On Core Mathematics Grade 6

Transcription

1 Teacher edition and Assessment Guide Sampler On Core Mathematics Grade 6 Bridge the gap between your program and the Common Core State Standards. A complete program of activities, practice, and assessment for each Common Core State Mathematics Standard. Teacher Edition and Assessment Guide Sampler includes: - On Core Program Overview - Table of Contents for Grade 6 - Teaching Support and Student Lessons - Assessments

2 What is On Core Mathematics? On Core Mathematics is a comprehensive, ready-made resource providing instruction, practice and assessment for each Common Core State Mathematics Standard at your grade level. Designed to be used hand-in-hand with your current elementary math series, On Core offers you a flexible way to fill in any gaps between your series and the new standards. Whether you use just the lessons you need, or decide use the entire student workbook for comprehensive Common Core coverage, On Core provides a complete Common Core solution in just four components: Student Edition: provides a searchable database of additional worksheets, projects, and hands-on activities correlated to the Common Core State Standards. Helps teachers focus on the mathematical practices. Teacher Edition: Instructional support for each Common Core Standards lesson. The three part, researchbased lesson plan (Introduce, Teach, and Practice), that uses manipulatives and powerful visual models, provides everything needed to use the content. Assessment Guide: One page of assessment for each standard in multiple-choice, free-response and constructed response formats. Exam View Online Assessment: Administer premade print or online assessments or create your own with this powerful online tool aligned to the Common Core Standards.

3 Grade 6 Table of Contents Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. Lesson 1 6.RP.1 Investigate Model Ratios Lesson 2 6.RP.1 Ratios and Rates Lesson 3 6.RP.2 Find Unit Rates Lesson 4 6.RP.3a Equivalent Ratios and Multiplication Tables Lesson 5 6.RP.3a Problem Solving Use Tables to Compare Ratios Lesson 6 6.RP.3a Algebra Use Equivalent Ratios Lesson 7 6.RP.3a Algebra Equivalent Ratios and Graphs Lesson 8 6.RP.3b Algebra Use Unit Rates Lesson 9 6.RP.3c Investigate Model Percents Lesson 10 6.RP.3c Write Percents as Fractions and Decimals Lesson 11 6.RP.3c Write Fractions and Decimals as Percents Lesson 12 6.RP.3c Percent of a Quantity Lesson 13 6.RP.3c Problem Solving Percents Lesson 14 6.RP.3c Find the Whole from a Percent Lesson 15 6.RP.3d Convert Units of Length Lesson 16 6.RP.3d Convert Units of Capacity Lesson 17 6.RP.3d Convert Units of Weight and Mass Lesson 18 6.RP.3d Transform Units Lesson 19 6.RP.3d Problem Solving Distance, Rate, and Time Formulas iii

4 The Number System iv Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Lesson 20 6.NS.1 Investigate Model Fraction Division Lesson 21 6.NS.1 Estimate Quotients Lesson 22 6.NS.1 Divide Fractions Lesson 23 6.NS.1 Investigate Model Mixed Number Division Lesson 24 6.NS.1 Divide Mixed Numbers Lesson 25 6.NS.1 Problem Solving Fraction Operations Compute fluently with multi-digit numbers and find common factors and multiples. Lesson 26 6.NS.2 Divide Multi-Digit Numbers Lesson 27 6.NS.3 Add and Subtract Decimals Lesson 28 6.NS.3 Multiply Decimals Lesson 29 6.NS.3 Divide Decimals by Whole Numbers Lesson 30 6.NS.3 Divide with Decimals Lesson 31 6.NS.4 Prime Factorization Lesson 32 6.NS.4 Least Common Multiple Lesson 33 6.NS.4 Greatest Common Factor Lesson 34 6.NS.4 Problem Solving Apply the Greatest Common Factor Lesson 35 6.NS.4 Multiply Fractions Lesson 36 6.NS.4 Simplify Factors Apply and extend previous understandings of numbers to the system of rational numbers. Lesson 37 6.NS.5 Understand Positive and Negative Numbers Lesson 38 6.NS.6a Rational Numbers and the Number Line Lesson 39 6.NS.6b Ordered Pair Relationships Lesson 40 6.NS.6c Fractions and Decimals Lesson 41 6.NS.6c Compare and Order Fractions and Decimals Lesson 42 6.NS.6c Rational Numbers and the Coordinate Plane Lesson 43 6.NS.7a Compare and Order Integers Lesson 44 6.NS.7a Compare and Order Rational Numbers NS.7b Lesson 45 6.NS.7c Absolute Value Lesson 46 6.NS.7d Compare Absolute Values Lesson 47 6.NS.8 Distance on the Coordinate Plane Lesson 48 6.NS.8 Problem Solving The Coordinate Plane

