (such as a 9V power adaptor or 9V battery) or directly by a computer using a USB cable. The many pins on the board are used for different purposes. GND pins are used for "ground" (0V). If a device needs a constant voltage supply, use 3.3V or 5V pins. In order to collect information from sensors (input) or emit electronic signals to control actuators (output), the board has digital and analog I/O pins. Digital pins can be used for input or output, but only have two states: HIGH (5V) or LOW (0V). In order to simulate voltages between 0V and 5V, the Arduino uses pulse-width modulation (PWM)—the process of essentially fluctuating the state of a digital pin between LOW and HIGH at a fast, specific rate. In these hands-on activities, students connect actuators to digital pins. Avoid letting students use digital pins 0 and 1, as they can interfere with serial communication. Programming the Arduino is relatively easy, even for people with little to no programming experience. Downloading the Arduino IDE—software that provides a space and resources to create programs (or what they call "sketches") for the Arduino—is free and very easy to use. Every program must contain two functions: setup() and loop(). Whatever is put into the setup() function is executed once by the Arduino; conversely, whatever is written under the loop() function is repeated over and over by the Arduino until it loses power. However, the program is not lost. Once power is restored, the Arduino restarts and executes the program again. For this activity, students must be familiar with four particular functions: - pinMode(): function used to declare the state of a digital pin (INPUT or OUTPUT) - digitalWrite(): function to set the state of an (output) digital pin (HIGH or LOW) - analogWrite(): function to oscillate the state of an (output) digital pin between HIGH and LOW at various rates to simulate voltages between 0V and 5V - delay(): function to "pause" the Arduino (have it do nothing) in milliseconds. For a thorough list of Arduino structures and functions, refer to the Arduino Programming Notebook. Before the Activity - Make copies of all handouts, one each per person. - Test all of the equipment. Verify that all Arduinos and actuators work correctly. - As a test, load the Arduino IDE software on one computer (like students will do by following instructions on the Activity 1: Getting Started Handout), so you are aware of any issues that students may encounter, such as requiring administrator approval. - Gather all materials and place them in bins at the front of the classroom. - Set up the classroom board with instructions and notes, such as the pre-activity assessment questions. - Prepare to project an image of the Arduino on the classroom board (such as the one provided on the Arduino Overview Handout). With the Students—Introduction (25 minutes) - Divide the class into student pairs. - Administer the Know Your Audience pre-activity assessment, as described in the Assessment section (15 minutes). - Arduino overview presentation (10 minutes) - Hand out the Arduino Overview Handout. - Project a picture of the Arduino on the classroom board, such as the one on the student handout. - As a class, review the handout, pointing out the different parts of the Arduino on the projected image. Activity 1: Getting Started with the Arduino (25 minutes) - Direct student groups to collect the following materials from the front of the room and then return to their seats (5 minutes). Per student: computer/laptop. Per pair: Arduino, USB cable, LED, breadboard, 2 jumper wires. - Activity 1 Overview (10 minutes) - Explain that in order to program the Arduino, students need to download the Arduino IDE, which is the software used for making programs for the Arduino microcontroller. - Hand out the Activity 1: Getting Started Handout. Direct students to use the handout as a guide. - Also explain that though students each work on their own laptops, they share an Arduino with their partners. - Activity 1 Work Time (10 minutes) - During this time, students download the Arduino IDE and test their Arduinos, following the handout instructions. - Assist students as necessary, addressing technical issues as they arise. - All students must successfully complete Activity 1 before moving forward. Activity 2: Making an LED Blink (65 minutes) - Activity 2 Overview (5 minutes) A. Show students an Arduino correctly connected to an LED using a resistor, two jumper wires and a breadboard (see Figure 1). B. Explain that they are going to create this setup (Figure 1), and must do so carefully. - The resistor is necessary to decrease the current that flows through the LED. Without the resistor, it is possible to burn out the LED. - The LED has two metal prongs—a long one and a short one. Connect the long one to the wire going to Pin 13. Connect the short one to the wire going to GND. C. Explain that they will type up a sketch (program) that directs the Arduino to turn the LED on and off repeatedly (make it blink). D. Hand out the Activity 2: Making an LED Blink Worksheet. Review the document as a class. - Explain that, in order to get comfortable creating their own programs, students need to type them up on their own. However, since each student pair is sharing an Arduino and other hardware (breadboard, wires, LED and resistor), they must take turns testing their sketches. - Require that all reflection questions and alternatives be completed before moving on to the next activity. - Groups that finish Activity 2 early may move on to Activity 3, with teacher permission. - Activity 2 Work Time (50 minutes) - Students use this time to create the setup and type up the code provided. Then they move onto the reflection questions and alternatives. - During this time, circle the room to track student progress. Address technical issues that may arise, but encourage students to talk with their peers before asking for teacher help. - Remind students to talk and collaborate with their partners to achieve these tasks, though they must write up their sketches on their own. - For students who finish early, check that they have completed the worksheet's reflection questions and alternatives, and then give them the Activity 3: Making an LED Fade Worksheet so that they can continue working. - Activity 2 Class Reflection (10 minutes): As a class, review the reflection questions and alternatives. Activity 3: Making an LED Fade (55 minutes) - Activity 3 Overview (5 minutes) A. Explain to students that they are now going to create a new program to make the LED fade instead of blink. This requires the use of pulse-width modulation (PWM). Do not explain what this is; students will research this as part of the activity. B. Hand out the Activity 3: Making an LED Fade Worksheet. Review the document as a class. - Remind students that in order to get comfortable creating their own programs, they need to type them up on their own. - Require all reflection questions and alternatives to be completed before moving on to the next activity. - Groups that finish Activity 3 early may move on to the Arduino Design Challenge, with teacher permission. - Activity 3 Work Time (40 minutes) - Students use this time to create the setup (same as Activity 2) and type up the code provided. Then, they move onto the reflection questions and alternatives. - During this time, circle the room to track student progress. Address technical issues that arise. - Remind students to talk and collaborate with their partners to achieve these tasks, though they must write up their sketches on their own. - For students who finish early, check that they have completed the reflection questions and alternatives, and then give them the Arduino Design Challenge #1 Overview Handout to read or give them a clean-up task. - Activity 3 Class Reflection (10 minutes): As a class, review the reflection questions and alternatives. Final Assessment: Arduino Design Challenge (70 minutes) - Design Challenge: Introduction (5 minutes) - Introduce the term actuators. Explain that an LED is an example of an actuator. Then introduce two new actuators: piezo speaker (buzzer) and DC motor. These are integrated into circuits in the same way as LEDs, but they just require alligator clips to connect them to the jumper wires. - Hand out the Arduino Design Challenge #1 Overview Handout and review it as a class. Make sure the challenge requirements are clear and emphasize that, for homework, they will need to be able to explain both the software (program) and