Curriculum  /  Math  /  5th Grade  /  Unit 5: Multiplication and Division of Fractions  /  Lesson 2

Multiplication and Division of Fractions

Lesson 2

Math

Unit 5

5th Grade

Lesson 2 of 24

Objective

Write division expressions that represent fractions and vice versa.

Common Core Standards

Core Standards

  • 5.NF.B.3 — Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Foundational Standards

  • 4.NF.B.3
  • 4.NF.B.4
  • 3.OA.A.1
  • 3.OA.A.2
  • 3.OA.B.6

Criteria for Success

  1. Look for and express regularity in repeated reasoning to see that $$a\div b = \frac{a}{b}$$ (MP.8). 
  2. Write a solution to a division expression with a non-whole number quotient as a fraction or mixed number, if applicable. 
  3. Check the solution to a division problem with a fractional quotient using multiplication and/or repeated addition.
  4. (Optional) Connect simplifying fractions to the idea of simplifying a division calculation (e.g., $$40 \div 6 = \frac {40}{6} = \frac{20}{3} = 20 \div 3$$).

Tips for Teachers

In Grade 5, students connect fractions with division, understanding numerical instances of $$\frac{a}{b} = a \div b$$ for whole numbers $$a$$ and $$b$$, with $$b$$ not equal to zero (MP.8)” (NF Progression, p. 6). Thus, in this lesson, students look for and express regularity in repeated reasoning through multiple examples that help them see that $$a \div b = \frac{a}{b}$$. 

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Anchor Tasks

25-30 minutes

Problem 1

a.   Jada’s family made sandwiches to share at a family celebration. Complete the table to show how much sandwich each person gets.

Sandwiches Being Shared Number of People Sharing Sandwiches Division Expression Amount Each Person Gets
1 2    
1 3    
1 4    
1      

b.   Choose one row from the table and represent your thinking with a diagram.

c.   What do you notice in the table? What do you wonder?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 5 > Unit 2 > Lesson 2 > Activity 1

Grade 5 > Unit 2 > Lesson 2 > Activity 1, accessed on April 29, 2022, 11:52 a.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 2

a.   A group of athletes are sharing some number of liters of water at practice. Complete the table to show how much water each athlete gets.

Number of Liters of Water Being Shared

Number of People Sharing Water

Division Expression

Amount Each Person Gets

 Check
4 5      
    $$3 \div 2$$    
    $$9 \div 12$$    
      $$\frac7{10}$$  
      $$2\frac14$$  

b.   What do you notice in the table? What do you wonder?

Guiding Questions

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Student Response

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Problem 3

a.   Fill in the blanks to match the rules in the table.

 

Each person gets ____ pound(s) of blueberries.
 

more than 1

exactly 1

less than 1

 exactly $$\frac{1}{2}$$

_____ people share 7 pounds of blueberries

✔ 

      

_____ people share _____ pounds of blueberries

  

✔

    

_____ people share _____ pounds of blueberries

    

✔

  

_____ people share _____ pounds of blueberries

      

✔

b.   How many pounds of blueberries did each person get when they got more than 1 pound?

c.   How many pounds of blueberries did each person get when they got less than 1 pound?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 5 > Unit 2 > Lesson 5 > Activity 1 (Relate Pounds to People)

Grade 5 > Unit 2 > Lesson 5 > Activity 1, accessed on Nov. 14, 2022, 3:32 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 Set

15-20 minutes

Discussion of Problem Set

  • How did you decide which values of c and d were correct in #3?
  • #4f was hard since the fraction was written as a mixed number. How did you determine what numbers were being divided? 
  • Which equations in #6 were correct? Incorrect? How do you know?
  • How did you determine what number Lemuel was dividing by 15 in #7? 

Target Task

5-10 minutes

a.    Which expression is equivalent to $$\frac34$$?

  1. a.   $$3 \times 4$$

  2. b.   $$3 +4$$

  3. c.   $$3 \div 4$$

  4. d.   $$3-4$$

b.   Explain how you can use multiplication to prove that your answer from Part A is correct.

Student Response

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References

Smarter Balanced Assessment Consortium SBAC Item #3338

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 division problems when the quotient is a fraction or mixed number, including cases with larger values.

Lesson 3
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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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