5 Expressions and Equations Apply and extend previous understandings of arithmetic to algebraic expressions. Lesson 49 6.EE.1 Exponents Lesson 50 6.EE.1 Evaluate Expressions Involving Exponents Lesson 51 6.EE.2a Write Algebraic Expressions Lesson 52 6.EE.2b Identify Parts of Expressions Lesson 53 6.EE.2c Evaluate Algebraic Expressions and Formulas Lesson 54 6.EE.3 Problem Solving Combine Like Terms Lesson 55 6.EE.3 Generate Equivalent Expressions Lesson 56 6.EE.4 Identify Equivalent Expressions Reason about and solve one-variable equations and inequalities. Lesson 57 6.EE.5 Solutions of Equations Lesson 58 6.EE.5 Solutions of Inequalities Lesson 59 6.EE.6 Use Algebraic Expressions Lesson 60 6.EE.7 Write Equations Lesson 61 6.EE.7 Investigate Model and Solve Addition Equations Lesson 62 6.EE.7 Solve Addition and Subtraction Equations Lesson 63 6.EE.7 Investigate Model and Solve Multiplication Equations Lesson 64 6.EE.7 Solve Multiplication and Division Equations Lesson 65 6.EE.7 Problem Solving Equations with Fractions Lesson 66 6.EE.8 Write Inequalities Lesson 67 6.EE.8 Graph Inequalities Represent and analyze quantitative relationships between dependent and independent variables. Lesson 68 6.EE.9 Independent and Dependent Variables Lesson 69 6.EE.9 Equations and Tables Lesson 70 6.EE.9 Problem Solving Analyze Relationships Lesson 71 6.EE.9 Graph Relationships Lesson 72 6.EE.9 Equations and Graphs v

6 Geometry Solve real-world and mathematical problems involving area, surface area, and volume. Lesson 73 6.G.1 Algebra Area of Parallelograms Lesson 74 6.G.1 Investigate Explore Area of Triangles Lesson 75 6.G.1 Algebra Area of Triangles Lesson 76 6.G.1 Investigate Explore Area of Trapezoids Lesson 77 6.G.1 Algebra Area of Trapezoids Lesson 78 6.G.1 Area of Regular Polygons Lesson 79 6.G.1 Composite Figures Lesson 80 6.G.1 Problem Solving Changing Dimensions Lesson 81 6.G.2 Investigate Fractions and Volume Lesson 82 6.G.2 Algebra Volume of Rectangular Prisms Lesson 83 6.G.3 Figures on the Coordinate Plane Lesson 84 6.G.4 Three-Dimensional Figures and Nets Lesson 85 6.G.4 Investigate Explore Surface Area Using Nets Lesson 86 6.G.4 Algebra Surface Area of Prisms Lesson 87 6.G.4 Algebra Surface Area of Pyramids Lesson 88 6.G.4 Problem Solving Geometric Measurements vi 4