hardware (setup) of their designs. - Design Challenge Work Time (45 minutes) - Students first plan and sketch out their ideas. Once they obtain teacher approval, they get additional materials. - Students work in teams. For this challenge, it works well if one student codes while the other builds, and then they check each another. - During this time, walk around to track progress and address technical issues. Note: When possible, avoid giving students the answer right away, especially if they have resources that provide the information. Encourage students to look back at reflections, alternatives, diagrams and prior code, as well as talk with other students about issues they encounter. Push them to use resources other than the teacher. - Design Presentations (10 minutes) - Ask students to stand at tables or desks by their designs and be ready to show and explain to their peers how they work. - While one student stays with the setup to show it to their peers, the other partner visits other tables to see what other groups designed. - After 5 minutes, ask students to switch roles so all students have the opportunity to see other projects and explain their work. - During this time, walk around and make note of which students completed the challenge, using the example rubric in the challenge handout (or your own). Require unfinished projects to be completed by students on their own time. - Clean Up & Final Assessment (10 minutes) - Stop students and ask them to sketch the setup (hardware) from their designs. Tell them that this must be a detailed sketch that includes all hardware used: Arduino, breadboard, jumper wires, resistors and actuators. - Ask students to email themselves a copy of the program for their designs; suggest they cut and paste it into a Word® or a Google document for convenience. - THEN have students clean up. - Remind students that the design manual/guide is due the day after tomorrow. Arduinos can be short-circuited. To avoid this, have students double-check their hardware before connecting Arduinos to computers. If an Arduino is being short-circuited, do not touch it; simply unplug the USB cable from the computer and leave the Arduino alone for a few minutes (it may be hot). Know Your Audience: Before jumping into these activities, find out if any students are already familiar with Arduinos. One way to do this is to write a list of questions on the classroom board, such as: - What is an Arduino? (If you've never heard of that word before, that's okay!) - What is a microcontroller? - What do sensors and actuators do? List as many of each as you can name. - On a scale from 1 to 5, with 1 representing "no understanding" and 5 representing "complete understanding," rate the following: programming an Arduino, connecting hardware to an Arduino. Then lead a short class discussion, asking students to share what they think they know about these items. For the last question, have students hold up the number of fingers that corresponds to their answers (a quick visual poll). If some students believe they already know how to use Arduinos, consider asking them to skip the first part of each activity and move directly onto the alternatives. If they can do the alternatives without assistance, they are ready to move onto the extension activity. If students have access to fancier electronic devices (such as LCDs or servo-motors), consider letting them use those to design unique robotic devices with specific purposes. Activity Embedded Assessment Tracking Student Progress: During each activity when students are working in pairs (guided by the handouts and worksheets), observe and make note of individual student progress on each task. At the end of each activity, gauge students' depth of comprehension as they discuss and then submit their responses to the reflection questions and alternatives. It is helpful to have a clipboard with a tracking structure in order to document this progress; see the Example Student Progress Tracking System. If some students require more time to complete the alternatives tasks, follow up with them to remind them to come back during lunch or after school to finish them. If they do not, they will experience more difficulty during later activities. Performance-Based Assessment: Design Your-Own System! To demonstrate their understanding of actuators and Arduinos, students design new systems, as guided by the Arduino Design Challenge #1 Overview Handout. Provide students with two new components: piezo speaker (buzzer) and DC motor. Though students have not worked with these devices before, they function similarly to LEDs—they have two pins: one that connects to HIGH and the other to LOW. Working in pairs, students must use at least three actuators in their designs, with at least one of them being the buzzer or DC motor. Groups present their functioning systems to their peers and the teacher, explaining what they do and how they work. To complete the project, students submit detailed diagrams of their hardware systems and a thoroughly commented copy of the program. Review their completed "manual" of deliverables to gauge their depth of comprehension. Reflections: At the end of the activities, assign students to complete the Homework Handout to write in their notebooks about what they have learned in response to three questions. This requires them to describe the four Arduino functions used (what they do and how they work; see full descriptions in the Common Functions for Arduinos Reference Sheet) as well as make connections between what they did during the activity and real-world electronic systems they interact with every day. For more advanced students who complete the activities quickly and with ease, exploring sensors is a logical next step. Sensors are devices that detect some aspect of the environment around them. Often, they are variable resistors—components whose resistance depends on a physical property. For example, a photoresistor is a sensor that detects light. When the amount of light shown on a photoresistor is increased, the resistance of this element decreases. This change can be detected using an analog pin on the Arduino board. Provide students with a sensor (such as a photoresistor or force-sensitive resistor) and ask them to use the Arduino to collect measurements from the sensor. Activity 4: Using a Photoresistor Handout is an example of such an activity. Additional Multimedia Support Jeremy Blum's Arduino Tutorials: https://www.youtube.com/user/sciguy14/videos Ladyada Arduino Tutorial: http://www.ladyada.net/learn/arduino/index.html John Boxall's 10 Simple-But-Fun Arduino Projects by Popular Mechanics: http://www.popularmechanics.com/technology/how-to/a3099/10-simple-but-fun-projects-to-make-with-arduino-15603196/ Quarkstream Arduino Blog: https://quarkstream.wordpress.com/ Mr. Z's Programming Page: http://sofphysics.wikispaces.com/Programming+Page Banzi, Massimo. Getting Started with Arduino. Beijing, China: O'Reilly Media, 2011. Crowder, Richard M. Automation and Robotics: Tactile Sensing. January 1998. University of Southampton, UK. Accessed August 5, 2014. http://www.southampton.ac.uk/~rmc1/robotics/artactile.htm Hirzel, Timothy. Pulse-Width Modulation. Arduino. Accessed August 5, 2014. http://arduino.cc/en/Tutorial/PWM Input/output. Last updated August 6, 2014. Wikipedia, The Free Encyclopedia. Accessed August 7, 2014. http://en.wikipedia.org/wiki/Input/output Ladyada. Force Sensitive Resistor. Last updated July 30, 2013. AdaFruit Learning Systems. Accessed August 5, 2014. https://learn.adafruit.com/force-sensitive-resistor-fsr/overview Microcontroller UART Tutorial. 2014. Society of Robots. Accessed August 5, 2014. http://www.societyofrobots.com/microcontroller_uart.shtml Mrmak, Nebojsa, van Oorschot, Paul, and Pustjens, Jan-Willem. Your Guide to the World of Resistors. 2014. ResistorGuide.com. Accessed August 5, 2014. http://www.resistorguide.com/ ContributorsMichael Zitolo, Lisa Ali Copyright© 2015 by Regents of the University of Colorado; original © 2014 Polytechnic Institute of New York University Supporting ProgramSMARTER RET Program, Polytechnic Institute of New York University This activity was developed by the Science and Mechatronics Aided Research for Teachers with an Entrepreneurial ExpeRience (SMARTER): A Research Experience for Teachers (RET) Program in the School of Engineering funded by National Science Foundation RET grant no. 1132482. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government. Last modified: March 7, 2018

