Fraction Operations

Lesson 19

Objective

Solve word problems involving multiplication of fractions.

Materials and Resources

Common Core Standards

Core Standards

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  • 4.NF.B.4.C — Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Criteria for Success

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  1. Make sense of a three-act task and persevere in solving it (MP.1).
  2. Solve one- and two-step word problems that involve the multiplication of fractions (MP.4).

Tips for Teachers

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  • Today’s three-act task “helps illustrate Mathematical Practice Standard 4, Model with mathematics. Students apply the mathematics they know to solve problems arising in everyday life. As students think about the situation in real life, they have to select the mathematical thinking that will help them solve the problem. This selection of a mathematical model allows students to think about which mathematics might be useful in the real-life situation that they face. Students identify the mathematical elements of the situation and decide which solution pathway is best for them to follow” (Sugar in Six Cans of Soda, Illustrative Mathematics).
  • Let students work on each problem in the Problem Set independently and circulate to see whether students are solving correctly. If not, come back together to discuss how/what to draw on a tape diagram, then allow them to try again on their own.

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Anchor Tasks

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Problem 1

Act 1: Watch the following video: How Much Sugar (Act-1).

How much sugar is in the entire pack of soda cans?

Guiding Questions

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References

Questioning My Metacognition Do the Dew

Do the Dew by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed July 18, 2018, 4:23 p.m..

Modified by The Match Foundation, Inc.
Illustrative Mathematics Sugar in Six Cans of Soda

Sugar in Six Cans of Soda, accessed on April 27, 2018, 1:28 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

Problem 2

Act 2: Use the following information to solve.

  • One can of soda has $$3\frac{2}{9}$$ tablespoons of sugar in it. 
  • There are 12 cans in the entire pack.

Guiding Questions

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References

Questioning My Metacognition Do the Dew

Do the Dew by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed July 18, 2018, 4:23 p.m..

Modified by The Match Foundation, Inc.
Illustrative Mathematics Sugar in Six Cans of Soda

Sugar in Six Cans of Soda, accessed on April 27, 2018, 1:28 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

Problem 3

Act 3: Reveal the answer.

There are $$38\frac{2}{3}$$ tablespoons of sugar in a 12-pack.

Guiding Questions

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References

Questioning My Metacognition Do the Dew

Do the Dew by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed July 18, 2018, 4:23 p.m..

Modified by The Match Foundation, Inc.
Illustrative Mathematics Sugar in Six Cans of Soda

Sugar in Six Cans of Soda, accessed on April 27, 2018, 1:28 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

Discussion of Problem Set

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  • Who ran more in #3? Why? How could you have determined that without solving? 
  • How did you determine between what two whole numbers the answer lay in #5?
  • What expression did you write for #6(a)? What did your drawing look like in #6(b)? 
  • How did you solve #8? Did you draw a model? What did it look like? 
  • When you check for reasonableness, do you look at your equations and model? How do you figure out if your answer is reasonable? 

Target Task

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Problem 1

Solve. Show or explain your work.

Ryan makes $$6$$ backpacks. He uses $${{3\over4}}$$ yard of cloth to make each backpack. What is the total amount of cloth, in yards, Ryan uses to make all $$6$$ backpacks?

A.   $${1{1\over2}}$$

B.   $${2{1\over4}}$$

C.   $${4{1\over2}}$$

D.   $$6{{{3\over4}}}$$

References

PARCC Mathematics Practice Tests Grade 4 Mathematics Paper-Based Practice TestQuestion #16

Grade 4 Mathematics Paper-Based Practice Test from Mathematics Practice Tests is made available by Partnership for Assessment of Readiness for College and Careers. © Copyright 1998 - 2015 Pearson Education, Inc. or its affiliate(s). All rights reserved. Accessed Dec. 7, 2017, 11:14 a.m..

Problem 2

Solve. Show or explain your work.

If a bucket holds $${2{1\over2}}$$ gallons and $${43}$$ buckets of water fill a tank, how much does the tank hold?

References

Institute for Mathematics and Education Progressions for the Common Core State Standards in Mathematics, 3-5 Number and Operations - Fractionsp. 9

Progressions for the Common Core State Standards in Mathematics, 3-5 Number and Operations - Fractions, by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents. All contents copyrighted. All rights reserved. Accessed July 16, 2018, 4:49 p.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.

Modified by The Match Foundation, Inc.

Mastery Response

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