7 Statistics and Probability Develop understanding of statistical variability. Lesson 89 6.SP.1 Recognize Statistical Questions Lesson 90 6.SP.2 Describe Distributions Lesson 91 6.SP.2 Problem Solving Misleading Statistics Lesson 92 6.SP.3 Apply Measures of Center and Variability Summarize and describe distributions. Lesson 93 6.SP.4 Dot Plots and Frequency Tables Lesson 94 6.SP.4 Histograms Lesson 95 6.SP.4 Problem Solving Data Displays Lesson 96 6.SP.4 Box Plots Lesson 97 6.SP.5a Describe Data Collection SP.5b Lesson 98 6.SP.5c Investigate Mean as Fair Share and Balance Point Lesson 99 6.SP.5c Measures of Center Lesson SP.5c Patterns in Data Lesson SP.5c Investigate Mean Absolute Deviation Lesson SP.5c Measures of Variability Lesson SP.5d Effects of Outliers Lesson SP.5d Choose Appropriate Measures of Center and Variability vii

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9 LESSON 14 Pages Page 14, Assessment Guide COMMON CORE STANDARD CC.6.RP.3c OBJECTIVE Find the whole given a part and the percent. ESSENTIAL QUESTION How can you find the whole given a part and the percent? VOCABULARY MATERIALS PREREQUISITES Write equivalent fractions. Write a percent as ratio out of 100. Find the Whole from a Percent About the Math The relationship among the part, percent, and whole can be used to find the whole when the percent and part are given. Students will support their learning when they look for and express regularity in repeated reasoning. The Lesson Introduce Remind students that they have used equivalent ratios to find the part, given the percent and the whole. In this lesson they will use equivalent ratios to find the whole, given the percent and the part. Teach Point out to students that both ratios in Step 2 represent part whole. A percent is part out of 100, so 60 is the part and 100 is the whole. In the second ratio, 54 is the part and the whole is unknown. Explain to students that simplifying the known ratio makes it easier to find the equivalent ratio. Extend the process of finding the whole given a part and the percent by having students estimate first. Then have them check to see if their answers are reasonable. Practice Have students complete page 28. You may wish to review the process by discussing the first exercise. Name Find the Whole from a Percent Lesson 14 COMMON CORE STANDARD CC.6.RP.3c Lesson Objective: Find the whole given a part and the percent. Name Find the Whole from a Percent Lesson 14 CC.6.RP.3c You can use equivalent ratios to find the whole, given a part and the percent. 54 is 60% of what number? Step 1 Write the relationship among the percent, part, and whole. The percent is 60%. The part is 54. The whole is unknown. Step 2 Write the percent as a ratio. Step 3 Simplify the known ratio. Find the GCF of the numerator and denominator GCF percent 5 _ part whole 60% 5 54 j j Find the unknown value is 15% of n n _ is 50% of n is 10% of n is 75% of n is 40% of n is 16% of n is 2% of n is 28% of n is 25% of n Divide both the numerator and denominator by the GCF. Step 4 Write an equivalent ratio. Look at the numerators. Think: Multiply the denominator by 18 to fi nd the whole. So, 54 is 60% of 90. Find the unknown value j 3_ n n n is 40% of n is 25% of n is 20% of n is 50% of n 5. 4 is 80% of n is 15% of n is 90% of n is 75% of n is 30% of n Ratios and Proportional Relationships is 44% of n Michaela is hiking on a weekend camping trip. She has walked 6 miles so far. This is 30% of the total distance. What is the total number of miles she will walk? is 95% of n is 20% of n A customer placed an order with a bakery for cupcakes. The baker has completed 37.5% of the order after baking 81 cupcakes. How many cupcakes did the customer order? 20 miles 216 cupcakes Ratios and Proportional Relationships 7 15

10 Name Find the Whole from a Percent Lesson 14 COMMON CORE STANDARD CC.6.RP.3c Lesson Objective: Find the whole given a part and the percent. You can use equivalent ratios to find the whole, given a part and the percent. 54 is 60% of what number? Step 1 Write the relationship among the percent, part, and whole. The percent is 60%. The part is 54. The whole is unknown. Step 2 Write the percent as a ratio. Step 3 Simplify the known ratio. percent 5 _ part whole 60% 5 54 j j Find the GCF of the numerator and denominator Divide both the numerator and denominator by the GCF. Step 4 Write an equivalent ratio. GCF j 3_ n Look at the numerators. Think: Multiply the denominator by 18 to fi nd the whole. So, 54 is 60% of n n Find the unknown value is 40% of n is 25% of n is 20% of n is 50% of n 5. 4 is 80% of n is 15% of n is 90% of n is 75% of n is 30% of n Ratios and Proportional Relationships 8 27