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Today, the seaside mountain pass at Thermopylae in Greece looks very different than it did 2,500 years ago. The nearby Spercheios River has deposited enough sediment to considerably widen the once-narrow strip of land (Sacks 246). There is only a stone stature of a Spartan solider to remind us of the fierce battle that took place there in 480 BC between the Greeks and the invading Persia ns (Baker 65). The Greeks’ defense of the pass at Thermopylae culminated in a gloriously heroic but ultimately suicidal confrontation that was vitally important to the final outcome of the Persian Wars King Darius of Persia first invaded Greece in 492 BC and was unsuccessful (Pomeroy et al 187-188). In 480 BC Darius’ son and successor Xerxes decided to bring a victorious conclusion to the war that his father had started. King Xerxes controlled a Phoenician navy and up to 250,000 land troops (sources vary), and he expected to easily overpower the Greeks, who were constantly fighting among themselves (Pomeroy et al 194). The Greeks knew that the Persians were going to attack, and they consulted the Oracle at Delphi. The Oracle told the Spartans that a king’s death would save Greece, and she told the Athenians that wooden walls would save Greece (Pomeroy et al 194). At the critical time when King Leonidas of Sparta needed to dispatch his army, Sparta was celebrating a religious festival that prohibited warriors from leaving to do battle (Sacks 246). King Leonidas decided leave immediately with 300 members of his royal guard. He only took men who were in their thirties and who had sons to carry on their family’s name (Baker 63). The rest of the army was supposed to follow at the next full moon, when the festival was over. On the way to Thermopylae, other men who were eager to defend Greece joined Leonidas. By the time the Greek army arrived at Thermopylae, its numbers had swelled to between 7,000 and 10,000 men (Powell 27). At that time, the pass at Thermopylae was only about 55 feet wide at its narrowest point. The Aegean Sea bordered one side, and sheer cliffs bordered the other. Normal fighting tactics were impossible. The Greeks set up camp and then waited for orders from Leonidas. They combed their long hair and did gymnastic exercises to pass the time while they waited to fight. When Xerxes’ spies told him what the Greeks were doing, he laughed. He didn’t know that those were customary ways for Greeks to prepare for battle. Xerxes waited for four days, expecting the Greeks to retreat when they realized how many warriors they were up against. On the fourth day, Xerxes attacked (Baker 63). Though Xerxes had a huge army, in that small space he could only use a fraction of his men at a time. Xerxes sent group after group of Persian warriors into the pass. The Greeks, who had better armor and longer spears (Sacks 246), slaughtered each group of fighters. Even Xerxes’ elite legion of Immortals (so called because there was always an Immortal to replace any Immortal that fell in battle) failed to overpower the Greeks (Baker 64). This continued for two days. Two of Xerxes’ brothers were killed (Sacks 246). Xerxes realized that his tactics weren’t working, and he called his men back to their tents. Leonidas and his men were overjoyed. If they could hold out until the festival was over and their reinforcements came, they could win. But that night a Greek traitor named Ephialtes crept into the Persian camp and revealed a little-known path used by goatherds that led into the mountain and down behind the Greek camp. The local Phocian army had been instructed to guard this path in case the Persians found it. Ephialtes led the commander of the Immortals up the path. The Phocians raced to tell Leonidas that he and his men were surrounded (Pomeroy et al 195). When Leonides heard the bad news, he dismissed the men who had joined him along the way to Thermopylae. Possibly he wanted to save as many men as possible for later battles while still delaying the Persians. Only the Thebans, the Thespians, and his three hundred Spartans remained. According to 5th century BC historian Herodotus, the Thebans were forced to stay (Baker 65). The battle began at midmorning. The Persian troops, being whipped by their commanders, attacked from both ends of the pass. Many of them drowned in the sea or were trampled underfoot. The 1,400 Greeks fought until their spears and swords broke, then fought with their hands and teeth. Leonidas died early in the battle, and the Greeks defended his body fiercely. According to Herodotus, the Persians attempted to capture his corpse four times before they were successful. The battle did not end until every Greek solider was dead (Baker 65). At Xerxes’ command, Leonidas’ body was beheaded and displayed on a cross (Pomeroy et al 195). The Battle of Thermopylae was very important as a delay tactic and because it made the Persians overly confident. It allowed the Athenians time to evacuate their city and send the elderly citizens and the city’s treasure to the island of Salamis and the women and children to safety in Troezen while preparing the men for a naval battle (Pomeroy et al 194). After Thermopylae, Xerxes was so confident that when the Greeks sent him a message through a slave of Persian descent, he took their bait and fought a naval battle that he was not prepared for (Baker 89). A storm at Artemisium had badly damaged his fleet during the Battle of Thermopylae. Still, he sent his ships to the narrow straits at Salamis (Pomeroy et al 196). The Greeks soundly defeated Xerxes’ navy with their heavier vessels. Two more Greek victories destroyed Xerxes’ dreams of conquering Greece (Baker 89). The Greeks’ fearless performance at Thermopylae has captured the hearts and imaginations of generations. Historians say that the fighting at the Alamo is the only modern battle that was fought with comparable heroism. German troops trained during World War II were taught about the Battle of Thermopylae and were told that they were expected to perform similarly. And the challenges of the Vietnam War were chronicled in the film Go Tell the Spartans, which was named for this epitaph composed by Simonides for the heroes at Thermopylae: “‘Go tell the Spartans, stranger passing by, that here, obeying their commands, we lie’” (qtd in Pomeroy et al 196). Baker, Rosalie F., and Charles F. Baker III. Ancient Greeks. New York: Oxford UP, 1997. Pomeroy, Sarah, et al. Ancient Greece: A Political, Social, and Cultural History. New York: Oxford UP, 1999. Powell, Anton. Ancient Greece. New York: Facts On File, 1994. Sacks, David. Dictionary of the Ancient Greek World. New York: Oxford UP, 1996.

