Multiplication and Division of Fractions

Lesson 21

Math

Unit 5

5th Grade

Lesson 21 of 24

Objective


Solve real-world problems involving division with fractions and create real-world contexts for expressions involving division with fractions.

Common Core Standards


Core Standards

  • 5.NF.B.7.C — Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
  • 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.B.6

Criteria for Success


  1. Understand when a problem calls for the use of division and when other operations are called for in a problem involving a unit fraction and a whole number (MP.1, MP.4).
  2. Solve group size unknown division word problems that involve the division of a whole number by a unit fraction (MP.4). 
  3. Write a story context to match a given expression involving the division of a unit fraction and a whole number. 
  4. Write an expression to match a story context involving the division of a unit fraction and a whole number. 
  5. Solve one-, two-, and multi-step problems involving the division of a unit fraction and a whole number (MP.4).

Tips for Teachers


  • There are two interpretations for division: (a) equal group with group size unknown division (also called partitive or sharing division), and (b) equal group with number of groups unknown division (also called quotitive, measurement, or equal-sharing division). In Grade 5, students apply and extend this understanding of the two types of division with whole numbers to divide unit fractions by whole numbers and whole numbers by unit fractions. To develop an understanding of the division of a unit fraction by a whole number, they use unknown group size division, such as in the problem “$$\frac12$$ meter of cloth is cut into three equal pieces. How long is each piece of fabric?”. Inversely, to develop an understanding of the division of a unit fraction by a whole number, they use unknown number of groups division, such as in the problem, “Three meters of cloth are cut into $$\frac12$$ meter strips. How many strips are cut?” That way, as Bill McCallum notes, “students can build on their understanding of whole-number division without having to grapple with fractional groups, so long as they understand both of these interpretations of division” (“Fraction division part 2: Two interpretations of division”, Mathematical Musings). Thus, students are exclusively given group size unknown division problems in Lesson 19 and number of groups unknown division problems in Lesson 20 to help them build a strong conceptual understanding of fraction division before seeing other types of division problems in Lesson 21.
  • Students’ work with fraction division only spans three lessons, Lessons 19–21. You may choose to give students much more time with each of these concepts, perhaps spanning each lesson over two days. If you decide to do so, here are some recommendations for where to source additional practice problems that align to this lesson:

Lesson Materials

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Anchor Tasks

25-30 minutes


Problem 1

Jenny buys 2 feet of string. If this is one-third the amount she needs to make a bracelet, how many feet will she need?

a.   Draw a diagram to represent the problem.

b.   Write an expression to represent the problem.

c.   Find how many feet of string Jenny needs.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic G > Lesson 25Concept Development

Grade 5 Mathematics > Module 4 > Topic G > Lesson 25 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

a.   Match each division expression (cut out from Template: Fraction Division Sort) with a situation (cut out from Template: Fraction Division Sort). Some expressions do not have a matching situation.

b.   Answer each question. Be prepared to share your reasoning.

Guiding Questions

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Student Response

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References

Open Up Resources Grade 5 Unit 3 Lesson 15Activity 1

Grade 5 Unit 3 Lesson 15 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Nov. 19, 2019, 9:44 a.m..

Modified by Fishtank Learning, Inc.

Problem 3

a.   Write a story context that can be solved using the expression $${2\div{1\over4}}$$.

b.   Write a story context that can be solved using the expression $${{1\over3}\div4}$$.

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • What did you notice about #2 and #3? What are the similarities and differences? What did you notice about the division expressions and the solutions? 
  • What did you notice about #4 and #5? What are the similarities and differences? What did you notice about the division expressions and the solutions? 
  • How did you solve for #7? What strategy did you use?

Target Task

5-10 minutes


Problem 1

Anej has $$1\over2$$ of his birthday cake leftover. He wants to share it equally with his 3 friends. What fraction of the original cake should Anej and his 3 friends get? 

Student Response

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Problem 2

Norma has 8 red colored pencils. This is $$1\over3$$ of the total colored pencils she has. How many colored pencils does Norma have altogether?

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

Solve real-world problems involving multiplication and division with fractions.

Lesson 22
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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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