# Lesson 17

Base-ten Diagrams to Represent Division

### 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.

• Engagement
• MLR8

### Learning Goals

Teacher Facing

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

### Student Facing

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

### Required Materials

Materials to Gather

### Lesson Timeline

 Warm-up 10 min Activity 1 15 min Activity 2 20 min Lesson Synthesis 10 min Cool-down 5 min

### Teacher Reflection Questions

How did the representations in today’s lesson support students in dividing multi-digit numbers?

### Suggested Centers

• Compare (1–5), Stage 4: Divide within 100 (Supporting)
• Rolling for Fractions (3–5), Stage 2: Multiply a Fraction by a Whole Number (Supporting)

### Print Formatted Materials

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