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The origin of the ice age has greatly perplexed uniformitarian scientists. Much cooler summers and copious snowfall are required, but they are inversely related, since cooler air is drier. It is unlikely cooler temperatures could induce a change in atmospheric circulation that would provide the needed moisture. As a result, well over 60 theories have been proposed. Charlesworth states: 1 "Pleistocene phenomena have produced an absolute riot of theories ranging 'from the remotely possible to the mutually contradictory and the palpably inadequate.'" A uniformitarian ice age seems meteorologically impossible. The necessary temperature drop in Northern Canada has been established by a sophisticated energy balance model over a snow cover. Summers must be 10 degrees to 12 degrees C cooler than today, even with twice the normal winter snowfall. 2 The Milankovitch mechanism, or the old astronomical theory, has recently been proposed as the solution to the problem. Computer climate simulations have shown that it could initiate an ice age, or at least glacial/interglacial fluctuations. However, an in-depth examination does not support this. The astronomical theory is based on small changes in solar radiation, caused by periodic shifts in the earth's orbital geometry. It had been assumed too weak to cause ice ages by meteorologists, until the oscillations were "statistically" correlated with oxygen isotope fluctuations in deep-sea cores. The latter cycles are believed related mostly to glacial ice volume, and partially to ocean paleotemperature, although the exact relationship has been controversial. The predominant period from cores was correlated to the 100,000-year period of the earth's eccentricity, which changes the solar radiation at most 0.17% 3 This is an infinitesimal effect. Many other serious problems plague the astronomical theory. 4, 5 Although models can test causal hypotheses, Bryson says they ". . . are not sufficiently advanced, nor is our knowledge of the required inputs, to allow for climatic reconstruction. . . ." 6 The climate change following the Genesis Flood provides a likely catastrophic mechanism for an ice age. The Flood was a tremendous tectonic and volcanic event. Large amounts of volcanic aerosols would remain in the atmosphere following the Flood, generating a large temperature drop over land by reflecting much solar radiation back to space. Volcanic aerosols would likely be replenished in the atmosphere for hundreds of years following the Flood, due to high post-Flood volcanism, which is indicated in Pleistocene sediments. 7 The moisture would be provided by strong evaporation from a much warmer ocean, following the Flood. The warm ocean is a consequence of a warmer pre-Flood climate and the release of hot subterranean water during the eruption of "all the fountains of the great deep" (Genesis 7:11). The added quantity of water must have been large to cover all the pre-Flood mountains, which were lower than today. Evaporation over the ocean is proportional to how cool, dry, and unstable the air is, and how fast the wind blows. 8 Indirectly, it is proportional to sea surface temperature. A 10 degree C air-sea temperature difference, with a relative humidity of 50%, will evaporate seven times more water at a sea surface temperature of 30 degrees C than at 0 degrees C. Thus, the areas of greatest evaporation would be at higher latitudes and off the east coast of Northern Hemisphere continents. Focusing on northeast North America, the combination of cool land and warm ocean would cause the high level winds and a main storm track to be parallel to the east coast, by the thermal wind equation. 9 Storm after storm would develop near the eastern shoreline, similar to modern-day Northeasters, over the continent. Once a snow cover is established, more solar radiation is reflected back to space, reinforcing the cooling over land, and compensating the volcanic lulls. The ice sheet will grow as long as the large supply of moisture is available, which depends upon the warmth of the ocean. Thus, the time to reach maximum ice volume will depend upon the cooling time of the ocean. This can be found from the heat balance equation for the ocean, with reasonable assumptions of post-Flood climatology and initial and final average ocean temperatures. However, the heat lost from the ocean would be added to the atmosphere, which would slow the oceanic cooling with cool summers and warm winters. The time to reach maximum ice volume must also consider the heat balance of the post-Flood atmosphere, which would strongly depend upon the severity of volcanic activity. Considering ranges of volcanism and the possible variations in the terms of the balance equations, the time for glacial maximum ranges from 250 to 1300 years. 10 The average ice depth at glacial maximum is proportional to the total evaporation from the warm ocean at mid and high latitudes, and the transport of moisture from lower latitudes. Since most snow in winter storms falls in the colder portion of the storm, twice the precipitation was assumed to fall over the cold land than over the ocean. Some of the moisture, re-evaporated from non-glaciated land, would end up as snow on the ice sheet, but this effect should be mostly balanced by summer runoff. The average depth of ice was calculated at roughly half uniformitarian estimates. The latter are really unknown. As Bloom states, "Unfortunately, few facts about its thickness are known . . . we must turn to analogy and theory. . . ." 11 The time to melt an ice sheet at mid-latitudes is surprisingly short, once the copious moisture source is gone. It depends upon the energy balance over a snow or ice cover. 12 Several additional factors would have enhanced melting. Crevassing would increase the absorption of solar radiation, by providing more surface area. 13 The climate would be colder and drier than at present, with strong dusty storms that would tend to track along the ice sheet boundary. The extensive loess sheets south of and within the periphery of the past ice sheet attest to this. Dust settling on the ice would greatly increase the solar absorption and melting. A mountain snowfield in Japan was observed to absorb 85% of the solar radiation after 4000 ppm of pollution dust had settled on its surface. 14 Earth scientists believe there were many ice ages—perhaps more than 30—in regular succession during the late Cenozoic based on oxygen isotope fluctuations in deep-sea cores. 15 However, the ocean results have many difficulties, and sharply conflict with the long-held four ice-age continental scheme. Before the early 20th century, the number of ice ages was much debated. Some scientists believed in only one ice age, but the sediments are complex and have evidence of anywhere from one to four, or possibly more till sheets, separated by non-glacial deposits. Four ice ages became established mainly from gravel terraces in the Alps, and reinforced by soil stratigraphy. Much has been learned about glacial behavior and sedimentation since then. The Alps terraces are now viewed as possibly ". . . a result of repeated tectonic uplift cycles—not widespread climatic changes per se." 16 Variously weathered "interglacial soils" between till sheets are complex, and practically always have the top organic horizon missing. It is difficult to know whether they are really soils. 17 Besides, the rate of modern soil formation is unknown, and depends upon many complex factors, like the amount of warmth, moisture, and time. 18 Therefore, the number of glaciations is still an open question. There are strong indications that there was only one ice age. As discussed previously, the requirements for an ice age are very stringent. The problem grows to impossibility, when more than one is considered. Practically all the ice-age sediments are from the last, and these deposits are very thin over interior areas, and not overly thick at the periphery. Till can sometimes be laid down rapidly, especially in end moraines. Thus the main characteristics of the till favor one ice age. Pleistocene fossils are rare in glaciated areas, which is mysterious, if there were many interglacials. Practically all the megafaunal extinctions were after the last—a difficult problem if there was more than one. One dynamic ice age could explain the features of the till along the periphery by large fluctuations and surges, which would cause stacked till sheets. 19 Organic remains can be trapped by these oscillations. 20 Large fluctuations may be caused by variable continental cooling, depending upon volcanic activity. In addition, most of the snow and ice should accumulate at the periphery, closest to the main storm tracks. Large surface slopes and warm basal temperatures at the edge are conducive to rapid glacial movement. 21 In summary, the mystery of the ice age can be best explained by one catastrophic ice age as a consequence of the Genesis Flood. 1 Charlesworth, J.K., 1957, The Quaternary Era, Vol. 2, London, Edward Arnold, p. 1532. 2 Williams, L.D., 1979, "An Energy Balance Model of Potential Glacierization of Northern Canada," Arctic and Alpine Research, v. 11, n. 4, pp. 443-456. 3. Fong, P., 1982, "Latent Heat of Melting and Its Importance for Glaciation Cycles," Climatic Change, v. 4, p. 199. 4 Oard, M.J., 1984, "Ice Ages: The Mystery Solved? Part 2: The Manipulation of Deep-Sea Cores,"Creation Research Society Quarterly, v. 21, n. 3, pp. 125-137. 5 Oard, M.J., 1985, "Ice Ages: The mystery Solved? Part 3: Paleomagnetic Stratigraphy and Data Manipulation,"Creation Research Society Quarterly, v. 21, n. 4, pp. 170-181. 6 Bryson, R.A., 1985, "On Climatic Analogs in Paleoclimatic Reconstruction," Quaternary Research, v. 23, n. 3, p. 275. 7 Charlesworth, Op. Cit., p. 601. 8 Bunker, A.F., 1976, "A Computation of Surface Energy Flux and Annual Air-Sea Interaction Cycles of the North Atlantic Ocean," Monthly Weather Review, v. 104, n. 9, p. 1122. 9 Holton, J.R., 1972, An Introduction to Dynamic Meteorology, New York, Academic Press, pp. 48-51. 10 Oard, M.D., "An Ice Age Within the Biblical Time Frame," Proceedings of the First International Conference on Creationism, Pittsburgh (in press). 11 Bloom, A.L., 1971, "Glacial-Eustatic and Isostatic Controls of Sea Level," in K.K. Turekian, ed., Late Cenozoic Glacial Ages, New Haven, Yale University Press, p. 367. 12 Patterson, W.S.B., 1969, The Physics of Glaciers, New York, Pergamon, pp. 45-62. 13 Hughes, T., 1986, "The Jakobshanvs Effect:" Geophysical Research Letters, v. 13, n. 1, pp. 46-48. 14 Warren, S.G. and W.J. Wiscombe, 1980, "A Model for the Spectral Albedo of Snow. II. Snow Containing Atmospheric Aerosols," Journal of the Atmospheric Sciences, v. 37, n. 12, p. 2736. 15 Kennett, J.P. 1982, Marine Geology, New Jersey, Prentice-Hall, p. 747. 16 Eyles, N., W.R. Dearman and T.D. Douglas, 1983, "Glacial Landsystems in Britain and North America" in N. Eyles, ed., Glacial Geology, New York, Pergamon, p. 217. 17 Valentine, K. and J. Dalrymple, 1976, "Quarternary Buried Paleosols: A Critical Review," Quarternary Research, v. 6, n. 2, pp. 209-222. 18 Boardman, J., 1985, "Comparison of Soils in Midwestern United States and Western Europe with the Interglacial Record," Quaternary Research, v. 23, n. 1, pp. 62-75. 19 Paul, M.A., 1983, "The Supraglacial Landsystem," in N. Eyles, ed., Glacial Geology, New York, Pergamon, pp. 71-90. 20 Eyles, Dearman and Douglas, Op. Cit., p. 222. 21 Patterson, Op. Cit., p. 63-167. * Mr. Oard is a meteorologist with the U.S. Weather Bureau, Montana.