11 Name Find the Whole from a Percent Lesson 14 CC.6.RP.3c Find the unknown value is 15% of n n _ is 75% of n is 2% of n is 50% of n is 40% of n is 28% of n is 10% of n is 16% of n is 25% of n is 44% of n is 95% of n is 20% of n Michaela is hiking on a weekend camping trip. She has walked 6 miles so far. This is 30% of the total distance. What is the total number of miles she will walk? 14. A customer placed an order with a bakery for cupcakes. The baker has completed 37.5% of the order after baking 81 cupcakes. How many cupcakes did the customer order? 20 miles 216 cupcakes 28 9

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13 LESSON 49 Pages Page 49, Assessment Guide COMMON CORE STANDARD CC.6.EE.1 OBJECTIVE Write and evaluate expressions involving exponents. ESSENTIAL QUESTION How do you write and find the value of expressions involving exponents? VOCABULARY exponent, base MATERIALS PREREQUISITES Multiply with more than 2 factors. Find factors of numbers. Exponents About the Math Exponents can be considered as a shorthand method for representing repeated multiplication. Students will be able to relate powers of 10 to the base-ten number system. Each place value is 10 times the place to its right. Students will support their learning when they look for and make use of structure. The Lesson Introduce Remind students that multiplication is an easier way of writing repeated addition of the same addend. Then tell them that in this lesson they will learn an easier way to represent repeated multiplication of the same factor, such as Teach Discuss the meaning of exponent and base with the students. The exponent tells how many times a number is used as a factor. The base is the number that is being multiplied repeatedly. So, the multiplication above can be written as 2 7. Have students write a multiplication expression with a repeated factor for a partner to evaluate. Extend the process of writing expressions with exponents to include two different repeated factors. Then have students determine the exponent for a product, given the base. Practice Have students complete page 98. You may wish to review the process by discussing the first exercise. Name Exponents Lesson 49 COMMON CORE STANDARD CC.6.EE.1 Lesson Objective: Write and evaluate expressions involving exponents. Name Exponents Lesson 49 CC.6.EE.1 An exponent tells how many times a number is used as a factor. The base is the number being multiplied repeatedly. For example, in 2 5, 5 is the exponent and 2 is the base Write the expression 4 5 using equal factors. Then find the value. Step 1 Identify the base. The base is 4. Use one or more exponents to write the expression Find the value Step 2 Identify the exponent. The exponent is 5. Step 3 Write the base as many times as the exponent tells you. Place a multiplication symbol between the bases. 81 1,296 1 Step 4 Multiply. So, , , Write as an expression using equal factors. Then find the value , ; ; ; ; ; 10, ; 32, ; 14, ; ; ; 10,000, ,625 Expressions and Equations Write 144 with an exponent by using 12 as the base. 12. Each day Sheila doubles the number of pushups she did the day before. On the fifth day, she does push-ups. Use an exponent to write the number of push-ups Shelia does on the fifth day Write 343 with an exponent by using 7 as the base The city of Beijing has a population of more than 10 7 people. Write the population of Beijing without using an exponent. 2 5 more than 10,000, Expressions and Equations

14 Name Exponents Lesson 49 COMMON CORE STANDARD CC.6.EE.1 Lesson Objective: Write and evaluate expressions involving exponents. An exponent tells how many times a number is used as a factor. The base is the number being multiplied repeatedly. For example, in 2 5, 5 is the exponent and 2 is the base Write the expression 4 5 using equal factors. Then find the value. Step 1 Identify the base. The base is 4. Step 2 Identify the exponent. The exponent is 5. Step 3 Write the base as many times as the exponent tells you. Place a multiplication symbol between the bases. Step 4 Multiply. So, , ,024 Write as an expression using equal factors. Then find the value ; ; ; ; ; 10, ; 32, ; 14, ; ; ; 10,000, ,625 Expressions and Equations 12 97

