Multiplication and Division of Fractions

Lesson 17

Math

Unit 5

5th Grade

Lesson 17 of 24

Objective


Solve real-world problems involving multiplication with mixed numbers and create real-world contexts for expressions involving multiplication with mixed numbers.

Common Core Standards


Core Standards

  • 5.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 5.NF.B.6 — Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
  • 5.OA.A.2 — Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Foundational Standards

  • 3.OA.A.1
  • 3.OA.A.2
  • 3.OA.D.8
  • 4.OA.A.1
  • 4.OA.A.2
  • 4.OA.A.3

Criteria for Success


  1. Make sense of a three-act task and persevere in solving it (MP.1). 
  2. Write a story context to match a given expression involving the multiplication of two fractions, including mixed numbers (on the Problem Set) (MP.2). 
  3. Write an expression to match a story context involving the multiplication of two fractions, including mixed numbers (on the Problem Set) (MP.2). 
  4. Solve one-, two-, and multi-step problems involving the multiplication of two fractions (MP.4).

Tips for Teachers


This lesson follows a different structure than those in analogous lessons in previous topics, Lesson 7 and Lesson 12. This is for the sake of sustained work on a multi-step word problem that addresses the most challenging type of computation aligned to 5.NF.4. However, if students would benefit from more direct instruction aligned to Criteria for Success #2 and #3, create tasks similar to Lesson 6’s and Lesson 11’s Anchor Tasks #1 and #2 to include mixed number multiplication and include them before a consolidated three-act task as outlined in this lesson. 

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Anchor Tasks

25-30 minutes


Problem 1

Act 1: Watch the video The Big Pad (Act: 1).

a.   What do you notice? What do you wonder?

b.   What is the area, in square centimeters, of the big pad? Make an estimate.

Guiding Questions

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Student Response

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References

Questioning My Metacognition The Big Pad

The Big Pad by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed May 1, 2019, 2:46 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Act 2: Use the following information to determine the area, in square centimeters, of the big pad. 

  • The small pad is a square with a length of $$7\frac{3}{5}$$ cm.
  • The big pad is also a square and has a length equal to $$3\frac{2}{3}$$ small pads.

Guiding Questions

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Student Response

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References

Questioning My Metacognition The Big Pad

The Big Pad by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed May 1, 2019, 2:46 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Act 3: The area of the big pad is $$776\frac{124}{225}$$ square centimeters. 

Was your estimate reasonable? Why or why not?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

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References

Questioning My Metacognition The Big Pad

The Big Pad by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed May 1, 2019, 2:46 p.m..

Modified by Fishtank Learning, Inc.

Problem 4

Act 4 (the sequel): Look at the following image of the dimensions mentioned on the big pad -

Do these dimensions result in the same area as what we computed in Anchor Task #3? Why or why not? 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Questioning My Metacognition The Big Pad

The Big Pad by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed May 1, 2019, 2:46 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes


Discussion of Problem Set

  • Look at #2. What story context did you come up with? What is a story context that uses the same values but cannot be solved by multiplying them together? 
  • Look at #4. How did you solve? 
  • Look at #5. How did you solve? Is there more than one way to do so? 
  • Look at #8. What whole is being referred to where it says “$$\frac{3}{10}$$ of it”? How did that impact how you solved? 
  • Look at #9. How did you solve? Is there more than one way to do so? 

Target Task

5-10 minutes


Susanna is studying for final exams in college. For a whole week, she studied for her history exam for $$2\frac14$$ hours every day and for her science exam for $$\frac23$$ as much time as her science exam. How many hours will she spend studying in total over the course of the whole week? 

Student Response

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Additional Practice


The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Interpret multiplication as scaling.

Lesson 18
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Fractions as Division

Topic B: Multiplying a Fraction by a Whole Number

Topic C: Multiplying a Fraction by a Fraction

Topic D: Multiplying with Mixed Numbers

Topic E: Dividing with Fractions

Topic F: Fraction Real-World Problems and Line Plots

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