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Determining Parts of Speech The part of speech of a word can be identified from its form and meaning. The form of a word refers to the ending it takes and what position it takes in a sentence. Form alone gives us a lot of information on the part of speech of a word. It is sometimes useful to look at the meaning of a word when we need to determine the part of speech. - A word is a noun if it takes the subject or object position in a sentence. - Countable nouns have two forms, singular and plural. The plural form of most words is marked by the plural ending (s/es/ies).

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To make the concept of gear ratio easier to understand, let’s first review some properties of circles. The radius of a circle is defined as the length from the center of the circle to the outside of the circle. If we draw a line that starts at one side of the circle, goes through the center, and then stops at the opposite side of the circle, we would have the diameter of the circle. The diameter is twice as long as the radius. Finally, if we measured the distance around the circle, we’d get the circumference. It turns out that the circumference is equal to the diameter multiplied by Pi. Pi is often represented by the Greek symbol, , and is equal to 3.1415927… or a very strange ratio of 22 / 7 ! Now we can apply these concepts to look at how gears work. Look at the gears in the diagram. The radius of the gear is the distance from the center of the gear (where it rotates) to the outside of the gear. If gear A measures 10 in [25.4 cm] in radius and gear B measures 5 in [12.7 cm] in radius, then the radius of gear A is twice as large as gear B. We say that the gear ratio of gear A to gear B is 2:1. Additionally, we know that the diameter is twice the radius, and the circumference is times the diameter, so if the radius of gear A is twice the radius of gear B, then the circumference of gear A is also twice that of gear B. In the diagram of the two gears you can see that twice the circumference means that the gear has twice the number of teeth. Imagine gear A starts to rotate. As its teeth touch the teeth of gear B a force is exerted. In the diagram this is shown as FA. If gear A rotates clockwise, the teeth of gear A push downwards on the teeth of gear B. This will cause gear B to move counter-clockwise. In this case, gear A is called the driving gear, and gear B is called the driven gear. If the gear ratio of A to B is 2:1, then there are twice as many teeth on gear A as on gear B. If you look where the two gears connect, you can see that the gear teeth alternate, that is a tooth from gear A is followed by a tooth from gear B, then one from gear A, then one from gear B, and so on. Since we said that gear A has twice as many teeth as gear B, then it will take twice as long for gear A to rotate once all the way around. This means that the gear A will rotate two times slower than gear B. This is very useful because we now have a way of speeding up and slowing down torque rotation! We said that a gear that is half the size of another will rotate twice as fast. A gear that is one fourth the size of another will rotate four times as fast. This relationship is called a reciprocal. ½ is the reciprocal of 2, and ¼ is the reciprocal of 4. To find the reciprocal of a number, you take one divided by the number. Reciprocal of number = 1 ÷ number We say that the gear ratio of two gears is the reciprocal of the ratio of their rotation speeds. To calculate torque on two gears, use the formula for torque. Torque = Force · Length of lever arm Gear A is exerting a force on gear B, but remember Newton’s third law states gear B will, in turn, exert an equal force back on gear A. This means that the force on each gear is the same. The force applied to each gear occurs where the gear teeth are in contact on the outside of each gear, so the length of the lever arm for each gear is equal to the radius of the gear. Since the radius of gear A is twice the radius of gear B, the torque on gear A will be twice the torque on gear B. This is very useful because we now have a way of enlarging or reducing torque! Let’s review what gear ratio means. If the gear ratio of gear A to gear B is 4:1, we know the following. The radius, diameter, and circumference of gear A are all four times larger than gear B. We know that the torque on gear A will be four times greater than the torque on gear B. Finally we know that gear A will rotate at one fourth the speed of gear B. A larger gear will rotate slower than a smaller gear and have a greater torque, and the two gears will rotate in opposite directions. When working with pulleys connected by a belt, the principles behind gear ratio, rotation speed, and torque are exactly the same. In the diagram, the pulley on the left has a radius equal to half the radius of the pulley on the right. This means that the pulley on the left will rotate twice as fast, but will have only half the torque. Torque and gear ratios are important in designing what is called the hovercraft’s transmission. Lightweight engines produce most of their horsepower at high rpm (revolutions per minute). Unfortunately, this would spin a propeller too fast for safety. To get maximum thrust from a propeller, the tips of the blades should rotate between 683.4 and 714.5 mph [1100 – 1150 km/h]. At speeds above this, the flow of air begins to detach itself from the propeller, decreasing efficiency and increasing noise. Propeller tip speed on a hovercraft should never run higher than 460 mph [641 km/h] tip speed for safety. It's often necessary to use a belt or gear driven system to slow the propeller but still let the engine reach its maximum horsepower. Using a small pulley on the engine and a larger pulley on the propeller will allow the propeller to turn more slowly than the engine. This is ideal for a two or four-bladed propeller, since they produce more thrust at slower speeds. They also produce less noise and develop more thrust per horsepower than fans with many blades. Recall that the pitch of a propeller refers to the angle at which it is set, and a greater pitch means that the propeller can push more air and produce more thrust. Pushing greater amounts of air, however, requires more torque. If the pitch of the propeller is too great, it will strain the engine, making it unable to reach its maximum rpm. Too great a pitch can also cause the blade to "stall" where upon it will push almost no air. Choosing the right propeller pitch to maximize thrust while still allowing the engine to reach its maximum rpm is a very important step in designing a hovercraft. The graph below is an example of what the characteristics of an engine and propeller could look like. The red curve shows the power output of the engine. Notice how it increases as rpm increases until it reaches a maximum at about 3400 rpm. It then quickly decreases as the speed continues to increase. The green curve represents how much power needs to be supplied to the propeller in order to keep it turning at the given speed. Notice how the faster the propeller spins, the more power is required. At lower rpm’s the red curve is higher than the green curve, meaning that the engine produces more power than is needed to keep the propeller spinning. At about 3700 rpm, the two curves intersect, meaning that the engine produces just enough power to keep the propeller spinning at that rpm. This is the most efficient engine speed to run at because no engine power is being wasted. Notice that at higher rpm’s the engine cannot produce the horsepower necessary to power the propeller. This is only an example power profile. In fact, this graph could change drastically depending on the conditions the hovercraft is operating in. For example, the propeller’s curve can change quite a bit depending on if wind is blowing, and on what direction it’s blowing. No matter how the propeller or engine power profile changes, the engine speed at which the two curves intersect will indicate the point of maximum efficiency and maximum static thrust. Continue to Experiment

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Inclusion is a term used to describe one option for the placement of special education students in public schools. These inclusive programs are sometimes referred to as mainstreaming, which is the selective placement of students with disabilities in regular education classrooms. This controversial educational concept has its share of advocates on both sides and continues to be a source of contention with educators and parents. They all agree that schools must focus on meeting the needs of students with special needs in the most appropriate setting for each individual. The Individuals with Disabilities Act (IDEA) is a federal law that requires students to be educated in the Least Restrictive Environment (LRE). They must receive an education with supports set forth in their Individual Education Plan (IEP), which is different for each student. The federal laws that govern the education of special needs children do not require that they receive an inclusive education. They only require that all students with disabilities be educated in the least restrictive environment and that their unique needs are met. What Inclusive Education Programs Provide For Special Needs Students Inclusive education programs provide educational services for all students including those with special needs. These programs serve all children in the regular classroom on a full-time basis. If a student requires extra services such as speech therapy, these services are brought into the classroom. This program allows the student to remain in the regular education classroom setting at all times. This program is intended to meet the objectives of IDEA by educating students in the regular classroom while still providing for their unique needs. There are variables in inclusive education programs, which make a standard definition of inclusion misleading. Full inclusion is described as placing all students, regardless of disabilities and severity, in the regular classroom on a full-time basis. These students do not leave the regular classroom for services specified in their IEP, but these services are delivered to them in the regular classroom setting. Inclusion or mainstreaming refers to students being educated with non-disabled peers for most of their school day. A special education teacher collaborates with a general education teacher to provide services for students. The general education teacher is responsible for instructing all children, even those with an IEP. The special education teacher collaborates with the general teacher on strategies. Another placement option places disabled students in the general classroom with the special education teacher providing support and assisting the general education teacher in instructing the students. The special education teacher brings materials into the classroom and works with the special student during math or reading instruction. The special education teacher aids the general education teacher in planning different strategies for students with various abilities. When the IEP team meets to determine the best placement for a child with disabilities, they must consider which placement constitutes the least restrictive environment for the child based on individual needs. The team must determine which setting will provide the child with the appropriate placement. The primary objective of inclusive education is to educate disabled students in the regular classroom and still meet their individual needs. Inclusive education allows children with special needs to receive a free and appropriate education along with non-disabled students in the regular classroom. Effectiveness of Inclusive Special Education Programs Even though several studies have been conducted to determine the effectiveness of inclusive special education programs, no conclusion has been reached. Many positive signs have been observed with both special education and regular students. Some proponents of inclusive education programs argue that segregated special education programs are more detrimental to students and fail to meet their educational goals. Those who favor inclusion see some positive evidence that all students can benefit from these inclusive programs when the proper support services are enacted and some changes take place in the traditional classroom. Professional development classes for both special and general education teachers produce a better understanding of the concept of inclusive education. When provided with the proper tools, special needs students have the opportunity to succeed along with their non-disabled peers.

