Fraction Operations

Lesson 18

Objective

Multiply a whole number by a mixed number.

Common Core Standards

Core Standards

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  • 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

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  1. Multiply a mixed number by a whole number using a visual model, repeated addition, 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., $${{n \times {a\over b} }= { {n\times a} \over b}}$$

Tips for Teachers

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Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 1 (benefits from discussion) and Anchor Task 2 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.

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  • Student Handout Editor
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Anchor Tasks

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Problem 1

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

a.   $${2\times4}$$

b.   $${2\times{1\over3}}$$

c.   $${2\times4}{1\over3}$$

  1. What do you notice about #1? What do you wonder?

Guiding Questions

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Problem 2

Estimate the following products. Then solve.

a.   $${3\times5{1\over4}}$$

b.   $${4\times6{3\over5}}$$

c.   $${5\times9{7\over10}}$$

Guiding Questions

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Problem 3

Juliette decided to solve part (a) of Anchor Task #2 by doing the following:

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

Do you agree with Juliette’s strategy? Will it yield the same product?

Which strategy is more efficient, Juliette’s or the distributive property? What about for the other problems in Anchor Task #2? 

Guiding Questions

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Problem Set & Homework

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

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Solve. Show or explain your work.

1.   $${4 \times 5{3\over8}}$$

2.   $${3\times 4{3\over10}}$$

References

Mastery Response

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Additional Practice

Unit Practice

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