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# Math: Grade 7 Flip Chart

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Copyright © NewPath Learning. All rights reserved. www.newpathlearning.com Charts Charts Grade Grade Curriculum Mastery Flip Charts Combine Essential Math Skills with Hands-On Review! ® 33-7001 \|xiBAHBDy01220nzW Sturdy, Free-Standing Design, Perfect for Learning Centers! Reverse Side Features Questions, Math Problems, Vocabulary Review & more!

Phone: 800-507-0966 • Fax: 800-507-0967 www.newpathlearning.com NewPath Learning® products are developed by teachers using research-based principles and are classroom tested. The company’s product line consists of an array of proprietary curriculum review games, workbooks, posters and other print materials. All products are supplemented with web-based activities, assessments and content to provide an engaging means of educating students on key, curriculum-based topics correlated to applicable state and national education standards. Copyright © 2009 NewPath Learning. All Rights Reserved. Printed in the United States of America. Curriculum Mastery® and NewPath Learning® are registered trademarks of NewPath Learning LLC. Math Curriculum Mastery® Flip Charts provide comprehensive coverage of key standards-based curriculum in an illustrated format that is visually appealing, engaging and easy to use. Curriculum Mastery® Flip Charts can be used with the entire classroom, with small groups or by students working independently. Each Math Curriculum Mastery® Flip Chart Set features • 10 double-sided laminated charts covering grade-level specific curriculum content on one side plus write-on/wipe-off charts on reverse side for student use or for small-group instruction. • Built-in sturdy free-standing easel for easy display • Spiral bound for ease of use • Activity Guide with black-line masters of the charts for students to fill-in, key vocabulary terms, corresponding quiz questions for each chart, along with answers Ideal for • Learning centers • In class instruction for interactive presentations and demonstrations • Hands-on student use • Stand alone reference for review of key science concepts • Teaching resource to supplement any program HOW TO USE Classroom Use Each Curriculum Mastery® Flip Chart can be used to graphically introduce or review a topic of interest. Side 1 of each Flip Chart provides graphical representation of key concepts in a concise, grade appropriate reading level for instructing students. The reverse Side 2 of each Flip Chart allows teachers or students to fill in the answers and summarize key concepts. Note: Be sure to use an appropriate dry-erase marker and to test it on a small section of the chart prior to using it. The Activity Guide included provides a black-line master of each Flip Chart which students can use to fill in before, during, or after instruction. On the reverse side of each black-line master are questions corresponding to each Flip Chart topic which can be used as further review or as a means of assessment. While the activities in the guide can be used in conjunction with the Flip Charts, they can also be used individually for review or as a form of assessment or in conjunction with any other related assignment. Learning Centers Each Flip Chart provides students with a quick illustrated view of grade-appropriate curriculum concepts. Students may use these Flip Charts in small group settings along with the corresponding activity pages contained in the guide to learn or review concepts already covered in class. Students may also use these charts as reference while playing the NewPath’s Curriculum Mastery® Games. Independent student use Students can use the hands-on Flip Charts to practice and learn independently by first studying Side 1 of the chart and then using Side 2 of the chart or the corresponding graphical activities contained in the guide to fill in the answers and assess their understanding. Reference/Teaching resource Curriculum Mastery® Charts are a great visual supplement to any curriculum or they can be used in conjunction with NewPath’s Curriculum Mastery® Games. Chart # 1: Chart # 2: Chart # 3: Chart # 4: Chart # 5: Chart # 6: Chart # 7: Chart # 8: Chart # 9: Chart #10: Multistep Equations Inequalities Exponents, Factors & Multiples Numerical & Geometric Pr oportions Finding Volume All About Percents Introduction to Probability The Pythagorean Theorem Slope Nonlinear Functions & Set Theory