15 Name Exponents Lesson 49 CC.6.EE.1 Use one or more exponents to write the expression Find the value , , Write 144 with an exponent by using 12 as the base. 11. Write 343 with an exponent by using 7 as the base Each day Sheila doubles the number of pushups she did the day before. On the fifth day, she does push-ups. Use an exponent to write the number of push-ups Shelia does on the fifth day. 13. The city of Beijing has a population of more than 10 7 people. Write the population of Beijing without using an exponent. 2 5 more than 10,000,

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17 LESSON 54 Pages Page 54, Assessment Guide COMMON CORE STANDARD CC.6.EE.3 OBJECTIVE Combine like terms by applying the strategy use a model. ESSENTIAL QUESTION How can you use the strategy use a model to combine like terms? VOCABULARY like terms MATERIALS PREREQUISITES Write and evaluate algebraic expressions. Problem Solving Combine Like Terms About the Math Variables can be used to write expressions when solving problems. Expressions containing like terms can be simplified by combining like terms. Students will support their learning when they model with mathematics. The Lesson Introduce Remind students that they have used variables to write expressions. In this lesson they will simplify expressions. Teach Discuss the meaning of like terms as terms that have the same variable to the same power. Remind students that constants are like terms. The model shows that 10h in the first row and 6h in the second row can be combined, in this case subtracted. Have students cross out 6h from each row to show that there are 4h left. Point out that 1 is a constant and does not have the variable h so it cannot be combined. Extend the process of combining like terms to include adding or subtracting the coefficients of the like terms to combine. Practice Have students complete page 108. You may wish to review the process by discussing the first exercise. Name Problem Solving Combine Like Terms Use a bar model to solve the problem. Each hour a company assembles 10 bikes and then packages 6 of those bikes for local shipment. An employee tests 1 bike each day. The expression 10h 2 6h 2 1 represents the number of bikes produced for international shipment in h hours. Simplify the expression by combining like terms. Read the Problem What do I need to find? What information do I need to use? I need to simplify the expression 10h 6h 1 I need to use the like terms. 10h and 6h. Lesson 54 COMMON CORE STANDARD CC.6.EE.3 Lesson Objective: Combine like terms by applying the strategy use a model. Name Problem Solving Combine Like Terms Read each problem and solve. 1. A box of pens costs $3 and a box of markers costs $5. The expression 3p 1 5p represents the cost in dollars to make p packages that includes 1 box of pens and 1 box of markers. Simplify the expression by combining like terms. Lesson 54 CC.6.EE.3 3p 1 5p 5 8p Solve the Problem How will I use the information? I can use a bar model to find the difference of like the terms. Draw a bar model to subtract from. Each square represents h, or 1h. h h h h h h h h h h h h h The model shows that 10h 2 6h 5. 10h 2 6h So, a simplified expression for the number of bikes is. 1. Bradley sells produce in boxes at the local farmer s market. He put 6 ears of corn and 9 tomatoes in each box. The expression 6b 1 9b represents the total pieces of produce in b boxes. Simplify the expression by combining like terms. 15b 6h 10 h h h h 6 h 4 h 4h 10h 4h Andre bought pencils in packs of 8. He gave 2 pencils to his sister and 3 pencils from each pack to his friends. The expression 8p 2 3p 2 2 represents the number of pencils Andre has left from p packs. Simplify the expression by combining like terms. 5p 2 2 Expressions and Equations 107 4h 2. On a heating bill, a gas company charges customers two different fees based on t therms used. The service fee costs $0.25 per therm and the distribution fee costs $0.10 per therm. The expression 0.25t t 1 40 represents the total bill in dollars. Simplify the expression by combining like terms. 3. A radio show lasts for h hours. During that time, there are 60 minutes of air time per hour and 8 minutes of commercials per hour. The expression 60h 2 8h represents the air time in minutes available for talk and music. Simplify the expression by combining like terms. 4. A publisher sends 100 books to each bookstore where its books are sold. About 3 books are sold at a discount to employees and about 40 books are sold during store supersales. The expression 100s 2 3s 2 40s represents the number of books for s stores that are sold at full price. Simplify the expression by combining like terms. 5. A sub shop sells a meal that includes an Italian sub for $6 and chips for $2. If a customer purchases more than 3 meals, he or she receives a $5 discount. The expression 6m 1 2m 2 5 shows the cost in dollars of the customer s order for m $ 3. Simplify the expression by combining like terms t h 57s 8m 2 5 Expressions and Equations 15 57

