S E S S I O N 4 A . 3 Multiplying Fractions Or Mixed Numbers
session 4A.3Multiplying Fractions orMixed NumbersMath Focus PointsMultiplying a fraction or mixed number and awhole numberUsing a representation and reasoning to multiply a wholenumber by a fraction or mixed numberToday’s PlanMaterialsMath Workshop1AMultiplying Fractions or MixedNumbers1a1b45 Min Student Activity Book, pp. 74–75 orC24–C25, Bicycle Race Training Makecopies. (as needed)1B Student Activity Book, p. 77 orC27, Cycling and Running Make copies.(as needed)C20, Fraction Bars Make copies. (asneeded) Bicycle Race TrainingCycling and Running DiscussionWhy Is It Multiplication? Student Activity Book, p. 77 or C27 (completed)15 MinSESSION FOLLOW-UPClass Student Activity Book, p. 78 orDaily PracticeC28, Training for a Race Make copies. (asneeded)Ten-Minute MathEstimation and Number Sense: Closest Estimate Write each of the followingproblems on the board, one at a time:15101. 5 7 8 215452. 36 5 7Give students approximately 30 seconds to look at the three possible estimates anddetermine which is the closest to the actual answer. Ask several students to explainhow they chose an estimate, including how they thought about each of the numbers.CC40Investigation 4AINV12 TE05 U04 S4A.3.indd 40Multiplying and Dividing Fractions6/15/11 6:34 PM
1 Math WorkshopMultiplying Fractions orMixed NumbersName3 Session Follow-UpDateWhat’s That Portion?45 MinCycling and RunningSolve the following problems, using fraction bars asnecessary. Write an equation for each problem.1. The Astounding Race is a bicycle race that is 100 mileslong. Lourdes is going to ride in the Monster BicycleRace, which is 2 45 times as long as the Astounding Race.How long is the Monster Bicycle Race?You’re going to finish Student Activity Book pages 74–75 orC24–C25 today, and there are similar problems on StudentActivity Book page 77 or C27. Continue using the strategiesyou’ve used, such as fraction bars or reasoning about fractions andmultiplication. For each problem, continue thinking about whatyou know about fractions and multiplication and considerwhether or not your answer makes sense. We’ll discussProblem 5 on Student Activity Book page 77 or C27 at theend of the session.2. Martin is going to ride in the Great Bicycle Race, which7 as long as the 100-mile Astounding Race. Howis10long is the Great Bicycle Race?3. Samantha is training to run in a long distance race. Sheruns 1 31 miles every day for a week (7 days). Howmany miles does she run in one week?4. Tavon is training also, and runs 2 14 miles each day for5 days. How many miles does he run in 5 days? Pearson Education 5M ath Work shop2 Discussion5. The bike path near Hana’s home is 15 miles long. Shebikes 2 12 times the length of the path. How many milesdoes Hana ride?Session 4A.31A Bicycle Race TrainingUnit 477 Student Activity Book, Unit 4, p. 77;Resource Masters, C27INV12 SE05 U4.indd 776/13/11 12:41 PMIndividualsFor complete details about this activity see Session 4A.2,pages CC37–CC38.1B Cycling and RunningIndividualsStudents continue solving multiplication problems involvingfractions and mixed numbers on Student Activity Book page 77or C27.Ongoing Assessment: Observing Students at Work How do students solve the problems? Do they use fractionbars? Do they use relationships to other fractions to helpthem? For the mixed numbers, do they multiply first by thewhole number and then by the fraction and add theproducts together?differentiation: Supporting the Range of LearnersFor students who are still working on makingsense of multiplying with fractions, have them solve onlythe problems that involve fractions and not those withmixed numbers.Challenge students to write their own problemsinvolving multiplying fractions, mixed numbers, and wholenumbers. Students can exchange problems with a classmate tosolve and check.Session 4A.3INV12 TE05 U04 S4A.3.indd 41Multiplying Fractions or Mixed NumbersCC416/15/11 6:35 PM
