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Lesson 11 Use after Ready Instruction page 97 Add and Subtract Fractions in Word Problems Name: Use Benchmark Fractions Study the example problem showing comparing numbers by using the benchmark fraction 1 . Then solve problems 1–5. 2 ·· Example Ricci and his brother Lorenzo both have to practice for an upcoming karate tournament. Ricci practices for 3 hour, 8 ·· 3 and Lorenzo practices for hour. Which brother practices 4 ·· for a longer time? Compare both numbers to the benchmark fraction 1 . 2 ·· 3 8 0 3 4 1 1 2 Look at the number line. It shows that 3 is less than 1 8 ·· and 3 is greater than 1 . 4 2 ·· ·· 3 3 3 3 So, , and . . 8 ·· 4 4 ·· 8 ·· ·· 2 ·· Lorenzo practices for a longer time. 1 Use the number line in the example problem to compare each fraction below to 1 . Write each fraction 2 ·· in the correct box. 6 8 ·· 3 1 4 ·· 4 ·· Less than 1 2 ·· 5 2 8 ·· 4 ·· Equal to 1 2 ·· 7 8 ·· 2 8 ·· Greater than 1 2 ·· Vocabulary benchmark fraction a common fraction you can judge other numbers against 1 example: 1 , 1 , 3 2. 4 ·· 2 ·· 4 ·· ©Curriculum Associates, LLC Copying is not permitted. Lesson 11 Add and Subtract Fractions in Word Problems 113 Solve. 2 You can also use the number 1 as a benchmark. Use 1 the fractions from the box. 4 3 ·· Write each fraction that is 3 3 3 ·· b. less than 1. 15 ·· 7 5 ·· 10 ·· a. greater than 1. 12 3 ·· 2 5 ·· 16 10 ·· c. equal to 1. 3 Which fraction from problem 2 is greater than 1 1 ? 2 ·· Explain how you know. 4 You can also model comparisons to 1 using fraction 2 ·· strips. Write ., 5, or , to compare each set of 2 3 fractions below. 2 1 3 2 ·· ·· So, 2 2 . 3 6 ·· ·· 2 1 6 2 ·· ·· 1 2 2 6 5 Josan and Andrea are on a long-distance bike ride. They decide they will stop for water if either of their water bottles is less than half full. Josan’s bottle is 2 full. Andrea’s bottle is 5 full. Should they stop? 5 ·· 6 ·· Explain. Show your work. Solution: 114 Lesson 11 Add and Subtract Fractions in Word Problems ©Curriculum Associates, LLC Copying is not permitted. Lesson 11 • Use after Ready Instruction page 99 Name: Estimate using Benchmark Fractions Study the example problem showing how to estimate a sum using benchmark fractions. Then solve problems 1–5. Example David grew 1 3 inches last year and 1 5 inches this year. 4 ·· 8 ·· Estimate how much he grew in the two years. You can estimate 1 3 1 1 5 using benchmark fractions. 4 ·· 8 ·· The number line below shows common fractions used as benchmark fractions to estimate sums and differences. 0 1 4 1 2 3 4 1 1 1 3 14 12 14 2 1 3 is already one of the benchmark fractions, so just 4 ·· estimate 1 5 . 8 ·· 1 5 is a little greater than 1 1 . Estimate using 1 1 . 8 ·· 2 ·· 2 ·· 1 3 1 1 1 5 1 3 1 1 2 5 2 5 , or 3 1 . 4 ·· 2 ·· 4 ·· 4 ·· 4 ·· 4 ·· The sum is a little greater than 3 1 , so David grew a little more than 3 1 inches. 4 ·· 4 ·· 1 Look at the example problem. Explain how you know 1 5 is a little greater than 1 1 . 8 2 ·· ·· 2 Find the actual sum of 1 3 1 1 5 to determine how 4 8 ·· ·· much David grew in two years. Explain how you know your answer is reasonable. Show your work. Solution: ©Curriculum Associates, LLC Copying is not permitted. Lesson 11 Add and Subtract Fractions in Word Problems 115 Solve. Irene makes 4 2 cups of pancake batter. She splits the 3 ·· batter into 2 bowls. She mixes blueberries into 2 1 cups of batter and walnuts into the rest of the 4 ·· batter. 3 Estimate how much of the batter has walnuts in it. Explain your estimate. 