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By the time Fort Snelling was built in the 1820s, slavery was a reality in the Northwest Territory. Fur traders often utilized the labor of enslaved people and some officers at the post, including Colonel Josiah Snelling, owned enslaved people. Other officers rented the use of enslaved people from US Indian Agent Lawrence Taliaferro. It is estimated that throughout the 1820s and 1830s anywhere from 15 to more than 30 enslaved African Americans lived and worked at Fort Snelling at any one time. These people likely cooked, cleaned, and did laundry and other household chores for their owners. The officers and civilians who enslaved African Americans at the confluence were in violation of the Missouri Compromise of 1820, which stated that slavery was forbidden in the territory gained through the Louisiana Purchase north of the 36°30' latitude line (except within the boundaries of the state of Missouri). Slavery had existed in this region prior to the compromise, however, and it continued in spite of it. US Army officers received extra pay to retain a servant, something that was expected in the rigid class structure of the military. Some officers utilized enslaved labor instead, adding the extra pay to their overall income. Officers submitted pay vouchers, often using the descriptor “slave,” to collect this extra pay, which was provided to no other government officials. The US Army thus incentivized slavery and essentially paid its officers for enslaving people. When the First United States Infantry Regiment replaced the Fifth United States Infantry Regiment at Fort Snelling in 1828, slavery at the confluence entered its peak years. The commander of the unit was Lieutenant Colonel Zachary Taylor, future president of the United States. At least seven enslaved people had lived at the fort under the Fifth Infantry, but under the First Infantry, the number swelled to 30 or more. Indian Agent Taliaferro seized the opportunity and imported more enslaved people to the confluence, becoming the region’s largest slaveholder. Slavery continued at Fort Snelling, ending just before Minnesota statehood in 1858, with only a brief hiatus from 1845 to 1850. The practice of slavery spread to newly constructed Fort Ridgely in 1854. From 1855 to 1857, no fewer than nine people were enslaved at Fort Snelling, the highest number since the 1830s. Slavery at the fort did not end because of legal action. The Tenth United States Infantry Regiment, the last slave-holding unit to garrison the fort, was transferred to Utah in 1857.

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Teaching & Learning: Curriculum - English Language Arts Writing Glossary - Grade 1 Argumentation: A speech or writing intended to convince by establishing truth. Most argumentation begins with a statement of an idea or opinion, which is then supported with logical evidence. Another technique of argumentation is the anticipation and rebuttal of opposing views. Benchmark: Students will be able to draw, label and describe at least three attributes of an object using sensory words correctly. Character: A person who takes part in the action of a story, novel, or a play. Sometimes characters can be animals or imaginary creatures, such as beings from another planet. Characterization/Character Development: The method a writer uses to develop characters. There are four basic methods: (a) a writer may describe a character's physical appearance; (b) a character's nature may be revealed through his/her own speech, thoughts, feelings, or actions; (c) the speech, thoughts, feelings, or actions of other characters can be used to develop a character; and (d) the narrator can make direct comments about a character. Climax: The high point, or turning point, in a story-usually the most intense point near the end of a story. Conflict: In narration, the struggle between the opposing forces that moves the plot forward. Conflict can be internal, occurring within a character, or external, between characters or between a character and an abstraction such as nature or fate. Description: The process by which a writer uses words to create a picture of a scene, an event, or a character. A description contains carefully chosen details that appeal to the reader's senses of sight, sound, smell, touch, or taste. Dialogue: Conversation between two or more people that advances the action, is consistent with the character of the speakers, and serves to give relief from passages essentially descriptive or expository. Essay: A brief work of nonfiction that offers an opinion on a subject. The purpose of an essay may be to express ideas and feelings, to analyze, to inform, to entertain, or to persuade. An essay can be formal, with thorough, serious, and highly organized content, or informal, with a humorous or personal tone and less rigid structure. Exposition/Expository Text: Writing that is intended to make clear or to explain something using one or more of the following methods: identification, definition, classification, illustration, comparison, and analysis. Informational/Expository Text: Nonfiction writing in narrative or non-narrative form that is intended to inform. Main Idea: In informational or expository writing, the most important thought or overall position. The main idea or thesis of a piece, written in sentence form, is supported by details and explanation. Narration: Writing that relates an event or a series of events; a story. Narration can be imaginary, as in a short story or novel, or factual, as in a newspaper account or a work of history. Persuasion/Persuasive Writing: Writing intended to convince the reader that a position is valid or that the reader should take a specific action. Differs from exposition in that it does more than explain; it takes a stand and endeavors to persuade the reader to take the same position. Setting: The time and place of the action in a story, play, or poem. Short Story: A brief fictional work that usually contains one major conflict and at least one main character. Theme: A central idea or abstract concept that is made concrete through representation in person, action, and image. No proper theme is simply a subject or an activity. Like a thesis, theme implies a subject and predicate of some kind-not just vice for instance, but some such proposition as, "Vice seems more interesting than virtue but turns out to be destructive." Sometimes the theme is directly stated in the work, and sometimes it is given indirectly. There may be more than one theme in a given work. Thesis: An attitude or position taken by a writer or speaker with the purpose of proving or supporting it. Also used for the paper written in support of the thesis.

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The Civil Rights Act of 1964 was one of the most important pieces of domestic legislation of the post-World War II era. Congressional concern for civil rights lessened after Reconstruction and the U.S. Supreme Court’s decision in 1883 to nullify the constitutionality of the Civil Rights Act of 1875. The U.S. Congress did not address the issue again until 1957, when it was under pressure from the modern Civil Rights Movement, and then it was only a feeble attempt to redress civil wrongs. The passage of the Civil Rights Act of 1957 was a modest statute that created the Civil Rights Commission with the authority to investigate civil rights violations; however, it lacked enforcement provisions and it was a weak corrective for voting rights violations. The Civil Rights Act of 1960 only slightly reinforced the voting rights provisions. The 1964 act had eleven main provisions or titles. Several strengthened the Civil Rights Commission and the voting rights provisions in the 1957 and 1960 acts. The Civil Rights Act of 1964 is among the Civil Rights Movement’s most enduring legacies. It was directed specifically at removing barriers to equal access and opportunity that affected blacks. It greatly extended the reach of federal protection and led to a major restructuring of the nation’s sense of justice; it also expanded legal protections to other minority groups. Beneficiaries of blacks’ struggle for freedom included women, the disabled, gays and lesbians, the elderly, and other groups who experienced discrimination.