18 Name Problem Solving Combine Like Terms Use a bar model to solve the problem. Lesson 54 COMMON CORE STANDARD CC.6.EE.3 Lesson Objective: Combine like terms by applying the strategy use a model. Each hour a company assembles 10 bikes and then packages 6 of those bikes for local shipment. An employee tests 1 bike each day. The expression 10h 2 6h 2 1 represents the number of bikes produced for international shipment in h hours. Simplify the expression by combining like terms. Read the Problem What do I need to find? I need to simplify the 10h 6h 1 expression. What information do I need to use? I need to use the like terms 6h 10h and. How will I use the information? I can use a bar model to fi nd the difference of the like terms. 6h Solve the Problem Draw a bar model to subtract from. Each square represents h, or 1h. 10 h 10h h h h h h h h h h h h h h h h h 6 h 4 h The model shows that 10h 2 6h 5. 10h 2 6h So, a simplified expression for the number of bikes is. 1. Bradley sells produce in boxes at the local farmer s market. He put 6 ears of corn and 9 tomatoes in each box. The expression 6b 1 9b represents the total pieces of produce in b boxes. Simplify the expression by combining like terms. 15b 4h 4h 2 1 4h 2. Andre bought pencils in packs of 8. He gave 2 pencils to his sister and 3 pencils from each pack to his friends. The expression 8p 2 3p 2 2 represents the number of pencils Andre has left from p packs. Simplify the expression by combining like terms. 5p 2 2 Expressions and Equations

19 Name Problem Solving Combine Like Terms Lesson 54 CC.6.EE.3 Read each problem and solve. 1. A box of pens costs $3 and a box of markers costs $5. The expression 3p 1 5p represents the cost in dollars to make p packages that includes 1 box of pens and 1 box of markers. Simplify the expression by combining like terms. 3p 1 5p 5 8p 2. On a heating bill, a gas company charges customers two different fees based on t therms used. The service fee costs $0.25 per therm and the distribution fee costs $0.10 per therm. The expression 0.25t t 1 40 represents the total bill in dollars. Simplify the expression by combining like terms. 0.35t A radio show lasts for h hours. During that time, there are 60 minutes of air time per hour and 8 minutes of commercials per hour. The expression 60h 2 8h represents the air time in minutes available for talk and music. Simplify the expression by combining like terms. 52h 4. A publisher sends 100 books to each bookstore where its books are sold. About 3 books are sold at a discount to employees and about 40 books are sold during store supersales. The expression 100s 2 3s 2 40s represents the number of books for s stores that are sold at full price. Simplify the expression by combining like terms. 5. A sub shop sells a meal that includes an Italian sub for $6 and chips for $2. If a customer purchases more than 3 meals, he or she receives a $5 discount. The expression 6m 1 2m 2 5 shows the cost in dollars of the customer s order for m $ 3. Simplify the expression by combining like terms. 57s 8m

20 Assessment Guide Sample Pages The following pages from the On Core Assessment Guide support the student lessons presented earlier in this sampler: Lesson 14: Find the Whole from a Percent Lesson 49: Exponents Lesson 54: Problem Solving Combine Like Terms 18