Solving Multistep Equations with Fractions Solving Multistep Equations with Like Terms 8y + 2 – 3y = 17 Solve: = 10 Solve: 5x – 5 7 = 10 = 70 5x – 5 7 5x – 5 • Follow the order of operations in reverse when solving equations with more than one operation (multistep equations). • Goals of solving multistep equations: • Place the variables on one side of the equal sign and the numbers on the other side. • Have the number in front of the variable equal to one. • Place the variables on the same side. • The number in front of the variable must be equal to one. • Two inverse operations are needed to solve the equation above – subtraction & division. Solving Two-Step Equations Using Division Solving Equations with Variables on Both Sides Solving Two-Step Equations Using Multiplication 3 x + 8 = 23 3 x + 8 = 15 x = 5 – 8 – 8 4 groups of -3 = -12 5n + 3 = 28 x – 5 = 20 5n = 25 = 5n 5 – 3 – 3 – 2 – 2 – 3x – 3x 4 • • 4 7 • • 7 + 5 + 5 + 5 + 5 0 9 x Subtract 3 from both sides of the equation. Multiply both sides by 4. Multiply both sides by 7. Divide both sides of the equation by 5. Divide both sides by 5. 25 5 1 4 = 25 x 1 4 = n 5n + 3 = 28 5 5x 5 75 5 = = = x 15 y = x 3 6 = x 100 Solve: x – 5 = 20 Solve: 1 4 Add 5 to both sides. 8y + 2 – 3y = 17 5y + 2 = 17 Multiply both sides by 7. Combine like terms (8y – 3y). Combine like terms (8y – 3y). Subtract 2 from both sides. Subtract 2 from both sides. 5y + 2 = 15 Divide both sides by 5. 5y 5 15 5 = 5x – 7 = 3x + 5 5x – 7 = 3x + 5 2x – 7 = 5 Solve: + 7 + 7 2x – 7 = 12 Add 7 to both sides. 2x 2 12 2 = Subtract 3x from both sides. Divide both sides by 2. © Copyright NewPath Learning. All Rights Reserved. 93-4701 www.newpathlearning.com Multistep Equations

\|xiBAHBDy01675lz[ Solving Multistep Equations with Fractions Solving Multistep Equations with Like Terms 8y + 2 – 3y = 17 Solve: = 10 Solve: 5x – 5 7 = 10 = 70 5x – 5 7 5x – 5 7 5x • Follow the order of operations in reverse when solving equations with more than one operation (multistep equations). • Goals of solving multistep equations: • _________________________________________ _________________________________________ • _________________________________________ _________________________________________ • Place the variables on the same side. • The number in front of the variable must be equal to . Solving Two-Step Equations Using Division Solving Equations with Variables on Both Sides Solving Two-Step Equations Using Multiplication 3 x + 8 = 23 3 x + 8 = 15 x = 5 – 8 – 8 5n + 3 = 28 x – 5 = 20 = = – 2 – 2 4 • • 4 7 • • 7 + 5 + 5 Subtract 3 from both sides of the equation. Multiply both sides by 4. Multiply both sides by 7. Divide both sides of the equation by 5. Divide both sides by 5. 1 4 = 25 x 1 4 = n = = x = y x = x 100 5n + 3 = 28 Solve: x – 5 = 20 Solve: 1 4 Add 5 to both sides. 8y + 2 – 3y = 17 5y + 2 = 17 Combine like terms (8y – 3y). Subtract from both sides. 5y + 2 = 15 Divide both sides by 5. 5y = 5x – 7 = 3x + 5 2x – 7 = 5 5x – 7 = 3x + 5 Solve: 2x = Add 7 to both sides. 2x = Subtract 3x from both sides. Divide both sides by 2. Key Vocabulary Terms • equation • inverse operation • multistep equation • operation • order of operations • variable • Two inverse operations are needed to solve the equation above – subtra ction & . . = © Copyright NewPath Learning. All Rights Reserved. 93-4701 www.newpathlearning.com Multistep Equations

• An inequality is a mathematical sentence that does not have an exact solution. Instead, a range of solutions will satisfy the inequality. • All the solutions of an inequality with more than one solution are called the solution set. • Inequalities are used in many real–world situations. An example is a driving speed sign with a number which tells you that your speed must be 65mph. • Graph each inequality separately. • Combine both graphs. • Solve an addition or subtraction inequality the same way as you would solve an equation. • When you multiply or divide both sides of an inequality by a negative integer, reverse the direction of the inequality symbol. Graphing Simple Inequalities Graphing Compound Inequalities Solving Inequalities by Adding or Subtracting Solving Inequalities by Multiplying or Dividing 4 groups of -3 = -12 0 9 x x + 3 5 x + 3 5 x 2 – 3 – 3 Example Meaning Symbol • greater than • more than • above • less than • fewer than • below • greater than or equal to • no less than • at least • less than or equal to • no more than • at most room capacity age – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 1 3 2 1 0 – 4 – 3 – 2 – 1 0 > 50 > > – > – 14 3 5 6 4 > – > > > –> – An inequality uses one of the following symbols, instead of an equal sign: An open circle is used when the variable is or a number. > > A closed circle is used when the variable is or a number. > > – – > x – 4 x 1 or > x – 2 y 1 > – > – x 1 > – x – 2 > x 2 > – > – > – > – – 2x 6 – 2x 6 – 2x 6 – 2 – 2 x – 3 > > > > © Copyright NewPath Learning. All Rights Reserved. 93-4702 www.newpathlearning.com Inequalities

