Multiplication and Division of Fractions

Lesson 7

Math

Unit 5

5th Grade

Lesson 7 of 24

Objective


Solve real-world problems involving multiplication of fractions and whole numbers and create real-world contexts for expressions involving multiplication of fractions and whole numbers.

Common Core Standards


Core Standards

  • 5.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 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.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.D.8
  • 4.OA.A.1
  • 4.OA.A.2
  • 4.OA.A.3

Criteria for Success


  1. Understand when a problem calls for the use of multiplication and when other operations are called for in a problem involving a fraction and a whole number (MP.1, MP.4). 
  2. Write a story context to match a given expression involving the multiplication of a fraction and a whole number (MP.2). 
  3. Write an expression to match a story context involving the multiplication of a fraction and a whole number (MP.2). 
  4. Solve one-, two-, and multi-step problems involving the multiplication of a fraction and a whole number (MP.4).

Tips for Teachers


This lesson connects the work of solving real-world problems involving multiplication of fractions and mixed numbers (5.NF.6) with writing and interpreting numerical expressions (5.OA.A), connecting content across domains.

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Anchor Tasks

25-30 minutes


Problem 1

Some of the problems below can be solved by multiplying $$\tfrac{3}{5}\times15$$, while others need a different operation. For each one, explain whether or not it can be solved by multiplying these two numbers. If they cannot be solved by multiplying, tell what operation is appropriate. In all cases, solve the problem (if possible) and include appropriate units in the answer.

a.   There are 15 people at a party. $$\tfrac{3}{5}$$ of them are boys. How many people at the party are boys?

b.   Wesley ran 15 miles on Monday and $$\tfrac{3}{5}$$ mile on Tuesday. How many miles did Wesley run?

c.   If each person at a party eats $$\tfrac{3}{5}$$ of a pound of roast beef and there are 15 people at the party, how many pounds of roast beef are needed?

d.   Nathaniel has 15 cups of soup split into 5 equal-sized portions. He’ll serve three of the portions for dinner tonight. What is the total amount of soup, in cups, that Nathaniel will serve tonight?

e.   15 students in the fifth grade want to play soccer. $$\tfrac{3}{5}$$ of the students in fifth grade want to play basketball. How many students want to play either soccer or basketball?

f.   Helena is carpeting a long corridor. It is $$\tfrac{3}{5}$$ yards wide and 15 yards long. How much carpeting, in square yards, does Helena need?

g.   Lisbeth has $$\tfrac{3}{5}$$ of a pound of chocolate that she wants to share evenly with 15 people. How much chocolate will everyone get?

h.   Dawa has 15 pencils in her pencil case. Theo has $$\tfrac{3}{5}$$ as many pencils in his pencil case as Dawa does. How many pencils does Theo have?

i.   Tiffany has $15. She spends $$\tfrac{3}{5}$$ of her money on a teddy bear. How much money does she have left?

Guiding Questions

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Student Response

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References

Illustrative Mathematics To Multiply or Not to Multiply

To Multiply or Not to Multiply, accessed on April 24, 2018, 1:06 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 2

a.   Write a story context that can be solved by multiplying $$8\times \frac{3}{4}$$.

b.   Write a story context that can be solved by multiplying $${{2\over3} \times 4}$$.

Guiding Questions

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Student Response

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References

Institute for Mathematics and Education Progressions for the Common Core State Standards in Mathematics (Numbers and Operations - Fractions, 3-5)Page 13

Progressions for the Common Core State Standards in Mathematics (Numbers and Operations - Fractions, 3-5), by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents. All contents copyrighted. All rights reserved. Accessed April 16, 2018, 11:23 a.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.

Modified by Fishtank Learning, Inc.

Problem 3

Brit is buying a cake and a pie for an upcoming birthday party. The cake costs $32 and the pie costs $$\frac58$$ as much as the cake.

a.   Write an expression that represents the total cost of the cake and pie. 

b.   Find the total cost of the cake and pie.

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • Look at #1. I don’t think any of these options work because I think the expression that represents the situation is $$120\div5$$. Do you agree or disagree with me? Explain. 
  • Look at #4. How did you solve? 
  • Look at #5. How did you solve? 
  • Look at #6. I wrote the following story problem: “There are 9 students in a class. $$\frac{3}{4}$$ of them are girls. How many girls are in the class?” Does my story make sense? Why or why not? 
  • Look at #7. How did you solve? 

Target Task

5-10 minutes


In a bakery, $$1\over4$$ of the cookies for sale are gingersnaps and $$2\over3$$ are chocolate chip. There are 24 cookies for sale. How many cookies are neither gingersnaps nor chocolate chip?

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 fraction by a fraction without subdivisions using tape diagrams and number lines.

Lesson 8
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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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