4 Find the actual amount of batter that has walnuts in it. Explain how you know your answer is reasonable. Show your work. Solution: 5 Irene makes a second batch of 3 1 cups of pancake 4 ·· batter. She wants to know how much more batter she made in the first batch. She estimates that the difference between the sizes of the two batches 4 2 2 3 1 is 2 1 . Explain why this estimate is not 3 ·· 4 ·· 12 ·· reasonable. 116 Lesson 11 Add and Subtract Fractions in Word Problems ©Curriculum Associates, LLC Copying is not permitted. Lesson 11 • Use after Ready Instruction page 101 Name: Add and Subtract Fractions in Word Problems Solve the problems. 1 Write the missing numbers to show equivalent Remember to multiply both the numerator and denominator by the same number to show an equivalent fraction. fractions for some common numbers used as benchmarks. 0 1 4 1 2 3 4 1 1 1 3 14 12 14 a. 1 , c. 3 , b. 1 , d. 2, , 8 ···· 12 4 ···· ·· , 8 ···· 10 2 ···· ·· 2 , 8 ···· 12 4 ···· ·· , 2 ···· 4 ···· 2 The Graf family made two pizzas. They ate 1 1 pizza 8 ·· before watching a movie, and 1 pizza more after the 2 ·· movie. Which is a reasonable estimate for the amount Where is 1 ·· 81 located on the number line? of pizza left? A less than 1 C less than 1 1 B more than 1 D more than 1 1 2 ·· 2 ·· 4 ·· 4 ·· Tammy chose A as the correct answer. How did she get that answer? ©Curriculum Associates, LLC Copying is not permitted. Lesson 11 Add and Subtract Fractions in Word Problems 117 Solve. 3 Lexi bought 1 2 pounds of green grapes and 5 ·· 3 2 pounds of red grapes. Grapes are $2.99 a pound. 10 ·· Did Lexi spend more or less than $12 on grapes? Explain. Do I need to find the actual number of pounds of grapes, or can I answer the question using an estimate? 4 On Monday Marco practiced the piano for 7 hour. On 10 ·· Tuesday he practiced for 1 5 hours. He is supposed to 6 ·· 1 practice 1 hours each day. 4 ·· Use this information to write a question that involves adding or subtracting fractions. What fractions can I use to write an addition or subtraction question? 5 Look at the question you wrote in problem 4. Show how to estimate the answer. Then find the actual answer. Show your work. What benchmark fractions could I use to estimate? Solution: 118 Lesson 11 Add and Subtract Fractions in Word Problems ©Curriculum Associates, LLC Copying is not permitted. Practice Lesson 11 Add and Subtract Fractions in Word Problems Lesson 11 Use after Ready Instruction page 97 Add and Subtract Fractions in Word Problems Solve. Name: M Use Benchmark Fractions 2 You can also use the number 1 as a benchmark. Use Write each fraction that is benchmark fraction 1 . Then solve problems 1–5. a. greater than 1. Example c. Ricci and his brother Lorenzo both have to practice for an 4 ·· 8 ·· 2 So, 2 3 ·· C 1 5 Less than 1 2 8 ·· 7 4 ·· Equal to 1 2 ·· 2 3 . 6 ·· , 1 2 1 2 ·· 2. 6 ·· 2 6 Show your work. Students might use number lines, equations, or 8 ·· Vocabulary some other method to compare 2 and 5 to 1 . 5 ·· can judge other 6 6 ·· ·· 2 , or 4 , is less than 1 , or 5 . 10 2 10 ··· ·· ··· 1 example: ··14 , ··12 , ··34 2. Lesson 11 Add and Subtract Fractions in Word Problems Lesson 11 • Use after Ready Instruction page 99 6 ·· 2 ·· Yes, they should stop. Possible explanation: Andrea’s bottle is more than half Solution: full because 5 is more than 3 and 3 5 1 , but Josan’s bottle is less than half full because a common fraction you 5, 6, 3, 7 8 ·· 8 ·· 4 ·· 8 ·· Copying is not permitted. 2 2 ·· 2 full. Andrea’s bottle is 5 full. Should they stop? 6 ·· numbers against ©Curriculum Associates, LLC 10 ··· Explain. 