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Base-ten Diagrams to Represent

Division

Grade 4: Unit 6: Lesson 17

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Lesson Purpose

The purpose of this lesson is for students to find the quotients of two-digit and three-digit

dividends and one-digit divisors. They do so by decomposing the dividend by place

value—decomposing a larger unit to 10 of a smaller unit—and by reasoning in terms of equal-size

groups.

Lesson Narrative

In grade 3, students used base-ten representations to help them reason about division of a two-

digit number into equal-size groups. This lesson builds on that understanding and revisits it in the

context of three-digit dividends. Students recall that they can exchange or decompose one or more

units of a higher place value for 10 units of the next lower place value in order to have enough units

to put into equal groups.

The work here sets the groundwork for students to later decompose a dividend by place value (even

when not using base-ten blocks or diagrams). It is also the basis for dividing multi-digit numbers

using the standard division algorithm (in grade 5), which relies on dividing by place value, one digit

at a time.

Learning Goals

• Divide two- and three-digit by one-digit numbers using base-ten diagrams.

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Let’s divide using base-ten blocks or diagrams.

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Which One Doesn’t Belong: Base-ten Diagrams

Warm-Up

• Which One Doesn’t Belong?

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Which one doesn’t belong?

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Let’s Talk About It!

How is it that A and C both show 111?

How do we know that D also shows 111?

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Divide with Diagrams or Blocks

Activity 1

MLR8: Discussion Supports

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Explain Why the diagram represents 64.

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Priya draws a base-ten diagram to find the value of 64 ÷4 . A rectangle represents 10. A small square represents 1.

Use the diagram (or actual blocks) to help Priya complete the division.

Explain or show your reasoning.

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Use this base-ten diagram (or actual blocks) to find the value of 117 ÷ 3 .

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Let’s Talk About It!

Let’s share our thinking!

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Help Noah Get Unstuck

Activity 2

Engagement

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How does the diagram represent 235?

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This diagram represents 235.

To find 235÷5, Noah draws the following diagram but then gets stuck.

He says, “There are not enough of the hundreds or the tens pieces to put into 5 groups.”

Explain or show how Noah could find 235 ÷ 5 with his diagram.

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Find the value of 432 ÷ 6. Show your reasoning.

Use base-ten diagrams or blocks if you find them helpful.

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Let’s Talk About It!

Let’s share our thinking!

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Lesson Synthesis

How is this approach like earlier ones?
How is this approach different?

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Find the Value of a Quotient

Cool-Down

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Find the value of 134 ÷ 4. Show your reasoning.

The base-ten diagram represents 132. Use the diagram if you find it helpful.

Cool-Down: Find the Value of a Quotient

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Image Citations

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