Multiplication and Division of Fractions

Lesson 4

Math

Unit 5

5th Grade

Lesson 4 of 25

Objective


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

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 set in which the answer is a whole number (MP.4).
  2. Interpret $${a\over b}$$ of $$q$$ as $$a$$ parts of a partition of $$q$$ into $$b$$ equal parts. 
  3. Find the value of expressions in the form $${a\over b}$$ of $$q$$ in which the answer is a whole number using a set model.

Tips for Teachers


Lesson Materials

  • Two-sided counters (12 per student or small group)
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Anchor Tasks


Problem 1

a.   Kyle has 6 Skittles. $${{1\over3}}$$ of them are red. How many of Kyle's Skittles are red?

b.   Samantha also has 6 Skittles. $${{2\over3}}$$ of them are red. How many of Samantha’s Skittles are red?

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic C > Lesson 6Concept Development

Grade 5 Mathematics > Module 4 > Topic C > Lesson 6 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.   Find the value of each of the following.

i.   $$\frac{1}{3}$$ of 9

ii.   $$\frac{2}{3}$$ of 9

iii.   $$\frac{1}{5}$$ of 10

iv.   $$\frac{4}{5}$$ of 10

v.   $$\frac{1}{4}$$ of 12

vi.   $$\frac{2}{4}$$ of 12

b.   What do you notice about the solutions to the computations in the leftmost column of the table? What do you wonder?

c.   What do you notice about the solutions in each row of the table? What do you wonder?

Guiding Questions

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Problem 3

a.   Mrs. Pham has 8 apples. She wants to give $${{3\over4}}$$ of the apples to her students. How many apples will her students get?

b.   In a class of 24 students, $${{5\over6}}$$ of them are boys. How many boys are in the class?

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic C > Lesson 6Concept Development

Grade 5 Mathematics > Module 4 > Topic C > Lesson 6 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 Set


Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

  • Look at #1(a). How did you find $${{{{3\over3}}}}$$ of $$9$$? Why is $${{{{3\over3}}}}$$ of $$9$$ just $$9$$ itself? 
  • Look at #1(c). How did you use $${{1\over5}}$$ of $${{20}}$$ to find $${{4\over5}}$$ of $${{20}}$$?
  • Look at #4. How did you figure out how many students brought their lunches? How would you figure out how many students didn’t bring their lunches? 

Target Task


Problem 1

Find the value of each of the following.

a.   $${{1\over4}}$$ of $${{12}}$$

b.   $${{3\over4}}$$ of $${{12}}$$

Student Response

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Problem 2

There are 21 students in the chess club. $$2\over3$$ of them are girls. How many girls are in the chess club?

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 3

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Lesson 5

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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