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//Welcome to Democracy Prep 7th Grade Math A! // toc  **//Need help with your Homework?//** **during the following hours:**
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**Hey Scholars, check out this website. It has great support and challenges!**

[|ixi.com]

**__Challenge__** Put the numbers 1 through 9 (1, 2, 3, 4, 5, 6, 7, 8, 9) in the boxes so that each **row**, **column**, and **diagonal** add up to 15. Good Luck!



** D id you know that Euclid was one of the greatest mathematicians of all time? **

__ **Euclid** of Megara & Alexandria__ (ca 322-275 BC) Greece/Egypt
> Euclid may have been a student of Aristotle. He founded the school of mathematics at the great university of Alexandria. He was the first to prove that there are infinitely many prime numbers; he stated and proved the unique factorization theorem; and he devised //Euclid's algorithm// for computing gcd. He introduced the Mersenne primes and observed that**(M2+M)/2** is always perfect (in the sense of Pythagoras) if **M** is Mersenne. (The converse, that any even perfect number has such a corresponding Mersenne prime, was tackled by Alhazen and proven by Euler.) He proved that there are only five "Platonic solids," as well as theorems of geometry far too numerous to summarize; among many with special historical interest is the proof that rigid-compass constructions can be implemented with collapsing-compass constructions. Among several books attributed to Euclid are //The Division of the Scale// (a mathematical discussion of music), //The Optics//, //The Cartoptrics// (a treatise on the theory of mirrors), a book on spherical geometry, a book on logic fallacies, and his comprehensive math textbook //The Elements//. Several of his masterpieces have been lost, including works on conic sections and other advanced geometric topics. Apparently Desargues' Homology Theorem (a pair of triangles is coaxial if and only if it is copolar) was proved in one of these lost works; this is the fundamental theorem which initiated the study of projective geometry. Euclid ranks #14 on Michael Hart's famous list of the Most Influential Persons in History. //The Elements// introduced the notions of axiom and theorem; was used as a textbook for 2000 years; and in fact is still the basis for high school geometry, making Euclid the leading mathematics teacher of all time. Some think his best inspiration was recognizing that the Parallel Postulate must be an axiom rather than a theorem.There are many famous quotations about Euclid and his books. Abraham Lincoln abandoned his law studies when he didn't know what "demonstrate" meant and "went home to my father's house [to read Euclid], and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies."

Having Trouble with factors and multiples?

 **Here is a video about factors and multiples!**
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**Here are the rules of divisibility:**

 * **Divisibility Tests ** || **Example ** ||
 * A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8. || 168 is divisible by 2 since the last digit is 8. ||
 * A number is divisible by 3 if the sum of the digits is divisible by 3. || 168 is divisible by 3 since the sum of the digits is 15 (1+6+8=15), and 15 is divisible by 3. ||
 * A number is divisible by 4 if the number formed by the last two digits is divisible by 4. || <span style="font-family: ArialMT,sans-serif; font-size: 14pt;">316 is divisible by 4 since 16 is divisible by 4. ||
 * <span style="font-family: ArialMT,sans-serif; font-size: 14pt;">A number is divisible by 5 if the last digit is either 0 or 5. || <span style="font-family: ArialMT,sans-serif; font-size: 14pt;">195 is divisible by 5 since the last digit is 5. ||
 * <span style="font-family: ArialMT,sans-serif; font-size: 14pt;">A number is divisible by 6 if it is divisible by 2 **<span style="font-family: ArialMT,sans-serif;">AND **<span style="font-family: ArialMT,sans-serif; font-size: 14pt;"> it is divisible by 3. || <span style="font-family: ArialMT,sans-serif; font-size: 14pt;">168 is divisible by 6 since it is divisible by 2 **<span style="font-family: ArialMT,sans-serif;">AND **<span style="font-family: ArialMT,sans-serif; font-size: 14pt;"> it is divisible by 3. ||
 * <span style="font-family: ArialMT,sans-serif; font-size: 14pt;">A number is divisible by 8 if the number formed by the last three digits is divisible by 8. || <span style="font-family: ArialMT,sans-serif; font-size: 14pt;">7,120 is divisible by 8 since 120 is divisible by 8. ||
 * <span style="font-family: ArialMT,sans-serif; font-size: 14pt;">A number is divisible by 9 if the sum of the digits is divisible by 9. || <span style="font-family: ArialMT,sans-serif; font-size: 14pt;">549 is divisible by 9 since the sum of the digits is 18 (5+4+9=18), and 18 is divisible by 9. ||
 * <span style="font-family: ArialMT,sans-serif; font-size: 14pt;">A number is divisible by 10 if the last digit is 0. || <span style="font-family: ArialMT,sans-serif; font-size: 14pt;">1,470 is divisible by 10 since the last digit is 0. ||