1 Math Workshop2 Discussion3 Session Follow-UpDiscussionWhy Is It Multiplication?15 MINClassMath Focus Points for DiscussionMultiplying a fraction or mixed number by a whole numberLet’s start by discussing your answer to Problem 5 on StudentActivity Book page 77 or C27. Who used fraction bars to solvethis problem? Who solved it another way?Students might say:“I used fraction bars. I drew three barstogether. The first two bars are each15 miles. I divided the third bar in half, toshow 1 2 of 15, and that’s 7 1 2 . So theanswer is 37 1 2 miles.”“I thought about the numbers. 15 2 30, and 15 1 2 7 1 2 , so it’s 37 1 2 .”We’ve been multiplying whole numbers by fractions and mixednumbers. When we started, some of you weren’t sure these werereally multiplication problems. I’m curious what people arethinking now. What makes these multiplication problems?Have students turn and talk with a partner and then collect someresponses. Likely responses include that the problems can still bethought of as “groups” of another number, and the “group” can bea fraction or mixed number, and vice versa. Students should alsorecognize that they can still reason and make sense of the numbersand the operations.CC42Investigation 4A Multiplying and Dividing FractionsINV12 TE05 U04 S4A.3.indd 426/15/11 6:36 PM
1 Math Workshop2 DiscussionNameSESSION FOLLOW-UP3 Session Follow-UpDateWhat’s That Portion?Daily PracticeTraining for a RaceDaily PracticeSolve the following problems, drawing your ownfraction bars as needed. Write an equation foreach problem.Daily Practice: For reinforcement of this unit’s content,have students complete Student Activity Book page 78or C28.note Students use fractionbars to solve problems involvingmultiplying a whole number bya fraction or a mixed number.Renaldo bikes around a lake that has a perimeter of20 miles.1. On Monday, Renaldo biked 12 of the way around thelake. How many miles did he ride?2. On Wednesday, Renaldo only had a short time to bike,so he biked 14 of the way around the lake. How manymiles did he ride?3. On Thursday, Renaldo biked 15 of the way around thelake. How many miles did he ride?4. On Friday, Renaldo biked 35 of the way around the lake.How many miles did he ride?78Unit 4 Pearson Education 55. The next week, Renaldo biked 2 12 times the distancearound the lake. How many miles did he ride?Session 4A.3 Student Activity Book, Unit 4, p. 78;Resource Masters, C28INV12 SE05 U4.indd 78Session 4A.3INV12 TE05 U04 S4A.3.indd 43Multiplying Fractions or Mixed Numbers5/18/11 7:12 PMCC436/10/11 11:35 AM
NameDateWhat’s That Portion?Cycling and RunningSolve the following problems, using fraction bars asnecessary. Write an equation for each problem.1. The Astounding Race is a bicycle race that is 100 mileslong. Lourdes is going to ride in the Monster BicycleRace, which is 2 45 times as long as the Astounding Race.How long is the Monster Bicycle Race?2. Martin is going to ride in the Great Bicycle Race, which7 as long as the 100-mile Astounding Race. Howis 10long is the Great Bicycle Race?3. Samantha is training to run in a long distance race. Sheruns 1 13 miles every day for a week (7 days). Howmany miles does she run in one week?4. Tavon is training also, and runs 2 14 miles each day for5 days. How many miles does he run in 5 days?5. The bike path near Hana’s home is 15 miles long. Shebikes 2 12 times the length of the path. How many milesdoes Hana ride?Unit 4 Session 4A.3INV12 BLM05 U4.indd 27C27 Pearson Education, Inc., or its affiliates. All Rights Reserved. 56/20/11 12:23 PM
NameDateWhat’s That Portion?Daily PracticeTraining for a RaceSolve the following problems, drawing your ownfraction bars as needed. Write an equation foreach problem.note Students use fraction bars tosolve problems involving multiplyinga whole number by a fraction or amixed number.Renaldo bikes around a lake that has a perimeter of20 miles.1. On Monday, Renaldo biked 12 of the way around thelake. How many miles did he ride?2. On Wednesday, Renaldo only had a short time to bike,so he biked 14 of the way around the lake. How manymiles did he ride?3. On Thursday, Renaldo biked 15 of the way around thelake. How many miles did he ride?4. On Friday, Renaldo biked 35 of the way around the lake.How many miles did he ride?5. The next week, Renaldo biked 2 12 times the distancearound the lake. How many miles did he ride?Unit 4 Session 4A.3INV12 BLM05 U4.indd 28C28 Pearson Education, Inc., or its affiliates. All Rights Reserved. 56/21/11 3:07 PM
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 CC40 invesTigATion 4A Multiplying and Dividi
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