Multiplication and Division of Fractions

Lesson 9

Math

Unit 5

5th Grade

Lesson 9 of 24

Objective


Multiply a fraction by a fraction with subdivisions using tape diagrams and number lines.

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

  • 4.NF.B.4

Criteria for Success


  1. Multiply a fraction by a fraction in which further subdivision is needed (in simple cases) using tape diagrams and number lines. 
  2. Solve word problems that involve the multiplication of a fraction by a fraction in which further subdivision is needed (in simple cases) (MP.4). 
  3. Estimate the size of a product of two fractions in comparison to the size of its factors.

Tips for Teachers


Lesson Materials

  • Strips of paper (2 per student) — These should measure about 5.5" by 1"
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Anchor Tasks

25-30 minutes


Problem 1

a.   A large box of paper clips weighs $${{1\over5}}$$ kilogram. A small box of paper clips weighs $${{1\over2}}$$ as much as a large box of paper clips. What is the weight, in kilograms, of a small box of paperclips? 

b.   Valencia has $${{1\over3}}$$ hour until bedtime. She uses $${{3\over4}}$$ of that time to read a bedtime story. How much time, in hours, does Valencia spend reading a bedtime story?

c.   EXTENSION: How much time, in minutes, does Valencia spend reading a bedtime story?

Guiding Questions

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Student Response

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Problem 2

a.   Zack had $${{2\over3}}$$ of the lawn left to cut. After lunch, he cut $${{3\over4}}$$ of the grass he had left. How much of the whole lawn did Zack cut after lunch?

b.   Alisa had $${{5\over6}}$$ a liter of juice in a bottle. She drank $${{1\over2}}$$ of the juice that was in the bottle. How many liters of juice did she drink?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Drinking Juice

Drinking Juice, accessed on April 24, 2018, 1:36 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 Fishtank Learning, Inc.
John A. Van de Walle Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II)p. 243

Van de Walle, John A. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013.

Illustrative Mathematics Folding Strips of Paper

Folding Strips of Paper, accessed on April 24, 2018, 1:36 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 Fishtank Learning, Inc.

Problem 3

Solve. Show or explain your work.

a.   $${{1\over2}}$$ of $${{1\over4}}$$

b.   $${{2\over3}}$$ of $${{1\over3}}$$

c.   $${{3\over4} \times {2\over5}}$$

d.   $${{{1\over2}}} \times {3\over4}$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • Look at #1a and #1b. How can two different problems have the same solution?
  • Look at #2 and #3. Why was the problem less than its factor? 
  • How is the use of the number line in each part of #5 similar and different?

Target Task

5-10 minutes


Problem 1

Solve. Show or explain your work.

a.   $${{2\over3}}$$ of $${{1\over4}}$$

b.   $${{5\over6} \times {3\over4}}$$

Student Response

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Problem 2

Ladonna spent $$1\over4$$ of the time it took her to do her homework on her math homework and $$1\over2$$ of the rest of the time on her history homework. What fraction of the time Ladonna spent doing her homework did she spend on her history homework?

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

Multiply a fraction by a fraction with more complicated subdivisions using an area model.

Lesson 10
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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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