# Multiplying Fractions or Mixed Numbers

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1 s e s s i o n 4 A. 3 Multiplying Fractions or Mixed Numbers Math Focus Points Multiplying a fraction or mixed number and a whole number Using a representation and reasoning to multiply a whole number by a fraction or mixed number Today s Plan Math Workshop Multiplying Fractions or Mixed Numbers 1a Bicycle Race Training 1b Cycling and Running Discussion Why Is It Multiplication? SESSION FOLLOW-UP 4 Min 1 Min Class Materials 1A Student Activity Book, pp or C4 C, Bicycle Race Training Make copies. (as needed) 1B Student Activity Book, p. 77 or C7, Cycling and Running Make copies. (as needed) C0, Fraction Bars Make copies. (as needed) Student Activity Book, p. 77 or C7 (completed) Student Activity Book, p. 78 or C8, Training for a Race Make copies. (as needed) Ten-Minute Math Estimation and Number Sense: Closest Estimate Write each of the following problems on the board, one at a time: 1. 7_ _ Give students approximately 30 seconds to look at the three possible estimates and determine which is the closest to the actual answer. Ask several students to explain how they chose an estimate, including how they thought about each of the numbers. CC40 Investigation 4A Multiplying and Dividing Fractions

2 1 Math Workshop Multiplying Fractions or Mixed Numbers Name 3 Session Follow-Up 4 Min Cycling and Running Solve the following problems, using fraction bars as necessary. Write an equation for each problem. 1. The Astounding Race is a bicycle race that is 100 miles long. Lourdes is going to ride in the Monster Bicycle Race, which is _4 times as long as the Astounding Race. How long is the Monster Bicycle Race? You re going to finish Student Activity Book pages 74 7 or C4 C today, and there are similar problems on Student Activity Book page 77 or C7. Continue using the strategies you ve used, such as fraction bars or reasoning about fractions and multiplication. For each problem, continue thinking about what you know about fractions and multiplication and consider whether or not your answer makes sense. We ll discuss Problem on Student Activity Book page 77 or C7 at the end of the session.. Martin is going to ride in the Great Bicycle Race, which 7 as long as the 100-mile Astounding Race. How is 10 long is the Great Bicycle Race? 3. Samantha is training to run in a long distance race. She runs 1_31 miles every day for a week (7 days). How many miles does she run in one week? 4. Tavon is training also, and runs _14 miles each day for days. How many miles does he run in days? Pearson Education M ath Work shop Discussion. The bike path near Hana s home is 1 miles long. She bikes _1 times the length of the path. How many miles does Hana ride? Session 4A.3 1A Bicycle Race Training Unit 4 77 Student Activity Book, Unit 4, p. 77; Resource Masters, C7 INV1_SE0_U4.indd 77 6/13/11 1:41 PM Individuals For complete details about this activity see Session 4A., pages CC37 CC38. 1B Cycling and Running Individuals Students continue solving multiplication problems involving fractions and mixed numbers on Student Activity Book page 77 or C7. Ongoing Assessment: Observing Students at Work How do students solve the problems? Do they use fraction bars? Do they use relationships to other fractions to help them? For the mixed numbers, do they multiply first by the whole number and then by the fraction and add the products together? differentiation: Supporting the Range of Learners For students who are still working on making sense of multiplying with fractions, have them solve only the problems that involve fractions and not those with mixed numbers. Challenge students to write their own problems involving multiplying fractions, mixed numbers, and whole numbers. Students can exchange problems with a classmate to solve and check. Session 4A.3 INV1_TE0_U04_S4A.3.indd 41 Multiplying Fractions or Mixed Numbers CC41 6/1/11 6:3 PM

3 1 Math Workshop Discussion 3 Session Follow-Up D i s c u s s i o n Why Is It Multiplication? 1 MIN Class Math Focus Points for Discussion Multiplying a fraction or mixed number by a whole number Let s start by discussing your answer to Problem on Student Activity Book page 77 or C7. Who used fraction bars to solve this problem? Who solved it another way? Students might say: I used fraction bars. I drew three bars together. The first two bars are each 1 miles. I divided the third bar in half, to show 1_ of 1, and that s 7 1_. So the answer is 37 1_ miles. I thought about the numbers. 1 30, and 1 1_ 7 1_, so it s 37 1_. We ve been multiplying whole numbers by fractions and mixed numbers. When we started, some of you weren t sure these were really multiplication problems. I m curious what people are thinking now. What makes these multiplication problems? Have students turn and talk with a partner and then collect some responses. Likely responses include that the problems can still be thought of as groups of another number, and the group can be a fraction or mixed number, and vice versa. Students should also recognize that they can still reason and make sense of the numbers and the operations. CC4 Investigation 4A Multiplying and Dividing Fractions

4 Pearson Education 1 Math Workshop Discussion 3 Session Follow-Up S E S S I O N F O L L O W - U P : For reinforcement of this unit s content, have students complete Student Activity Book page 78 or C8. Name Training for a Race Solve the following problems, drawing your own fraction bars as needed. Write an equation for each problem. Renaldo bikes around a lake that has a perimeter of 0 miles. 1. On Monday, Renaldo biked 1_ of the way around the. On Wednesday, Renaldo only had a short time to bike, so he biked 1_ of the way around the lake. How many 4 miles did he ride? note Students use fraction bars to solve problems involving multiplying a whole number by a fraction or a mixed number. 3. On Thursday, Renaldo biked 1_ of the way around the 4. On Friday, Renaldo biked 3_ of the way around the lake. How many miles did he ride?. The next week, Renaldo biked 1_ times the distance around the 78 Unit 4 Session 4A.3 Student Activity Book, Unit 4, p. 78; Resource Masters, C8 Session 4A.3 Multiplying Fractions or Mixed Numbers CC43

5 Name Cycling and Running Solve the following problems, using fraction bars as necessary. Write an equation for each problem. 1. The Astounding Race is a bicycle race that is 100 miles long. Lourdes is going to ride in the Monster Bicycle Race, which is 4_ times as long as the Astounding Race. How long is the Monster Bicycle Race?. Martin is going to ride in the Great Bicycle Race, which is 7 as long as the 100-mile Astounding Race. How 10 long is the Great Bicycle Race? 3. Samantha is training to run in a long distance race. She runs 1 1_ miles every day for a week (7 days). How 3 many miles does she run in one week? 4. Tavon is training also, and runs 1_ miles each day for 4 days. How many miles does he run in days?. The bike path near Hana s home is 1 miles long. She bikes 1_ times the length of the path. How many miles does Hana ride? Unit 4 Session 4A.3 C7 Pearson Education, Inc., or its affiliates. All Rights Reserved.

6 Name Training for a Race Solve the following problems, drawing your own fraction bars as needed. Write an equation for each problem. note Students use fraction bars to solve problems involving multiplying a whole number by a fraction or a mixed number. Renaldo bikes around a lake that has a perimeter of 0 miles. 1. On Monday, Renaldo biked 1_ of the way around the. On Wednesday, Renaldo only had a short time to bike, so he biked 1_ of the way around the lake. How many 4 miles did he ride? 3. On Thursday, Renaldo biked 1_ of the way around the 4. On Friday, Renaldo biked 3_ of the way around the lake. How many miles did he ride?. The next week, Renaldo biked 1_ times the distance around the Unit 4 Session 4A.3 C8 Pearson Education, Inc., or its affiliates. All Rights Reserved.

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