Curriculum  /  Math  /  4th Grade  /  Unit 5: Fraction Operations  /  Lesson 16

Fraction Operations

Lesson 16

Math

Unit 5

4th Grade

Lesson 16 of 21

Objective

Multiply a whole number by a fraction.

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 fraction using a visual model. 
  2. Generate a general method for multiplying a whole number by a unit fraction, i.e., $$n \times \frac{1}{b}=\frac{n}{b}$$ (MP.8). 
  3. Generate a general method for multiplying a whole number by a non-unit fraction, i.e., $${n\times{{a\over b}}={{n\times a}\over b}}$$ (MP.8).
  4. Understand a multiple of $${a\over b}$$ as a multiple of $${1\over b}$$.

Tips for Teachers

  • You might decide to stretch this lesson over two days. One way you could do this would be to have Anchor Tasks 1 and 2 on the first day and Anchor Task 3 on the second day. Divvy up Problem Set and Extra Practice Problems accordingly.
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Anchor Tasks

25-30 minutes

Problem 1

a.   Here are two tables with expressions. Find the value of each expression. Use a model if it's helpful. Leave the last two rows of each table blank for now. 

Set A Set B
expression value
$$1\times\frac{1}{8}$$  
$$2\times\frac{1}{8}$$  
$$3\times\frac{1}{8}$$  
$$4\times\frac{1}{8}$$  
$$5\times\frac{1}{8}$$  
$$6\times\frac{1}{8}$$  
   
   
expression value
$$2\times \frac{1}{3}$$  
$$2\times \frac{1}{4}$$  
$$2\times \frac{1}{5}$$  
$$2\times \frac{1}{6}$$  
$$2\times \frac{1}{7}$$  
$$2\times \frac{1}{8}$$  
   
   

b.   Study your completed tables. What patterns do you see in how the expressions and values are related?

c.   In the last two rows of the table of Set A, write $$\frac{11}{8}$$ and $$\frac{13}{8}$$ in the "value" column. Write the expressions with that value.

d.   In the last two rows of the table of Set B, write $$\frac{2}{12}$$ and $$\frac{2}{15}$$ in the "value" column. Write the expressions with that value.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 4 Unit 3 Lesson 3 Activity 1

Grade 4 Unit 3 Lesson 3 Activity 1, accessed on Nov. 11, 2022, 4:07 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.

Problem 2

a.   

  1. Draw a model to represent $$\frac{2}{3}$$.
  2. Show how you would use or adjust the model above to represent $$4\times \frac{2}{3}$$.
  3. Based on your model in Part (ii), what is the value of $$4\times \frac{2}{3}$$?

b.   Find the value of each expression below. Draw a model if it would be helpful.

  1. $$2\times \frac{1}{5}$$
  2. $$2\times \frac{3}{5}$$
  3. $$2\times \frac{4}{5}$$
  4. $$6\times \frac{4}{5}$$

c.   Willa said that to multiply a whole number by a fraction, she’d multiply the whole number and the numerator and use the same denominator. Do you agree with Willa? Explain your reasoning.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 4 Unit 3 Lesson 4 Activity 2

Grade 4 Unit 3 Lesson 4 Activity 2, accessed on Nov. 11, 2022, 4:14 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 3

a.   Find the number that makes each equation true. Draw a model if it is helpful.

$$\frac{12}{5} = 12\space \times $$ _____

 $$\frac{12}{5} = 3\space \times $$ _____

 $$\frac{12}{5} = 6\space \times $$ _____

 $$\frac{12}{5} = 2\space \times $$ _____

 $$\frac{12}{5} = 4\space \times $$ _____

 $$\frac{12}{5} = 1\space \times $$ _____

b.   Here are two sets of numbers:

Set A Set B
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 $$\frac17, \frac27,\frac37,\frac47,\frac57,\frac67,\frac77$$
  1. Choose a number from Set A and a number from Set B to complete this equation and make it true:

$$\frac67 =$$ _____ $$\times$$ _____

  1. Choose a different number from Set A and a number from Set B to complete the equation to make it true:

$$\frac67 =$$ _____ $$\times$$ _____

c.   Explain or show how you know that the two equations you wrote are both true.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 4 Unit 3 Lesson 5 Activity 1

Grade 4 Unit 3 Lesson 5 Activity 1, accessed on March 25, 2022, 9:32 a.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.

Problem Set

15-20 minutes

Discussion of Problem Set

  • What did Angie do to solve? Will her strategy work all the time? 
  • How did you record your solutions to #6? 
  • For which problems in #6 would repeated addition be a particularly inefficient strategy? Why? 
  • Look at your answers for #6(c) and #6(d). Convert each answer to a mixed number. What do you notice? How are the expressions in #6(c) and #6(d) similar? 
  • How did Goldie solve in #7? How is this similar to showing $${{3\over4}+{3\over4}+{3\over4}}$$?

Target Task

5-10 minutes

Problem 1

Which of the following is equivalent to $${7\times {3\over8}}$$? There are three correct answers.

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Student Response

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Problem 2

Explain how to find $${3 \times {4\over5}}$$ using a number line. Find the product.

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 whole number by a mixed number.

Lesson 17
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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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