Multiplication and Division of Fractions

Lesson 8

Math

Unit 5

5th Grade

Lesson 8 of 24

Objective


Multiply a fraction by a fraction without 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 not needed using tape diagrams and number lines (see Tips for Teachers below).  
  2. Solve word problems that involve the multiplication of a fraction by a fraction in which further subdivision is not needed (MP.4). 
  3. Estimate the size of a product of two fractions in comparison to the size of its factors. 
  4. Understand why a fraction less than 1 times a fraction less than 1 results in a fraction less than either factor (MP.2).

Tips for Teachers


This lesson exclusively looks at fraction multiplication problems in which the units or fractional parts do not need to be subdivided or partitioned further. For example, “students who solve [the problem $$\frac13$$ of $$\frac34$$]  with a picture or using a number line do not need to subdivide the unit fractions that comprise 34  to find $$\frac13$$ of $$\frac34$$ since it is naturally composed of 3 pieces” (Illustrative Mathematics).

Lesson Materials

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

25-30 minutes


Problem 1

The distance between Rosa’s house and her school is $${{3\over4}}$$ mile. She ran $${{1\over3}}$$ of the way to school. How many miles did she run?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Running to School

Running to School, accessed on Sept. 28, 2017, 2:09 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.

Problem 2

a.   You have $${{4\over5}}$$ of a loaf of bread. If you use $${{3\over4}}$$ of the bread that is left of the loaf to make sandwiches, how much of a whole loaf did you use?

b.   $${{6\over10}}$$ of the first-grade students are girls. $${{2\over3}}$$ of the first-grade girls have brown eyes. What fraction of first-grade students are girls with brown eyes?

Guiding Questions

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Student Response

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References

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.

Modified by Fishtank Learning, Inc.

Problem 3

Solve. Show or explain your work.

a.   $${{{{1\over2}}}}$$ of $${{2\over3}}$$

b.   $${{{{1\over2}}}}$$ of $${{4\over9}}$$

c.   $${{3\over5}}$$ $$\times$$ $${{5\over8}}$$

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. What is the same about these two problems? What is different? Why is that?
  • Look at #1a and #1c. What is the same about these two problems? What is different? Why is that?
  • Look at #3. What was Sam’s error? 
  • Look at #4a. Why is taking 3 fourths of 4 fourths equal to 3 fourths? Is that true for all numbers? 3 fourths of 8 eighths? 3 fourths of 9 twelfths?
  • Look at #4d. Could you have simplified either fraction before computing? Would you get the same answer?

Target Task

5-10 minutes


Problem 1

Solve. Show or explain your work.

$${{1\over3}}$$ of $${{3\over8}}$$

Student Response

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Problem 2

In a park, $$5\over6$$ of the space is filled with sports fields. If soccer fields account for $$2\over5$$ of the space for sports fields, what fraction of the park is soccer fields? 

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 subdivisions using tape diagrams and number lines.

Lesson 9
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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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