21 Name Lesson 14 CC.6.RP.3c 1. 9 is 15% of what number? A 24 B 60 C 85 D Carmen has saved 80% of the money she needs to buy a new video game. If she has saved $36, how much does the video game cost? A $28.80 C $63.80 B $45 D $80 2. A train is traveling from Orlando, Florida to Atlanta, Georgia. So far, it has traveled 75% of the distance, or 330 miles. How far is Orlando from Atlanta? A 247 miles B 255 miles C 405 miles D 440 miles 4. The sixth-graders at Amir s school voted for the location of their class trip. The table shows the results. Class Trip Votes Location Percent History Museum 25% Art Museum 35% Aquarium 40% If 126 students voted for going to the art museum, how many sixth-graders are at Amir s school? A 226 C 360 B 315 D Marcus is saving money to buy a new DVD player. So far, he has saved 60% of the money he needs, or $45. What is the cost of the DVD player? Explain how you know. $75; I needed to answer the question, 60% of what number is 45? I wrote and used equivalent ratios to find that the answer is $ Ratios and Proportional Relationships

22 Name Lesson 49 CC.6.EE.1 1. The bill with the greatest value ever printed in the United States had a value of 10 5 dollars. Which is another way to write that amount? A $10,000 B $50,000 C $100,000 D $500, John is making a patio in his yard. He needs a total of 15 2 concrete blocks to cover the area. How many blocks does John need? A 30 B 125 C 152 D Carlos represented 729 with a base and an exponent. Which of the following is NOT possible? A The base is less than the exponent. B The base and the exponent are equal. C The base and the exponent are multiples of 3. D The base is an odd number and the exponent is an even number. 4. Which is a way to write with exponents and two bases? A B C D James wrote 256 as 2 8. Janet wrote 256 as 4 4. Explain how you know both of the students are correct. Write a word problem for which Janet s representation could be used to answer the question. 2 8 means I grouped the 2s by 2 to get Then I multiplied 16 by 16, which is 256. Since my second step was equivalent to 4 4, I know the two numbers are equivalent. Possible word problem: Janet baked cookies for the bake sale. She put 4 cookies in a bag and 4 bags in a basket. Then she put 4 baskets in a box. Finally, she put 4 boxes in a bin. How many cookies did she bake if she filled 4 bins? Expressions and Equations 20 49

23 Name Lesson 54 CC.6.EE.3 1. Sandwiches cost $5, French fries cost $3, and drinks cost $2. The expression 5n 1 3n 1 2n gives the total cost in dollars for buying a sandwich, French fries, and a drink for n people. Which is another way to write this expression? A 10n B 10 n 3 C 30n D 30 n 3 3. Dana has n quarters. Ivan has 2 fewer than three times the number of quarters Dana has. The expression n 1 3n 2 2 gives the number of quarters they have altogether. Which is another way to write this expression? A 2 n 2 B 2n C 4 n D 4n Jackets cost $15 and decorative buttons cost $5. The delivery fee is $5 per order. The expression 15n 1 5n 1 5 gives the cost in dollars of buying jackets with buttons for n people. Which is another way to write this expression? A 25n B 25 n 2 C 20n 1 5 D 20 n Scarves cost $12 and snowmen pins cost $2. Shipping is $3 per order. The expression 12n 1 2n 1 3 gives the cost in dollars of buying scarves with pins for n people. Which is another way to write this expression? A 14 n B 14n 1 3 C 17 n 2 D 17n 5. Debbie is n years old. Edna is 3 years older than Debbie, and Shawn is twice as old as Edna. The expression n 1 n (n 1 3) gives the sum of their ages. Simplify the expression by combining like terms. Explain how you found your answer. 4n 1 9; First, I used the Distributive Property to rewrite the expression as n 1 n (2 3 n) 1 (2 3 3), or n 1 n n 1 6. Then I used the Commutative Property of Addition to switch the order of 3 and 2n. Finally, I combined the like terms: n 1 n 1 2n n Expressions and Equations

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28 On Core Mathematics Kindergarten Grade 6 For more information, contact your sales representative at Houghton Mifflin Harcourt Alliance Initiative Comprehensive support for all your Common Core needs! Professional Services and Training Content Curriculum Management Data Systems hmheducation.com/commoncore ExamView is a registered trademark of einstruction Corporation.. All rights reserved. Printed in the U.S.A. 03/11 MS15240 F