• An inequality is a mathematical sentence that does not have an exact solution. Instead, a range of solutions will satisfy the inequality. • All the solutions of an inequality with more than one solution are called the so . • Inequal ities are used in many real–world situations. An example is a driving speed sign with a number which tells you that your speed must be 65mph. • Graph each inequality separately. • Combine both graphs. • Solve an addition or subtraction inequality the same way as you would solve an equation. • When you multiply or divide both sides of an inequality by a negative integer, revers ethe direction of the inequality . Graphing Simple Inequalities Graphing Compound Inequalities Solving Inequalities by Adding or Subtracting Solving Inequalities by Multiplying or Dividing Example Meaning Symbol • greater than • more than • above • less than • fewer than • below • greater than or equal to • no less than • at least • less than or equal to • no more than • at most room capacity age – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 1 3 2 1 0 – 4 – 3 – 2 – 1 0 > – An inequality uses one of the following symbols, instead of an equal sign: An op en circle is used when the variable is or a number. > > A c losed circle is used when the variable is or a number. > > – – > x – 4 x 1 or > x – 2 y 1 > – > – x 1 > – x – 2 > x + 3 5 x + 3 5 x 2 – 3 – 3 x 2 > – > – > – > – – 2x 6 – 2x 6 – 2x 6 x > > > © Copyright NewPath Learning. All Rights Reserved. 93-4702 www.newpathlearning.com Key Vocabulary Terms • closed circle • compound inequality • greater than • greater than or equal to • inequality • less than • less than or equal to • negative integer • open circle • simple inequality • solution • solution set • variable Inequalities \|xiBAHBDy01669kzU

Prime Factorization of 120 Prime Factorization Least Common Factor Greatest Common Factor Exponents Powers of Ten & Scientific Notation • An exponent tells how many times to multiply a number, called the base, by itself. • A number written with a base and an exponent is in exponential form. • Prime factorization is taking a number and breaking it down into its prime factors. • A prime number has exactly two factors – 1 and itself. • A composite number has more than two factors. • The greatest common factor (GCF) of two or more numbers is the largest number that divides evenly into each of the numbers. • The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the numbers. • Move the decimal point 6 places to get a number that is greater than or equal to 1 and less than 10. • The exponent is equal to the number of decimal places you moved the point. The Prime Factorization of 120 is Formula Formula 4 = 4 x 4 x 4 = 64 3 10 = 10 x 10 x 10 x 10 = 10,000 = 2.38 x 10 2,380,000 4 6 base exponent Power of ten scientific notation standard form Greatest Common Factor of 36 & 54 Least Common Multiple of 5 & 6 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 54: 1, 2, 3, 6, 9, 18, 27, 54 The GCF is 18 5: 5, 10, 15, 20, 25, 30, 35,... 6: 6, 12, 18, 24, 30, 36, 42,... The LCM is 30 5 • 2 • 3 • 2 • 2 = 5 • 3 • 2 3 5 • 2 • 3 • 2 • 2 5 • 2 • 3 • 4 10 • 12 120 © Copyright NewPath Learning. All Rights Reserved. 93-4703 www.newpathlearning.com Exponents, Factors & Multiples

Prime Factorization of 120 Prime Factorization Least Common Factor Greatest Common Factor Exponents Powers of Ten & Scientific Notation • An exponent tells how many times to multiply a number, called the base, by itself. • A number written with a base and an exponent is in exponential form. • Prime factorization is _________________ _______________________________________ _______________________________________ • A prime number has exactly two factors – and itself. • A composite numb er has more than two factors. • The greatest common factor (GCF) of two or more numbers is ______________ ______________________________________ ______________________________________ • The least common multiple (LCM) of two or more numbers is ____________ ____________________________________ ____________________________________ • Move the decimal point 6 places to get a number that is greater than or equal to 1 and less than 10. • The is equal to the number of decimal places you moved the point. The Prime Factorization of 120 is 4 = 4 x 4 x 4 = 64 3 10 = 10 x 10 x 10 x 10 = 10,000 = 2.38 x 2,380,000 4 Power of ten scientific notation standard form Greatest Common Factor of 36 & 54 Least Common Multiple of 5 & 6 36: , , , , , , , , 54: , , , , , , , The GCF is 18 5: 5 , 5 , 5 , 5 , 5 , 5 ,... 6: 5 , 5 , 5 , 5 , 5 , 5 ,... The LCM is 30 5 • 2 • 3 • 2 • 2 = 5 • 3 • 2 5 • 2 • 3 • 2 • 2 5 • 2 • 3 • 4 10 • 12 120 Key Vocabulary Terms • base • composite number • exponent • exponential form • factor • greatest common factor • least common factor • multiple • power of ten • prime factorization • prime number • scientific notation • standard form © Copyright NewPath Learning. All Rights Reserved. 93-4703 www.newpathlearning.com Exponents, Factors & Multiples \|xiBAHBDy01667qzZ

