Curriculum  /  Math  /  5th Grade  /  Unit 5: Multiplication and Division of Fractions  /  Lesson 1

Multiplication and Division of Fractions

Lesson 1

Math

Unit 5

5th Grade

Lesson 1 of 24

Objective

Relate equal shares of objects to division expressions and visual representations of fractions.

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. Solve equal share problems where the divisor does not evenly divide the dividend (MP.4).
  2. Understand that division of whole numbers with a fractional quotient can be modeled in more than one way.  
  3. Connect situations, visual models, and expressions where a divisor does not evenly divide the dividend, and find the quotient. 

Tips for Teachers

  • Students can use the group size unknown interpretation of division (also called partitive or sharing division) to explain that $$\frac{a}{b} = a \div b$$. Equal group with group size unknown division involves problems where students are given the total number of objects to be partitioned into a certain number of equal groups, but the group size is unknown. Thus, today’s contextual problems are strictly group size unknown division problems to help them develop an understand of fractions as division. They also only encounter cases with small values that can be easily represented with visual models. 

Lesson Materials

  • Template: Equal Shares (1 per pair of students) — This material should be cut into pieces before the lesson.
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Anchor Tasks

25-30 minutes

Problem 1

__________ graham crackers are shared equally by __________ people.

a.   Choose numbers to fill in the blanks. You can only use each number once: 2, 3, 5.

b.   Represent the situation with a diagram or drawing.

c.   Explain or show how you know that each person will get the same amount of graham cracker.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic B > Lesson 2 — Concept Development

Grade 5 Mathematics > Module 4 > Topic B > Lesson 2 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.
Illustrative Mathematics Grade 5 > Unit 2 > Lesson 1 > Activity 1

Grade 5 > Unit 2 > Lesson 1 > Activity 1, accessed on April 29, 2022, 11:14 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

Han’s work shows how 3 people could equally share 2 graham crackers.

a.   How do you know that each person gets about the same amount of graham cracker? Explain or show your thinking. Organize it so it can be followed by others.

b.   Draw a diagram to show a different way that 3 people could share 2 graham crackers so each person got about the same amount of graham cracker.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 5 > Unit 2 > Lesson 1 > Activity 2 (The Same Amount)

Grade 5 > Unit 2 > Lesson 1 > Activity 2 (The Same Amount), accessed on April 29, 2022, 10:50 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 3

a.   Using the set of cards (cut out from Template: Equal Shares), match each representation with a situation and expression. Some situations and expressions will have more than one matching representation.

b.   Choose one set of matched cards.

  1. Show or explain how the diagram(s) and expression represent the number of sandwiches being shared.
  2. Show or explain how the diagram(s) and expression represent the number of people sharing the sandwiches.
  3. How much sandwich does each person get in the situation?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 5 > Unit 2 > Lesson 2 > Activity 2 (Card Sort: Sandwich Match)

Grade 5 > Unit 2 > Lesson 2 > Activity 2, accessed on Nov. 14, 2022, 2:29 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

  • Look at #1 and #3. What was similar about these problems? What was different? How did you decide what quantity was being divided? 
  • Share the situation you wrote for #2. What equation did you write to represent it? 
  • Look at #4. Why are both Carly and Gina correct?
  • Would you rather share 2 pizzas with 2 friends or 3 pizzas with 3 friends? Why? 

Target Task

5-10 minutes

A group of 4 friends are sharing 5 brownies. If the brownies are divided equally among the friends, how many brownies should each friend get?

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

Write division expressions that represent fractions and vice versa.

Lesson 2
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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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