Multiplication and Division of Fractions

Lesson 5

Math

Unit 5

5th Grade

Lesson 5 of 25

Objective


Multiply a fraction by a whole number where the product is a whole number or a fraction.

Common Core Standards


Core Standards

  • 5.NF.B.4.A — Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
  • 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.

Foundational Standards

  • 4.NF.B.4

Criteria for Success


  1. Solve contextual problems involving finding some fractional part of a quantity in which the answer is a whole number or a fraction (MP.4).
  2. Relate the concept of finding a fractional group of a set to finding any number of groups of a set, and connect this to multiplication (MP.2). 
  3. Interpret $$\frac{a}{b} \times q$$ as a parts of $$a$$ partition of $$q$$ into $$b$$ equal parts. 
  4. Find the value of expressions in the form $$\frac{a}{b} \times q$$.
  5. Understand that finding the unit fraction of a whole number is the same as dividing the whole number by the denominator of the unit fraction, and use that to find any fraction of a whole number.  
     
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Anchor Tasks


Problem 1

a.   Rosie has 15 yards of fabric. She uses $${{2\over3 }}$$ of it to make a dress. How much fabric, in yards, does she use to make the dress?

b.   Rosie also bought 11 feet of ribbon. She uses $${{1\over2}}$$ of it to make a bow for her dress. How much ribbon, in feet, does she use to make the bow?

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic C > Lesson 7Concept Development

Grade 5 Mathematics > Module 4 > Topic C > Lesson 7 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

a.   How would you write “5 groups of 12” as a mathematical expression? How does that inform how you would write “$${{1\over4}}$$ group of 12” as a mathematical expression?

b.   Use your observation from Part (a) to solve the following:

  1. $${1\over5} \times 20$$
  2. $${{3\over8}\times 16}$$
  3. $${1\over6} \times19$$
  4. $${{3\over4} \times 26}$$

Guiding Questions

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Problem 3

a.   Frederick says $$\frac16 \times 18 = 18 \div 6$$. Do you agree or disagree? Justify your thinking.

b.   How would you modify Frederick’s equation to represent $$\frac56 \times 18$$?

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #1(a) and 1(b). What do you notice about your solutions?
  • Look at #1(c) and 1(d). What do you notice about your solutions?
  • Look at #1(e) and 1(f). We know that 4 fifths and 1 seventh aren’t equal, so how did we get the same answer? 
  • Look at #3(b). How did you solve? How many degrees is a straight angle? (This is connected to Grade 4 content of 4.MD.5—7.) 
  • Look at #3(c). What made this problem a bit challenging? How did you solve? Was there more than one correct way to solve? (Students could have found the fraction of people on the field trip that were children and then multiplied by 48, or they could have found a fourth of 48 and then subtracted that product from 48.) 
  • Look at #3(d). What made this problem even more challenging than #3(c)? How did you solve? Was there more than one correct way to solve?
  • Look at #4. Why does Alicia’s thinking make sense?

Target Task


Problem 1

Solve. Show or explain your work.

a.   $${{3\over4} \times 32}$$

b.   $${{2\over5} \times 8}$$

Student Response

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Problem 2

On Monday, Mrs. Johnson went on a walk that was $$4$$ miles long. On Tuesday, she goes on a walk that is $${{2\over3}}$$ as long as her walk on Monday. How long was Mrs. Johnson’s walk on Tuesday?

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.

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 4

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Lesson 6

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 Expressions and Real-World Problems

Topic G: Line Plots

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