Mathematics Grade 7 CROSSWalk for the Co on Core State Standards
Table of Contents Common Core State Standards Correlation Chart... 6 Domain 1 The Number System....13 Domain 1: Diagnostic Assessment for Lessons 1 8...14 Lesson 1 Relate Fractions, Decimals, and Percents... 16 Lesson 2 Solve Problems with Percents...22 Lesson 3 Terminating and Repeating Decimals...29 Lesson 4 Add and Subtract Rational Numbers...33 Lesson Multiply and Divide Rational Numbers...40 Lesson 6 Complex Fractions...48 Lesson 7 Add and Subtract Integers...4 Lesson 8 Multiply and Divide Integers...62 Domain 1: Cumulative Assessment for Lessons 1 8...68 Domain 2 Ratios and Proportional Relationships....71 Domain 2: Diagnostic Assessment for Lessons 9 12...72 Lesson 9 Ratios and Rates...74 Lesson 10 Proportions...79 Common Core State Standards 7.RP.3 7.RP.3 7.NS.2.d 7.NS.1.b, 7.NS.1.d, 7.NS.3 7.NS.2.a, 7.NS.2.c, 7.NS.3 7.RP.1, 7.RP.3 7.NS.1.a, 7.NS.1.b, 7.NS.1.c, 7.NS.1.d, 7.NS.3 7.NS.2.a, 7.NS.2.b, 7.NS.2.c, 7.NS.3 7.RP.1, 7.RP.2.c 7.RP.2.a Lesson 11 Proportional Relationships...84 Lesson 12 Represent Proportional Relationships...89 Domain 2: Cumulative Assessment for Lessons 9 12...9 Domain 3 Expressions and Equations...97 Domain 3: Diagnostic Assessment for Lessons 13 18...98 Lesson 13 Write Algebraic Expressions... Lesson 14 Simplify and Evaluate Algebraic Expressions.. 10 Lesson 1 Add and Subtract Algebraic Expressions...112 Lesson 16 Write Algebraic Equations...117 Lesson 17 Use Algebra to Solve Word Problems...122 7.RP.2.a, 7.RP.2.b, 7.RP.3 7.RP.2.a, 7.RP.2.b, 7.RP.2.c, 7.RP.2.d 7.EE.2, 7.EE.4 7.EE.1 7.EE.1 7.EE.2, 7.EE.4 7.EE.3, 7.EE.4.a 4
Lesson 18 Inequalities...128 Domain 3: Cumulative Assessment for Lessons 13 18..... 13 Domain 4 Geometry...137 Domain 4: Diagnostic Assessment for Lessons 19 27....138 Lesson 19 Similar Figures...140 Common Core State Standards 7.EE.4.b 7.G.1 Lesson 20 Scale Drawings....146 7.G.1 Lesson 21 Construct Geometric Shapes....13 Lesson 22 Cross Sections of Three-Dimensional Figures...19 Lesson 23 Circles....164 7.G.2 7.G.3 7.G.4 Lesson 24 Angles...170 Lesson Area....177 Lesson 26 Surface Area...183 Lesson 27 Volume...188 Domain 4: Cumulative Assessment for Lessons 19 27..... 192 7.G. 7.G.6 7.G.6 7.G.6 Domain Statistics and Probability...19 Domain : Diagnostic Assessment for Lessons 28 3....196 Lesson 28 Probability....199 Lesson 29 Compound Events....20 Lesson 30 Samples....211 Lesson 31 Measures of Central Tendency...218 Lesson 32 Measures of Variation....226 Lesson 33 Mean Absolute Deviation....234 Lesson 34 Make Predictions Using Data....241 Lesson 3 Compare Data Sets...246 Domain : Cumulative Assessment for Lessons 28 3..... 4 Glossary...8 Summative Assessment: Domains 1................. 263 Math Tools...277 7.SP., 7.SP.6, 7.SP.7.a, 7.SP.7.b 7.SP.8.a, 7.SP.8.b, 7.SP.8.c 7.SP.1, 7.SP.2 7.SP.4 7.SP.4 7.SP.3 7.SP.2, 7.SP.4 7.SP.3, 7.SP.4
Domain 1 Lesson 1 Relate Fractions, Decimals, and Percents Common Core State Standard: 7.RP.3 Getting the Idea Rational numbers are numbers that can be expressed in the form a, where a and b are b integers and b fi 0. Fractions, decimals, and percents are rational numbers that can be used to show parts of a whole. Percent means per hundred. For example, 70% of a number means 70 times the quantity. The symbol for percent is %. You can convert rational numbers to different forms. To convert a percent to a fraction, write the percent as the numerator over a denominator of. Then simplify the fraction using the greatest common factor (GCF). Example 1 Write 72% as a fraction in simplest form. Write the percent as a fraction with a denominator of. Simplify. Step 2 Solution 72% 18 Remove the percent sign. Write the percent as the numerator and as the denominator. 72% 72 Simplify the fraction using the GCF. The GCF of 72 and is 4. Divide the numerator and denominator by 4. 72 72 4 4 4 4 18 Example 2 What is 84% written as a decimal? Remove the percent sign and move the decimal point two places to the left. 84% 84. 0.84 Solution 84% 0.84 16