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This workbook includes primary sources to help students explore some of the core concepts, or protections, found in the Bill of Rights, and how they’ve been tested throughout American history. Each chapter leads you to consider the implications of one core concept and includes: - Background Information - A key question or questions to frame your thinking - Questions to help you analyze the document - A primary source document or documents - Discussion questions to help you consider the impact or importance of the concept The concepts covered include: - No Law Respecting an Establishment of Religion, or Prohibiting the Free Exercise Thereof (First Amendment) - Freedom of Speech (First Amendment) - Freedom of the Press (First Amendment) - Right of the People Peaceably to Assemble (First Amendment) - Right to Petition the Government for a Redress of Grievances (First Amendment) - Right of the People to Keep and Bear Arms (Second Amendment) - Unreasonable Searches and Seizures (Fourth Amendment) - Deprived of Life, Liberty, or Property, Without Due Process (Fifth Amendment) - The Right to Counsel (Sixth Amendment) - Cruel and Unusual Punishments (Eighth Amendment) All of the primary source documents come from the holdings of the U.S. National Archives. The year 2016 marked the 225th anniversary of the ratification of the first 10 amendments to the Constitution, known as the Bill of Rights. The National Archives commemorated the occasion with exhibits, educational resources, and national conversations examining the amendment process and struggles for rights in the United States. The initiative was presented in part by AT&T, Seedlings Foundation, and the National Archives Foundation. Learn more about eBooks from the National Archives and Records Administration at http://www.archives.gov/publications/ebooks

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P5 Numeracy is through 5 main areas of; Shape and Space Handling Data and Add Understand Place Value within 1000/ 10000, representing whole numbers in terms of units or tens or hundreds or a combination of any of these, and approximating to the nearest 10 or 100 Use simple fraction machines to reinforce known addition, subtraction, and multiplication facts. Develop recall of times tables. Read, write simple fraction notation. Consolidation of written addition and subtraction calculation to within 999 / 9999 (term 3). Use multiplication methods to multiply a two digit number by 2,3,4 or 5. Deduce relevant division facts from 2,3,4,5 10 multiplication facts. Appreciate equivalence of fractions where numerator is one. Share a set of objects to develop an understanding of fractions of quantities. Use knowledge of 4 operations to calculate the input where the output is given in simple function machines. Length – estimate, measure and record lengths in cm and or m and cm. know which unit of measurement to use in different situations. Perimeters of shapes. Measure in mm. Area – appreciate conservation of area. Find areas of shape by counting squares (whole and half) Time – recognise 5 min intervals on the clock face. Measure short times using analogue and digital clocks. Know important dates on the calendar. Appreciate and use relationship between hours and minutes. Perform simple calculations by counting on time. Volume- know the equivalents of 1 litre, ½ l, ¼ l and ¾ l and 1/10 l. Use these to explore containers of different sizes. Measure – scales and problems Weights –Estimate , measure and record weights using kg and gwith a variety of weighing devices. Shape and Space Co-ordinates – understand use of co-ordinates in the first quadrant.. plot positions fromgiven co-ordinates. Identify co-ordinate given points. Symmetry – draw lines of symmetry on 2d shapes. 3D shapes - Angles – can make identify angles as being either smaller than or larger than a right angle. Use terms acute and obtuse. Know and use four compass directions NSEW Construct and explore nets of other prisms. Handling Data – Constructing, using and interpreting simple bar graphs. Grouped Tallies. Tables and Averages. Probability- discussions about events that are ‘likely’, ‘certain’ , ‘not likely’ , ‘very likely’ to happen. Gather information for an activity, with help from the teacher . Record results, initially in a given format. Discuss their work. Within a group be able to gather information for an activity. Recognise general patterns and relationships, and make predictions about them. Work in the above areas will be suitably differentiated to meet the individual needs of all children in Primary 5.Some children will be offered Numeracy/Literacy support and others have access to extension activities. Literacy is Primary 5 is taught following the guidelines from The NI Curriculum. Literacy is predominantly taught through these three areas: Talking and Listening • Ability to read and write with confidence, fluency and understanding • To use a full range of reading cues to self-monitor their reading and self-correct their own mistakes • To understand the sound and spelling system and use this to read and spell accurately • To have an interest in words and word meanings, and to increase their vocabulary banks • To know, understand and be able to write in a range of genres in fiction and poetry, and understand and be familiar with some of the ways that narratives are structured through basic literary ideas of setting, character and plot • To plan, draft, revise and edit their own writing • To be interested in books, read with enjoyment and evaluate and justify preferences • To develop their powers of imagination, inventiveness and critical awareness through reading and writing • To develop talking and listening skills through verbal recounts, ‘show and tell’ sessions, various discussions and reports. Accelerated reading programme Through the accelerated reading programme and are children tested to identify their reading age and provided with suitable reading materials. The children can acquire points for each book read by completing the online computer test. These points can then be traded for prizes. It has proven to be a wonderful source of motivation for all the children. The World Around Us ICT is cross curricular and children will develop their ICT skills via the five E's; Explore , Express, Exchange, Evaluate and Exhibit. Children will also have access to Mathletics , which can also be accessed from home. Personal Development and Mutual Understanding In this subject we will be trying to develop children’s personal, emotional, social and health needs and prepare them to contribute to their communities in ways that make a positive and lasting impact. There are two important strands in this subject: Personal Understanding and Health • Myself and my attributes • I have feelings • Stay safe and Healthy Finally Religion is taught through the Alive 05 programme, and often this complements discussions from PDMU lessons. Children will be given the opportunity to speak openly about their feelings, interests and concerns during these lessons. •Theme related art •Charcoal, paint & pencil work Developing: listening, performing and composing skills. •Listening to short extracts of music • Listening to sounds made by classroom instruments • Perform a variety of songs and hymns •Compose their own music PRIMARY 5 HOMEWORK Homework should take approximately one hour at most .If your child is still struggling to finish his/her homework after that period of time please sign the work and send it in. Homework presentation should be of a high standard and should be signed by a parent. •Please bring correct dinner money in on a Monday morning- £2.50 per day £12.50 per week. Please do not pay for dinners more than a week in advance • Please label uniform and PE uniform •PE Day – P5: Monday P5 A Swimming Wednesday P5B swimming Thursday •Healthy Break Monday – Friday

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Search Within Results Common Core: Math CCLS - Math: K.G.3 - Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres). - State Standard: - Identify shapes as two-dimensional (lying in a plane, “flat”) or three- dimensional (“solid”). - Topic C closes the module with discrimination between flats and solids. In Lesson 9, students are identifying and sorting flat and solid shapes. The goal of this lesson is to focus the student’s... - Objective: Culminating Task—collaborative groups create displays of different flat shapes with examples, non-examples, and a corresponding solid shape. - Objective: Identify and sort shapes as two-dimensional or three-dimensional and recognize two-dimensional and three-dimensional shapes in different orientations and sizes. - Objective: Explain decisions about classification of solid shapes into categories. Name the solid shapes. - Grade K Module 2: Two-Dimensional and Three-Dimensional Shapes Module 2 explores two-dimensional and three-dimensional shapes. Students learn about flat and solid shapes independently as well as...