2 ·· 2 4 ·· 2 ·· water bottles is less than half full. Josan’s bottle is benchmark fraction 2, 1 8 ·· 4 ·· 10 ··· 5 ·· Greater than 1 2 ·· 10 ··· 10 ··· They decide they will stop for water if either of their 2 8 ·· 10 ··· 5 Josan and Andrea are on a long-distance bike ride. in the correct box. 4 ·· 1 . 3 ·· 1 Use the number line in the example problem to compare each fraction below to 1 . Write each fraction 2 ·· 3 10 ··· fractions below. 2 ·· Lorenzo practices for a longer time. 4 ·· 10 ··· strips. Write ., 5, or , to compare each set of 4 2 ·· ·· So, 3 , 3 and 3 . 3 . 8 ·· 4 4 ·· 8 ·· ·· 6 10 ··· 4 You can also model comparisons to 1 using fraction 2 ·· M 1 Look at the number line. It shows that 3 is less than 1 8 ·· equal to 1. 2 ·· 3 4 and 3 is greater than 1 . 16 10 ·· greater than 1 1 . 2 ·· 1 2 2 5 ·· 3 3 ·· 10 ··· Compare both numbers to the benchmark fraction 1 . 0 15 ·· 7 5 ·· Explain how you know. 16 ; Possible answer: 10 is 1. 16 is 10 1 6 , or 1 6 . 6 is more than 5 , or 1 , so 1 6 is for a longer time? 3 8 3 3 ·· 3 ··· 15 ··· 10 ·· 5 ·· 12 3 ·· 3 10 ·· 3 Which fraction from problem 2 is greater than 1 1 ? 2 ·· M 8 ·· and Lorenzo practices for 3 hour. Which brother practices 4 3 ·· 4 , 7 , 16 3 ·· 5 ··· 10 ·· 1 , 12 , 3 , 2 b. less than 1. upcoming karate tournament. Ricci practices for 3 hour, 1 the fractions from the box. Study the example problem showing comparing numbers by using the 2 ·· M Unit 1 6 ·· 2 ·· 5 ·· 113 113 114 114 Lesson 11 Add and Subtract Fractions in Word Problems ©Curriculum Associates, LLC Copying is not permitted. Name: Solve. Estimate using Benchmark Fractions Irene makes 4 2 cups of pancake batter. She splits the Study the example problem showing how to estimate a sum using benchmark fractions. Then solve problems 1–5. 3 ·· batter into 2 bowls. She mixes blueberries into 2 1 cups of batter and walnuts into the rest of the 4 ·· Example batter. David grew 1 3 inches last year and 1 5 inches this year. 4 ·· 8 ·· Estimate how much he grew in the two years. C You can estimate 1 3 1 1 5 using benchmark fractions. 4 ·· 8 ·· 3 Estimate how much of the batter has walnuts in it. Explain your estimate. Estimates and explanations will vary, but the estimate should be about 2 1 cups. 2 ·· The number line below shows common fractions used as benchmark fractions to estimate sums and differences. 0 1 4 1 2 1 3 4 1 1 3 14 12 14 2 M 1 3 is already one of the benchmark fractions, so just 4 ·· estimate 1 5 . 8 ·· 1 5 is a little greater than 1 1 . Estimate using 1 1 . 8 2 2 ·· ·· ·· 1 3 1 1 1 5 1 3 1 1 2 5 2 5 , or 3 1 . 4 2 4 4 4 4 ·· ·· ·· ·· ·· ·· The sum is a little greater than 3 1 , so David grew a little 4 ·· more than 3 1 inches. 4 ·· B 4 Find the actual amount of batter that has walnuts in it. Explain how you know your answer is reasonable. Show your work. Students might use fraction strips, equations, or some other method to subtract 2 1 from 4 2 . 4 ·· 3 ·· 2 5 cups. Explanations will vary but should indicate that the answer 2 5 is 12 ··· 12 ··· Solution: close to the estimate from problem 3. M 1 Look at the example problem. Explain how you know 1 5 is a little greater than 1 1 . 8 2 ·· ·· Possible answer: You can rewrite 1 1 as 1 4 . 1 5 is 1 more. 2 8 8 ·· 8 ·· ·· ·· 5 Irene makes a second batch of 3 1 cups of pancake 4 ·· batter. She wants to know how much more batter she made in the first batch. She estimates that the difference between the sizes of the two batches M 2 Find the actual sum of 1 3 1 1 5 to determine how 4 8 ·· ·· 4 2 2 3 1 is 2 1 . Explain why this estimate is not 3 ·· much David grew in two years. Explain how you know 4 ·· 3 ·· 4 ·· 4 ·· 12 ··· 4 ·· 12 ··· 3 ·· 8 ·· 12 ··· 3 3 inches. The answer is a little greater than 3 1 , as estimated. 