Numerical Proportions Geometric Proportions corresponding sides corresponding angles A B C D E F • Numerical Proportions compare two numbers. • Ratios are used to compare quantities with the same unit. • Rates are used to compare quantities measured with different units. • Cross products are used to find a missing quantity in a proportion. • Geometric proportions compare two similar figures. • Similar figures have equal corresponding angles and corresponding sides that are in proportion. • Identify the corresponding sides in the two triangles. • Use ratios of the corresponding sides to determine whether the triangles ΔGHI and ΔJKL are similar. • The triangles are similar since their corresponding sides are equivalent. • A cross product is the product of the numerator in one ratio and the denominator in the other ratio. Cross Product Rule • When two ratios are equal, then the cross products, a•d and b•c, are equal. 3 6 1 2 = a b c d = m 5 12 4 = 4m 4 60 4 = 3 5 6 10 = 5 • 6 = 30 3 • 10 = 30 = m • 4 5 • 12 = 4m 60 = m 15 • Cross multiply. • Divide each side by 4 to isolate the variable. Determining whether two triangles are similar G I H 3 cm 6 cm 4 cm K J L 24 cm 12 cm 16 cm 4 16 6 24 = 3 12 = ? ? GH JK IH LK = IG LJ = ? ? 1 4 1 4 = 1 4 = • An equation with two equal ratios is called a proportion. © Copyright NewPath Learning. All Rights Reserved. 93-4704 www.newpathlearning.com GH corresponds to JK IH corresponds to LK IG corresponds to LJ Numerical & Geometric Proportions

Numerical Proportions Geometric Proportions • Numerical Proportions compare two numbers . • Ratios are used to compare quantities with the . • Rate s are used to compare quantities measured with different units. • are used to find a missing quantity in a proportion. • Geometric proportions compare two . • Similar figures have equal corresponding and corresponding that are in . • Identify the corresponding sides in the two triangles. • Use ratios of the corresponding sides to determine whether the triangles ∆GHI and ∆JKL are similar. • The triangles are similar since their corresponding sides are equiva lent. • A cross product is the product of the in in one ratio and the in the other ratio. 3 6 1 2 = Cross Product Rule • When two ratios are equal, then the cross products, a•d and b•c, are equal . a b c d = m 5 12 4 = 3 5 6 10 = 5 • 6 = 5 • 6 = = • • = = m 15 • Cross multiply. • Divide each side by to isolate the variable. A B C D E F Determining whether two triangles are similar • An equation with two equal ratios is called a proportion. G I H 3 cm 6 cm 4 cm K J L 24 cm 12 cm 16 cm = © Copyright NewPath Learning. All Rights Reserved. 93-4704 www.newpathlearning.com Numerical & Geometric Proportions Key Vocabulary Terms • corresponding angle • corresponding side • cross multiply • cross product • denominator • equation • equivalent • geometric proportion • numerator • numerical proportion • proportion • rate • ratio • similar figure • triangle • variable GH corresponds to JK GH corresponds to JK GH corresponds to JK = = ? ? = = \|xiBAHBDy01678mzV

8 cm (d) (h) (r) 9 cm 5 cm 5 cm 14 • 12 3.14 • 16 • 9 3.14 • 4 2 • 9 diameter (d) = radius (r) = radius (r) = r = 4 cm 3 cm 3 cm 3 cm 3 cm 8 cm 3 cm 4 cm 6 cm Area of a rectangular base 3 cm Rectangular Prism Prism (h) ( ) (w) (b) ( ) (h) (r) (h) 8 cm V = x w x h V = r 2 h V V