Curriculum  /  Math  /  5th Grade  /  Unit 5: Multiplication and Division of Fractions  /  Lesson 22

Multiplication and Division of Fractions

Lesson 22

Math

Unit 5

5th Grade

Lesson 22 of 24

Objective

Solve real-world problems involving multiplication and division with 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?
  • 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.
  • 5.NF.B.7 — Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

Criteria for Success

  1. Make sense of a three-act task and persevere in solving it (MP.1). 
  2. Solve multi-step word problems involving multiplication and division of fractions (including interpreting a fraction as division; multiplying fractions, including mixed numbers; and division of a unit fraction by a whole number or vice versa) (MP.4). 
  3. Assess the reasonableness of one’s answer by reasoning about the size of the product or quotient (e.g., multiplying a number by $$\frac12$$ should result in a product smaller than the other factor), by using estimation to round fractional values to whole numbers (in select cases, namely with mixed-number multiplication), and by checking one’s work using inverse operations (in select cases, where students are able to perform the inverse operation) (MP.1, MP.2).
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Anchor Tasks

25-30 minutes

Problem 1

Act 1: Look at the following recipe - 

What do you notice? What do you wonder? 

Guiding Questions

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Student Response

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Problem 2

Act 2: Use the following information to determine how many batches of cake can be made, how many servings can be made, and how much of each ingredient is needed to make that much cake.

  • This is how many eggs there are:

  • This is how much oil there is:

  • There are 4 boxes of cake mix.
  • Water will come from the tap.
  • Each box of cake makes 12 servings.

Guiding Questions

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Student Response

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Problem 3

Act 3: There is enough of each ingredient to make $$2\frac{2}{3}$$ boxes, which would produce 32 servings of cake. To make $$2\frac23$$ boxes, you need $$2\frac23$$ cups of water, $$\frac89$$ cups of vegetable oil, and 8 eggs. 

Was your answer reasonable? Why or why not?

Guiding Questions

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Student Response

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Problem 4

Act 4 (the sequel): 

Keaton wants to make enough cake so that every student in his fifth grade could have some. There are 100 students in fifth grade. How much more of each ingredient above would Keaton need?

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • For any problem, did you draw a tape diagram to help solve the problems? What does it look like?
  • For #1 and #2, there are different ways to solve the problems. Share and compare your strategy with a partner. 
  • How did you solve #3a and b? What operations did you use to solve? When did you know which operation to use? 
  • Compare and contrast #5 and #6. 
  • How did you solve #7? How did you know which operation to use when? 

Target Task

5-10 minutes

Bryn made 12 necklaces. She wants to make $$\frac14$$ as many bracelets as necklaces. She has $$\frac12$$ yard of string to make all of the bracelets. How much string, in yards, can Bryan use for each bracelet? 

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.

Lesson Map

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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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