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Unit 4

An Algorithm Using Partial Quotients

Lesson 12

Wrapping Up Multiplication and Division with Multi-Digit Numbers

Expressions and Equations

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Let's make sense of an algorithm using partial quotients.

Unit 4 ● Lesson 12

Learning

Goal

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Incomplete Solution

Unit 4 ● Lesson 12 ● Warm-up

What do you notice? What do you wonder?

This is an algorithm used to divide whole numbers. The algorithm is not complete. What might you do next?

Notice and Wonder

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Elena’s Work

Unit 4 ● Lesson 12 ● Activity 1

Find the value of 448 ÷ 16. Show your thinking. Organize it so it can be followed by others.

Discuss how you found the value of 448 ÷ 16 with your partner.

This is Elena’s work. Describe the steps Elena took to find the value of 448 ÷ 16.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Elena’s Work

Unit 4 ● Lesson 12 ● Activity 1

Share your description of how Elena found the value of 448 ÷ 16 with your partner.
Take turns being the speaker and the listener.

If you are the speaker, share your ideas and writing so far.
If you are the listener, ask questions and give feedback to help your partner improve their work.

Revise your initial draft based on the feedback you got from your partners.
How was Elena’s strategy the same as and different from your strategy?
How does the method Elena used help her organize her work?

Activity Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Complete the Solution

Unit 4 ● Lesson 12 ● Activity 2

Use Elena’s strategy to complete the following problems:

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Complete the Solution

Unit 4 ● Lesson 12 ● Activity 2

How did you complete the steps to find the value of 492 ÷ 12?
How did you find the value of 364 ÷ 14?
Do you have any questions about your classmates’ work?

Activity Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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An Algorithm Using Partial Quotients

Unit 4 ● Lesson 12

364 ÷ 14

What was the first multiple of 14 that you subtracted from 364? How did you choose that multiple?
Why are multiples of 10 good choices for an algorithm using partial products?

Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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What’s Next?

Unit 4 ● Lesson 12

Han started finding the value of a quotient.

Write the division expression that represents the quotient Han is finding.
Complete the algorithm that Han started.

Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.