Multiplication and Division of Fractions

Lesson 14

Math

Unit 5

5th Grade

Lesson 14 of 25

Objective


Multiply mixed numbers by fractions.

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.5 — Interpret multiplication as scaling (resizing), by:
  • 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.

Foundational Standards

  • 3.MD.C.7
  • 4.NF.B.4
  • 5.NF.A.1

Criteria for Success


  1. Multiply a mixed number by a fraction. 
  2. Relate the area model to the distributive property.
  3. Solve word problems that involve the multiplication of a mixed number by a fraction (MP.4). 
  4. Estimate the size of a product of a mixed number and a fraction in comparison to the size of its factors.

Tips for Teachers


Lesson Materials

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Anchor Tasks


Problem 1

a.   A construction worker is tiling a backsplash. The backsplash is $${4{{{1\over2}}}}$$ tiles long and $${{1\over2}}$$ tile tall. How many tiles are needed in total for the whole backsplash? Give an exact answer that includes the fractions of a tile she will need.

b.   A runway measures $${10{1\over3}}$$ yards long and $${{3\over4}}$$ yards wide. What is the area, in square yards, of the runway?

Guiding Questions

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Problem 2

a.   Kendra is making $${{1\over2}}$$ of a recipe. The full recipe calls for $${3 {1\over4}}$$ cups of flour. How many cups of flour should Kendra use?

b.   Claire walked $${2{2\over5}}$$ miles. Jason walked $${{2\over3}}$$ as far as Claire. How many miles did Jason walk?

Guiding Questions

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References

Illustrative Mathematics Half of a Recipe

Half of a Recipe, accessed on April 25, 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.

PARCC Released Items Math Spring Operational 2015 Grade 5 End of Year Released ItemsQuestion #16

Math Spring Operational 2015 Grade 5 End of Year Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed Dec. 5, 2017, 3:47 p.m..

Problem 3

Solve. Show or explain your work.

a.   $${{2\over3} \times 4{1\over4}}$$

b.   $${3{2\over5} \times {1\over2}}$$

c.   $${{5\over4} \times 3{1\over3}}$$

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #1a. Before solving, would you have expected the product to be more or less than 1? Why? How can you use similar reasoning for #1c? 
  • Look at #4b. How is it possible for the product to be 1? 
  • Look at #5 and #6. What was similar about these problems? What was different about these problems?
  • Look at #7. How did you solve?

Target Task


Problem 1

Solve. Show or explain your work.

a.   $${{2\over3} \times 9{1\over6}}$$

b.   $${5{1\over2} \times {3\over4}}$$

Student Response

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Problem 2

Penelope buys a pumpkin that weighs $${6 {1\over4}}$$ kilograms. Penelope’s sister buys a pumpkin that weighs half as much. What is the weight of Penelope’s sister’s pumpkin?

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.

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 13

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Lesson 15

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 Expressions and Real-World Problems

Topic G: Line Plots

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