Example 3 What is 2 written as a decimal? Write an equivalent fraction with a denominator of 10. Lesson 1: Relate Fractions, Decimals, and Percents Find a fraction equivalent to 2 that has a denominator of 10. Since 3 2 10, multiply the numerator and denominator by 2. 2 2 3 2 3 2 4 10 Step 2 Write the decimal equivalent of 4 10. 4 is read four tenths. 10 4 10 0.4 Solution 2 0.4 Example 4 Write 0.6 as a fraction in simplest form. Write the digits after the decimal point as the numerator. The denominator is the place value of the last digit. Simplify. Step 2 Solution 0.6 13 20 Write the digits 6 as the numerator of the fraction. The denominator is because the last digit,, is in the hundredths place. 0.6 6 Simplify using the GCF. The GCF of 6 and is. 6 6 4 4 13 20 17
To convert a decimal to a percent, multiply the decimal by and insert a percent sign. Multiplying a decimal by is the same as moving the decimal point 2 places to the right. Example What is 0.87 written as a percent? Multiply the decimal by. Move the decimal point two places to the right. 0.87 3 87. Insert a percent sign. 87.% Solution 0.87 87.% Example 6 Write 16 as a percent. Write an equivalent fraction. Step 2 Solution Percent means per hundred, so write an equivalent fraction with a denominator of. 3 4, so multiply the numerator and denominator by 4. 16 16 3 4 3 4 64 Insert a percent sign next to the numerator. 64 16 64% 64% 18 Domain 1: The Number System
Lesson 1: Relate Fractions, Decimals, and Percents If the denominator is not a factor of, convert the fraction to a decimal. Then convert the decimal to a percent. Some decimals, such as 1, are repeating decimals. 3 To write a repeating decimal as a percent, write the percent and the part that repeats as a fraction. Example 7 What is 2 written as a percent? 3 Convert the fraction to a decimal. Then convert the decimal to a percent. Divide the numerator by the denominator. 2 3 2 4 3 0. 6 Step 2 Multiply the decimal by. 0. 6 3 66. 6 Solution Insert a percent sign. 66. 6 % or 66 2 3 % 2 66 2 3 3 % Coached Example Maria received % of the vote in a student council election. What decimal and fraction, written in simplest form, are equivalent to the amount of the vote Maria received? To convert a percent to a decimal, remove the percent sign and move the decimal point 2 places to the. The decimal is equivalent to %. To convert a percent to a fraction, write the percent as the numerator over a denominator of. What is the GCF of the numerator and denominator? Divide the numerator and denominator by. Simplify. % written as a decimal is. % written as a fraction is. 19
Lesson Practice Choose the correct answer. 1. About 60.7% of eligible voters voted in the election. Which decimal is equivalent to 60.7%? A. 0.0607 B. 0.607 C. 6.07 D. 60.7 4. Tomas correctly spelled 18 out of 20 words on his last spelling quiz. What decimal represents the portion of the words that Tomas spelled correctly? A. 0.18 B. 0.36 C. 0.8 D. 0.9 2. In a survey of patients, Dr. Molar found that 8% of his patients floss daily. Which fraction is equivalent to 8%? A. 4_ B. 2_ C. 4 D. 2 3. Kristen made _ 3 of her free throws for the 8 season. Which percent is equivalent to _ 3 8? A. 37.% B. 38% C. 38.% D. 37%. Which fraction is equivalent to 48%? A. 4_ B. 4_ 8 C. 12 D. 8 6. Sales at Cycle time increased by 370% this year. Which of the following is equivalent to 370%? 37 A. B. 3.7 C. 3 7 D. 37 20 Domain 1: The Number System
Lesson 1: Relate Fractions, Decimals, and Percents 7. Which rational number is not equivalent to the others? A. 7% B. 3_ 4 C. 0.7 D. 7 0 8. Which of the following shows a set of equivalent rational numbers? A. 2_ 0.4 % B. 2_ 3 0.6 66% C. 3 10 0.3 30% 73 D. 0.73 730% 9. The Lions won 3 out of 40 games this season. A. What fraction of games played did the Lions win? Write your answer in simplest form. B. Write a decimal and a percent equivalent to the fraction of games the Lions won. Show your work. 21