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Have you ever wondered about the differences between the words this, that, these and those? These words are called demonstratives. Demonstratives tell who or what you are talking about. They are often a source of confusion for English learners, because other languages use demonstratives in different ways than English does. act as pronouns or as determiners. A pronoun is a word that is used instead of a noun or noun phrase. A determiner is a word that comes before a noun and is used to show which thing is being referred to. In the second sentence of this story, you heard these as a determiner, when I said “These words are called demonstratives.” demonstratives identify or point to nouns. This points to an object that is near to you in space, thought, or time. The plural form of this is these. Here are two "This (in my hand) is my "These (people standing near me) are my friends." That points to an object that is comparatively far from you in space, thought, or time. The plural form of that So, for example, you could say "That (in your hand) is your "Those (people standing far from me) are my friends." serve as a signal for a noun phrase or take the place of a noun phrase. Here are two examples. In the first example, these acts as a determiner, while in the second example these acts as a pronoun. common in speech, writing and even popular songs. For example, in “My Favorite Things,” a song from the famous film “The Sound of Music,” the singer lists the objects that she loves. In the last line, she refers to these objects by singing, “These are a few of my favorite things.” Raindrops on roses and whiskers Bright copper kettles and warm Brown paper packages tied up with These are a few of my favorite things. In the song, these refers to raindrops on roses, whiskers on kittens, kettles, mittens and packages. information about whether a noun is general or specific. Demonstrative determiners tell you that the noun or noun phrase is specific. You use a specific determiner when you know that the person who is reading your writing or listening to you knows what you are referring to. In other words, you have a In the song “My Favorite Things,” the antecedents are the objects that the singer lists before she says, “These are a few of my favorite things.” In the book Rhetorical Grammar, Martha Kolln writes that if you do not use demonstratives to refer to a clear antecedent, such as a noun phrase, your writing loses clarity. Take, for example, the following sentence: The subject of the second sentence -- that -- refers to the whole idea in the first When this or that refers to a broad idea, Kolln writes, you can usually improve your sentence by turning the pronoun into a determiner. In other words, you can use a complete noun phrase in place of the demonstrative pronoun. So, for example, you could improve your sentence by writing: My friend just told me she is going to quit her job. That decision came as a surprise. By adding a noun, such as “decision,” to the sentence, you can make it easier for your reader to understand what you are referring to. The next time you are writing or speaking, ask yourself if the demonstrative that you are using has a clear antecedent. If you have to think about it, then your reader or listener will probably have a difficult time understanding what you mean! Words in This Story demonstrative - grammar : showing who or what is being referred to determiner – n. a word (such as “a,” “the,” “some,” “any,” “my,” or “your”) that comes before a noun and is used to show which thing is being referred to comparatively – adv. when measured or judged against refer – v. to have a direct connection or relationship to (something) antecedent - n. grammar. a word or phrase that is represented by another word (such as a pronoun) clarity – adj. the quality of being clear; the quality of being easily understood

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Click on the image at right to get the lesson app with instructor notes. Or you can install right from here by clicking the logo below: In this lesson, students will learn about dividing whole numbers using long division—what is often called the “standard” algorithm. This lesson presents the conceptual model underpinning long division and several examples to help develop fluency with this algorithm. Students are encouraged to estimate quotients and check their work using multiplication and addition after dividing. Module 1 Video The video for this lesson is connected to the first long division example (358 ÷ 6) and walks students step-by-step through the conceptual and procedural process of using the long division algorithm. In the app, you can pause and play the video when the buttons are present, but the video pauses at key moments during the explanation and waits for correct input into the algorithm before continuing. Module 2 Video This video shows a way to draw a square on the coordinate plane by starting with the coordinates of two of its vertices. Operating with absolute values is above grade level, but this module can be completed without knowing how to operate with absolute values.

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The ear consists of three main parts: - Outer Ear - Middle Ear - Inner Ear The Outer Ear The part of the ear that is visible on our heads is called the Pinna. It channels sound waves into the ear canal which amplifies the sound. The sound waves then travel toward a flexible, oval membrane at the end of the ear canal called the eardrum, which then begins to vibrate. The Middle Ear The vibrations of the eardrum then begin to set the ossicles, or bones within the middle ear, into motion. These are the three tiny bones (smallest in the human body) in the middle ear: Malleus (hammer), Incus (anvil) and Stapes (stirrup) and their job is to further amplify the sound. The stapes attaches to the oval window that connects the middle ear to the inner ear. The Eustachian tube, which opens into the middle ear, is responsible for equalizing the pressure between the air outside the ear to that within the middle ear. The Inner Ear The sound waves travel next into the inner ear and into a spiral shaped organ called the cochlea. This organ is filled with a fluid that moves in response to the vibrations, and as a result, thousands of nerve endings are then set into motion. These nerve endings transform the vibrations into electrical impulses that then travel along the auditory nerve to the brain. The brain then interprets these signals and this is how we hear. The inner ear also contains the vestibular organ that is responsible for balance.

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Read the Intro to Sharps for a more basic concept. The musical notes have the letters, ABCDEFG. These are not all the notes we may hear in music. To name the sounds between the letters, we must add sharps or flats. We may play a song in different Keys. The Key tells us which notes to sharp or flat. The Key's name is based on the first note of a song's Major Scale, or its Root. If a song is based around the 'A' note, then 'A' is our Root. (We're using Major Keys.) The above scale is the A Major scale. Listen to the Major Scale Scales are note patterns within a single Key, using letters, sequentially. These notes are in a song written in the Key of 'A'. There are 3 sharps, F# C# G#. The note, 'A' is our Root, or 1st note. Since the A Major scale has 3 sharps only, then these 3 sharp notes must make the correct sound for a major scale. How can we find the correct number of sharps for any major scale, starting from any root? We must order the sharps to any major scale with the following pattern: With this Order, we can find the Key for any major scale. This is done with FCGDAEB. Start from the first letter, 'F', and count up to G. (Remember the order is all sharps.) FCG is the end of our counting, because 'G#' is the last sharp in that order. So, F# C# G#, 3 sharps, are found in the Key of A Major. The A Major Scale has these 3 sharps also. Scales are note patterns within a single Key, using letters, sequentially. Now, when we play a song in the Key of A Major, we know the Root is 'A', and that we play 3 notes, FCG, all sharp. That's why the scale of A Major looks like this: "...the Root note is the name of the Key, and the Order of Sharps or Flats are tools to find the number of sharps or flats, for that Key." Notice that the major scale sharps are not in the same letter order, as the Order of Sharps, FCGDAEB. This is because a scale has a sound or tone, and the Order of Sharps is only a step counting tool to find the Key. Opposite sharps, a song can have only flats. For example, we may be playing a song in the Major Key of Eb. The scale notes in that Key are: This scale has 3 flats (BEA flats). The Key for Eb uses the Order of Flats for finding the number of flats. Here is the Order of Flats: This order is a tool, to only count the number of flats, in a Major flat Key. To find the number of flats in the Key of Eb, we use the Root, Eb, as the second to last flat. Count up to that note in the Order of Flats: BE, then add the last flat to complete the number: BEA flats. So, 3 flats are in the Key of Eb Major, which has these scale notes: Notice these flats are not in the same order as the Order of Flats, because we are following the major scale step pattern, WWHWWWH. This pattern makes a sound, but use the Order of Flats (BEADGCF) as a counting tool only to find the number of flats, not to determine the sound of a major scale. Allow me to add that the Root note is the name of the Key, and the Order of Sharps or Flats are tools to find the number of sharps or flats, for that Key. Here is their Order: The flats are the sharps' order backwards, or reversed. A phrase to remember the Sharps' order is: To remember the Flats' order, use: 2wholes, 1half, 3wholes, 1half steps These steps distance the tones apart, to sound like a Major Scale pattern. You can start on any note (root), and use this pattern of steps between each note. The half steps will fall on the 3rd and 7th notes (both half steps sound like they need to resolve to the next note). Remember that B to C and E to F are half steps. C w D w E h F w G w A w B h C F w G w A h Bb w C w D w E h F Now that you know how to make a major scale, see how to make a chord! On to the next page >>

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