7th Grade Math Standards

 * ||  ||   || 7th Grade Math A Standards || Trimester || Domain || Cluster || Unit ||
 * 7 || MA || 101 || Add and subtract fractions and decimals. || T1 || The Number System || Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. || Unit 1: Number Sense - Extending Operations to All Rational Numbers ||
 * 7 || MA || 102 || Add and subtract integers. || T1 ||^  ||^   ||^   ||
 * 7 || MA || 103 || Represent rational numbers on a number line. || T1 ||^  ||^   ||^   ||
 * 7 || MA || 104 || Use a number line to describe addition and subtraction, including demonstrating an understanding of absolute value as a distance on the number line. || T1 ||^  ||^   ||^   ||
 * 7 || MA || 105 || Multiply and divide fractions and decimals and interpret the products and quotients in a real-world context. || T1 ||^  ||^   ||^   ||
 * 7 || MA || 106 || Multiply and divide integers and interpret the products and quotients in a real-world context. || T1 ||^  ||^   ||^   ||
 * 7 || MA || 107 || Solve multi-step word problems involving positive and negative numbers in any form, including converting between different forms of rational numbers. || T1 ||^  ||^   ||^   ||
 * 7 || MA || 108 || Justify the reasonableness of answers using estimation strategies. || T1 ||^  ||^   ||^   ||
 * 7 || MA || 109 || Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, and irrational numbers). || T1 || The Number System || Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. || Unit 2: Number Sense - Classifying Numbers ||
 * 7 || MA || 110 || Convert a rational number to a decimal using long division and explain how the decimal expansion demonstrates that it is a rational number. || T1 ||^  ||^   ||^   ||
 * 7 || MA || 111 || Recognize the difference between rational and irrational numbers and provide examples of each. || T1 ||^  ||^   ||^   ||
 * 7 || MA || 112 || Classify irrational numbers as non-repeating/non-terminating decimals. || T1 ||^  ||^   ||^   ||
 * 7 || MA || 113 || Demonstrate and identify properties of numbers: including the Commutative Property, the Associative Property, the Distributive Property, the Zero Property, and the Identity and Inverse Properties of Addition and Multiplication. || T1 ||^  ||^   ||^   ||
 * 7 || MA || 114 || Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) || T2 || Expressions and Equations || Use properties of operations to generate equivalent expressions. || Unit 3: Algebra - Using Linear Expressions ||
 * 7 || MA || 115 || Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. || T2 ||^  ||^   ||^   ||
 * 7 || MA || 116 || Apply properties of operations to add and subtract linear expressions with rational coefficients. || T2 ||^  ||^   ||^   ||
 * 7 || MA || 117 || Factor linear expressions with rational coefficients. || T2 ||^  ||^   ||^   ||
 * 7 || MA || 118 || Expand linear expressions with rational coefficients. || T2 ||^  ||^   ||^   ||
 * 7 || MA || 119 || Use equivalent algebraic expressions to solve real-world problems and explain the real-world relationship between the equivalent expressions. || T2 ||^  ||^   ||^   ||
 * 7 || MA || 120 || Use variables to represent quantities in real-world or mathematical problems. || T2 || Expressions and Equations || Use properties of operations to generate equivalent expressions. || Unit 4: Algebra cont. - Using Alegebraic Equations ||
 * 7 || MA || 121 || Construct simple equations and inequalities to solve problems by reasoning about quanitities. || T2 ||^  ||^   ||^   ||
 * 7 || MA || 122 || Solve problems leading to equations of the form px + q = r or p(x + q) = r where p, q, and r, are rational numbers. || T2 ||^  ||^   ||^   ||
 * 7 || MA || 123 || Solve linear equations fluently. || T2 ||^  ||^   ||^   ||
 * 7 || MA || 124 || Compare an algebraic solution to an arithmetic solution, identifying the sequence of operations used in both. || T2 ||^  ||^   ||^   ||
 * 7 || MA || 125 || Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. || T2 ||^  ||^   ||^   ||
 * 7 || MA || 126 || Graph the solution set of an inequality and interpret it in the context of the problem. || T2 ||^  ||^   ||^   ||
 * 7 || MA || 127 || Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. || T3 || Geometry || Draw, construct and describe geometrical figures and describe the relationships between them. || Unit 5: Geometry - Applications of 2-D polygons and 3-D solids ||
 * 7 || MA || 128 || Identify and classify two-dimensional polygons, quadrilaterals, and triangles. || T3 ||^  ||^   ||^   ||
 * 7 || MA || 129 || Construct triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. || T3 ||^  ||^   ||^   ||
 * 7 || MA || 130 || Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. || T3 ||^  ||^   ||^   ||
 * 7 || MA || 131 || Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. || T3 ||^  || Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. ||^   ||
 * ||  || 132 || Identify and classify three-dimensional shapes. ||   ||^   ||^   ||^   ||
 * ||  || 133 || Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. ||   ||^   ||^   ||^   ||
 * 7 || MA || 134 || Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. || T3 ||^  ||^   ||^   ||
 * 7 || MA || 135 || Identify the parts of a circle. || T3 || Geometry || Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. || Unit 6: Geometry - Circles ||
 * 7 || MA || 136 || Define and demonstrate the relationship between the radius and diameter of a circle. || T3 ||^  ||^   ||^   ||
 * 7 || MA || 137 || Explain the relationship between the diameter and circumference of a circle in relation to pi. || T3 ||^  ||^   ||^   ||
 * 7 || MA || 138 || Know the formulas for the area and circumference of a circle and use them to solve problems. || T3 ||^  ||^   ||^   ||
 * 7 || MA || 139 || Give an informal derivation of the relationship between the circumference and area of a circle || T3 ||^  ||^   ||^   ||

Tangrams!
[|History of Tangrams]

[|Tangram Puzzles]

Video on Commutative Property of Multiplication
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Video on Associative Property of Multiplication
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Video on Distributive Property
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Solving Algebraic Equations Using Subtraction
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Graphing Ordered Pairs
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Multiplying Fractions
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Dividing Fractions
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Multiplying Decimals
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Dividing Decimals
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Adding and Subtracting Fractions
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Adding and Subtracting Decimals
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How to Simplify Square Roots
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Solving and Plotting Inequalities
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Subtracting Multiple Integers
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Use Subtraction to Add
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Multiplying Fractions Array
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Dividing Decimals
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