Curriculum  /  Math  /  5th Grade  /  Unit 5: Multiplication and Division of Fractions  /  Lesson 3

Multiplication and Division of Fractions

Lesson 3

Math

Unit 5

5th Grade

Lesson 3 of 24

Objective

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

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 word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers (MP.4).  
  2. Check the solution to a division problem with a fractional quotient using multiplication and/or repeated addition. 
  3. Explain how the fractional part of a mixed-number quotient is related to the remainder in the problem (MP.3).
  4. Determine which two whole numbers a mixed-number quotient is in between.

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).
  • As mentioned in Lesson 1, Students can use the group size unknown interpretation of division (also called partitive or sharing division) to explain that $$\frac{a}{b}=a\div b$$. Students will continue to see many group size unknown division problems to continue to develop this understanding, but they will also start to see some other division problem types to generalize this understanding.
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Anchor Tasks

25-30 minutes

Problem 1

32 students shared 6 pizzas equally. How much pizza will each student get? 

a.   Find the exact answer.

b.   Check your work.

Guiding Questions

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Student Response

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References

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

Grade 5 Mathematics > Module 4 > Topic B > Lesson 5 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

32 gallons of water is used to completely fill 6 fish tanks. If each tank holds the same amount of water, how many gallons will each tank hold?

a.   Find the exact answer. Write it as a fraction and as a mixed number.

b.   Determine which two whole numbers the answer is in between.

c.   Explain how the fractional part of the mixed number is related to the remainder in the problem.

d.   Check your work.

Guiding Questions

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Student Response

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References

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

Grade 5 Mathematics > Module 4 > Topic B > Lesson 4 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 3

Solve the following problems. Think about the main differences between each one. 

a.   A teacher has 21 batteries. Each calculator uses 4 batteries. How many calculators can the teacher fill with batteries?

b.   Four children can ride in a car. How many cars are needed to take 21 children to the museum?

c.   Ms. Cole bakes 21 cookies and wants to share them out fairly to 4 friends. How many cookies will each friend get?

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • How did you determine how many inches each piece of paper would be in #1? 
  • Look at #2. What was different about this problem compared to the previous one? How should the remainder have been interpreted in this problem versus the other ones? How can we make that distinction in general?
  • How did you determine which number was the dividend versus the divisor in each part of #3? 
  • In #4a, why do the quotient and remainder have different units? In other words, the 7 represents the number of glasses Jorge will fill and 1 represents the number of cups Jorge will have left. Why? 
  • What unit should Linda’s answer have in #4b?
  • Whose answer is correct in #4? Justify your reasoning. 
     

Target Task

5-10 minutes

Problem 1

Oxana builds a tower of 15 Jenga blocks stacked on top of each other. The tower is 9 inches tall. What is the height, in inches, of one Jenga block?

Student Response

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Problem 2

Mr. Keil is trying to split 22 cups of punch equally between 8 glasses. How many cups of punch should he put in each glass? Between what two whole numbers does your answer lie?

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 unit fraction by a whole number.

Lesson 4
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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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