Fraction Operations

Lesson 17

Math

Unit 5

4th Grade

Lesson 17 of 21

Objective


Multiply a whole number by a mixed number.

Common Core Standards


Core Standards

  • 4.NF.B.4.B — Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

Criteria for Success


  1. Multiply a whole number by a mixed number using a visual model, the distributive property, or converting the mixed number to a fraction greater than 1 (i.e., an "improper" fraction) and using the general method, i.e., $${{n \times {a\over b} }= { {n\times a} \over b}}$$
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Anchor Tasks


Problem 1

a.   Draw a model to represent each of the following. Then find the product.

  1. $${2\times4}$$
  2. $${2\times{1\over3}}$$
  3. $${2\times4}{1\over3}$$

b.   What do you notice about Part (a)? What do you wonder?

Guiding Questions

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Problem 2

a.   Here is Kellen’s strategy for finding the value of $$3\times2\tfrac14$$: “I know I can write $$2\tfrac14$$ as $$2+\tfrac14$$, so I can compute $$3\times2\tfrac14=(3\times2) + \left(3\times\tfrac14\right)$$. Since $$3\times2=6$$  and $$3\times\tfrac14=\tfrac34$$, then $$3\times2\tfrac14=6+\tfrac34=6\tfrac34$$.” Does Kellen’s strategy for finding the product of a whole number and a mixed number work? Show or explain your thinking.

b.    Estimate the following products. Then solve.

  1. $${3\times1{5\over8}}$$
  2. $${4\times6{3\over5}}$$
  3. $${5\times9{7\over10}}$$

Guiding Questions

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Problem 3

Juliette decided to solve $$3\times2\frac14$$ in a different way from Kellen’s strategy:

$${3\times2{1\over4} =3\times\left(2+\frac{1}{4}\right)=3\times{9\over4}}$$

a.   Does Juliette’s strategy work? Will it yield the same product as Kellen's strategy?

b.   Solve the computations from Part (b) of Anchor Task 2 using this method. Are your products the same regardless of which method you use?

c.   Which method do you prefer? Why?   

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • What were the two ways you solved #3? Which one was more efficient? 
  • How would you correct Nick’s work in #4? 
  • Which expressions were equivalent in #5? Which were not? How do you know? 
  • What did the student do incorrectly in #7? What is the correct product? 
  • Did anyone attempt #8? What did you get? 

Target Task


Solve. Show or explain your work.

a.   $${4 \times 3{7\over8}}$$

b.   $${2\times 6{2\over5}}$$

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 16

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Lesson 18

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Building, Adding, and Subtracting Fractions Less Than or Equal to 1

Topic B: Building, Adding, and Subtracting Fractions Less Than 2

Topic C: Building, Adding, and Subtracting Fractions Greater Than or Equal to 2

Topic D: Multiplication of Fractions

Topic E: Line Plots

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