8 ·· ©Curriculum Associates, LLC 26 8 ·· 12 ·· would also be true. But 3 1 2 5 5, so 3 1 1 2 1 is greater than 5. Show your work. Possible work: 1 3 1 1 5 5 3 3 Solution: 4 ·· reasonable. Answers will vary. Possible answer: If 4 2 2 3 1 5 2 1 is true, then 3 1 1 2 1 5 4 2 your answer is reasonable. 4 ·· Copying is not permitted. Practice and Problem Solving Lesson 11 Add and Subtract Fractions in Word Problems 115 115 116 116 Lesson 11 Add and Subtract Fractions in Word Problems ©Curriculum Associates, LLC Copying is not permitted. Unit 2 Number and Operations—Fractions ©Curriculum Associates, LLC Copying is not permitted. Practice Lesson 11 Add and Subtract Fractions in Word Problems Lesson 11 • Use after Ready Instruction page 101 Unit 1 Name: Solve. Add and Subtract Fractions in Word Problems Solve the problems. B M 1 Write the missing numbers to show equivalent 0 1 4 1 2 3 4 1 1 3 2 2 3 a. 1 , , 6 9 c. 3 , , 4 5 b. 1 , , d. 2, 8 ···· 12 4 ···· ·· Explain. less than $12; Possible explanation: Lexi bought less than 1 1 pounds of green grapes and less 4 , 2 ·· 2 ·· 4 pounds altogether. Grapes are a little less than $3 a pound. She spent less than 4 3 $3, or $12 8 for grapes. 2 ···· 4 ···· 2 The Graf family made two pizzas. They ate 1 1 pizza 8 ·· before watching a movie, and 1 pizza more after the 2 ·· movie. Which is a reasonable estimate for the amount M 1 Where is 1 ·· located 8 on the number line? of pizza left? A less than 1 B more than 1 C 2 ·· 4 On Monday Marco practiced the piano for 7 hour. On 10 ·· Tuesday he practiced for 1 5 hours. He is supposed to 6 ·· practice 1 1 hours each day. 4 ·· Use this information to write a question that involves adding or subtracting fractions. less than 1 1 4 ·· What fractions can I use to write an addition or subtraction question? Possible answer: How much longer should D more than 1 1 2 ·· Do I need to find the actual number of pounds of grapes, or can I answer the question using an estimate? than 2 1 pounds of red grapes. That is less than 8 ···· 12 4 ···· ·· 8 ···· 10 2 ···· ·· M 1 14 12 14 Did Lexi spend more or less than $12 on grapes? Remember to multiply both the numerator and denominator by the same number to show an equivalent fraction. fractions for some common numbers used as benchmarks. 3 Lexi bought 1 2 pounds of green grapes and 5 ·· 2 3 pounds of red grapes. Grapes are $2.99 a pound. 10 ·· 4 ·· Marco have practiced on Monday? Tammy chose A as the correct answer. How did she get that answer? Answers will vary. Possible answer: She correctly C estimated that since 1 1 is a little greater than 1, 8 ·· they ate a little more than 1 1 1 pizzas. So, there 2 ·· 5 Look at the question you wrote in problem 4. Show how to estimate the answer. Then find the actual answer. Show your work. Students might use benchmark fractions or some other method to estimate; and fraction strips, equations, or some other method to find the actual answer. is a little less than 1 of a pizza left. 2 ·· What benchmark fractions could I use to estimate? Solution: Estimates and answers will vary. ©Curriculum Associates, LLC Copying is not permitted. Lesson 11 Add and Subtract Fractions in Word Problems 117 117 118 118 Lesson 11 Add and Subtract Fractions in Word Problems ©Curriculum Associates, LLC Copying is not permitted. Key B Basic M Medium C Challenge Practice and Problem Solving ©Curriculum Associates, LLC Copying is not permitted. Unit 2 Number and Operations—Fractions 27