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Practice an Algorithm Using Partial Quotients

Grade 5: Unit 4: Lesson 14

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Lesson Purpose

The purpose of this lesson is for students to practice using an algorithm using partial quotients.

Lesson Narrative

In previous lessons, students learned to use an algorithm using partial quotients to evaluate division expressions involving two-digit divisors. In this lesson, students extend their work in two ways. First, using partial quotients requires care in finding multiples and subtracting those multiples or partial quotients. Students identify and correct errors in multiplication and subtraction. Then they find quotients of larger numbers. Here the multiplication and subtraction demands increase and students see the first cases where they can subtract 100 or a multiple of 100 of the divisor from the dividend.

Learning Goals

•Divide four-digit dividends by two-digit divisors using an algorithm using partial quotients.

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Let’s practice using an algorithm using partial quotients.

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Which One Doesn’t Belong:

Different Ways

Warm-Up

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Find the Mistake

Activity 1

MLR8: Discussion Supports

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Launch

•Groups of 2

Student Work Time

•1–2 minutes: quiet think time

•3–5 minutes: partner work time

•Monitor for students who:

◦are able to clearly identify and describe the errors.

◦are able to use the algorithm to calculate the quotients correctly.

Student Responses

36; Error: Subtraction of 1,656 and 920 is wrong.
54; Error: The multiplication is wrong.
31; Error: The first group of 24’s that is taken away is 20, not 200. It also does not show subtracting the final 24.

Activity Synthesis

•Invite students to share where they notice errors and describe the errors.

•“What can you do to make sure you are not making the same errors in your calculation?”

Before I calculate, I can estimate. While I work on the problem, I can double check when I subtract or multiply. After I calculate, I can multiply the quotient by the divisor and make sure I get the dividend.

•Encourage students to consider what they can do before, during, and after they calculate.

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Practice Problems

Activity 2

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Launch

•Groups of 2

Student Work Time

•8-10 minutes: independent work time

•“When you check in with your partner, consider the following questions.”

•Display:

◦“How do the calculations represent each partial quotient?”

◦“What suggestions can you give your partner to improve their work for next time?”

•2-3 minutes: partner discussion

Student Responses

48
45
415
124

Activity Synthesis

•Ask a few students to share their work.

•“How was your work similar to or different from your partner’s?”

We both tried to subtract multiples of 10 or 100 and then when the remaining amount was small we subtracted smaller multiples. My partner used fewer steps.

•“What did you notice in your partner’s work that shows they understand how to use an algorithm that uses partial quotients?”

My partner picked multiples that could mostly be calculated in their head and worked on subtracting the partial quotients.

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Lesson Synthesis

Today, we practiced using an algorithm using partial quotients to divide multi-digit numbers.

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Divide Four-digit Numbers

Cool-Down

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Cool Down: Divide Four-digit Numbers

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Image Citations

https://pixabay.com/photos/watermelon-sweet-juicy-fruit-melon-1969949/

https://pixabay.com/photos/watermelon-melon-colorful-cool-cut-1846051/

https://pixabay.com/photos/watermelon-summer-red-green-food-4748608/

https://pixabay.com/photos/water-melon-fruit-sweet-melon-food-1652093/

https://pixabay.com/photos/melon-watermelon-fruit-food-summer-3630346/

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