# Lesson 16

Base-ten Blocks to Divide

## Warm-up: What Do You Know About Base-ten Blocks? (10 minutes)

### Narrative

The purpose of this What Do You Know About _____? is to invite students to share what they know about base-ten blocks in the context of division. Some students may choose to reflect on base-ten blocks and division while others may simply describe what they know about base-ten blocks. Any reflection offered by students is useful for activating prior knowledge for the lesson.

### Required Materials

Materials to Gather

### Launch

- Display a pile of base-ten blocks.
- “What do you know about base-ten blocks?”
- 1 minute: quiet think time

### Activity

- Record responses.

### Student Facing

What do you know about base-ten blocks?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

- “Which blocks would we use to represent the number 324?”
- “You have used base-ten blocks to represent large numbers. Today you are going to see how they can be helpful to divide larger numbers.”

## Activity 1: Blocks to Divide (25 minutes)

### Narrative

The purpose of this activity is for students to find quotients using base-ten blocks and represent their methods. Students solve two problems, one where decomposing a hundred or ten is not necessary and one where it is. Students use base-ten blocks to represent the problem and find the quotient, then they work in small groups to create a visual display of how they used the base-ten blocks. This builds on work students have done in previous grades representing operations with base-ten representations.

The base-ten blocks help highlight the important role place value plays in division (MP7). There are not enough hundreds in 104 to divide into 8 equal groups but there are enough tens to put 1 ten in 8 equal groups and then the 2 remaining tens can be broken into ones to complete the division.

### Required Materials

Materials to Gather

### Required Preparation

- Each group of 3–4 students needs a set of base-ten blocks that includes 4 hundreds blocks, 10 ten blocks, and 25 ones blocks.

### Launch

- Groups of 3–4
- Give each group at least 4 hundreds blocks, 10 tens blocks and 25 ones blocks.

### Activity

- “Work with your group to represent each expression with base-ten blocks, then find the quotient.”
- 5–6 minutes: group work time

**MLR7 Compare and Connect**

- Give each group tools for making a visual display.
- “Create a visual display that shows how you used the base-ten blocks to find the quotient, including details such as notes, diagrams, drawings, and so on, to help others understand your thinking.”
- 2–5 minutes: group work
- 5–7 minutes: gallery walk
- “As you look at the displays from other groups, record things that are the same and things that are different.”

### Student Facing

Use the base-ten blocks to represent each expression. Then find the value of each expression.

- \(488\div 4\)
- \(104\div 8\)

### Student Response

For access, consult one of our IM Certified Partners.

### Advancing Student Thinking

Students may show their reasoning and computation only by writing expressions or equations. Consider asking:

- “How can you use base-ten blocks to represent the division and show your way of thinking about it?”
- “What does the answer you found mean in terms of the blocks?”

### Activity Synthesis

- “What is the same and what is different between the representations?”
- 30 seconds quiet think time
- 1 minute: partner discussion

## Activity 2: Show Us Your Blocks (10 minutes)

### Narrative

The purpose of this activity is for students to find quotients and represent their thinking with base-ten blocks. The numbers in the expressions are designed to encourage students to think about when the base-ten blocks may be helpful and when they become cumbersome. In future lessons, students will be asked to interpret base-ten representations but may use any method or representation that makes sense to them.

*Representation: Develop Language and Symbols.*Synthesis: Use gestures or annotations such as labels or arrows to make connections between representations visible on displayed student work.

*Supports accessibility for: Conceptual Processing, Visual-Spatial Processing*

### Required Materials

Materials to Gather

### Launch

- Groups of 2
- Give students access to base-ten blocks.
- “You are going to solve some problems on your own. Use base-ten blocks and represent your thinking in your book.”

### Activity

- 5–6 minutes: independent work time
- 2 minutes: partner discussion
- Monitor for students who draw base-ten representations using small and large squares and rectangles labeled with numbers, to share in the lesson synthesis.

### Student Facing

Find the value of each expression. Explain or show how you used base-ten blocks to find the value.

- \(96\div4\)
- \(86\div2\)
- \(108\div9\)

### Student Response

For access, consult one of our IM Certified Partners.

### Advancing Student Thinking

Students may use mental math to solve problems. Consider asking: “How might your use the blocks to check your mental math?”

### Activity Synthesis

- See lesson synthesis.

## Lesson Synthesis

### Lesson Synthesis

Display student work showing base-ten representations for the last expression (\(108\div9\)).

“How did this student represent their reasoning?” (They drew the 10 tens and then crossed out 2 tens and drew 20.)

“Do you have any questions or suggestions that could help them make their work clearer?” (They could add numbers to label the parts.)

Repeat with other student’s work, as time allows.

“Take a minute, and if you’d like, revise your work to make it easier for someone else to understand.”

## Cool-down: Division Reflection (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.