# Lesson 12

Decompose to Subtract

## Warm-up: What Do You Know About 354? (10 minutes)

### Narrative

The purpose of this What Do You Know About _____ is to invite students to share what they know and how they can represent the number 354. It gives the teacher an opportunity to hear how students think about representing a three-digit number by decomposing or renaming units. This will be helpful as students decompose units to subtract within 1,000 in future activities.

### Launch

• Display the number.
• “What do you know about 354?”
• 1 minute: quiet think time

### Activity

• Record responses.
• “How could we represent the number 354?”

### Student Facing

What do you know about 354?

How could we represent the number 354?

### Activity Synthesis

• “Why might you need to represent 354 in different ways?” (You might want to show the value of each digit to compare numbers. You might want to decompose to subtract.)

## Activity 1: Subtract from 354 (15 minutes)

### Narrative

The purpose of this activity is for students to subtract one-digit and two-digit numbers from a three-digit number using the methods that make sense to them. Each difference would require students to decompose a ten to subtract by place. They may count back or count on by place to find the difference. They may also use their understanding of place value and their experiences decomposing a ten when they subtracted within 100. In the synthesis, focus on connecting and comparing these different methods and making sense of representations that show decomposing a unit when subtracting by place.

When students use base-ten blocks, number lines, or equations to find the value of each difference they use appropriate tools strategically (MP5).

This activity uses MLR7 Compare and Connect. Advances: representing, conversing.

Engagement: Provide Access by Recruiting Interest. Optimize meaning and value. Invite students to share ideas of items to sell (cupcakes, sports cards, video games, etc.) and use that as the context around the problems to solve. Discuss the action of selling to represent subtraction.
Supports accessibility for: Attention, Conceptual Processing

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Find the value of each expression in any way that makes sense to you. Explain or show your reasoning.”
• 3–4 minutes: independent work time
• 3–4 minutes: partner discussion
• Monitor for an expression that generates a variety of student methods or representations to share in the synthesis, such as:
• using base-ten blocks
• drawing a number line
• writing their reasoning in words
• writing equations

### Student Facing

Find the value of each expression in any way that makes sense to you. Explain or show your reasoning.

1. $$354 - 7$$
2. $$354 - 36$$
3. $$354 - 48$$

### Activity Synthesis

MLR7 Compare and Connect
• Invite one previously identified student who used a method that did not explicitly show decomposing a ten to share.
• Invite one previously identified student to show how they decomposed a ten to subtract with base-ten blocks or a base-ten diagram.
• “What is the same and what is different about the ways _____ and _____ represented the problem?” (____ used base-ten blocks and showed decomposing a ten. _____ showed a number line and counting back 36. They used the same numbers. They found the same difference.)

## Activity 2: Decompose with Base-ten Blocks (20 minutes)

### Narrative

The purpose of this activity is for students to practice decomposing a unit to subtract by place. In this activity, all students use base-ten blocks to find the value of each difference. Some students may be able to find the difference without blocks, but since this is the first time they decompose a unit when subtracting beyond 100, the blocks allow all students to see the work of decomposing a unit. This concrete experience will help students interpret other representations and anticipate when they may need to decompose units in future lessons. The blocks also provide a support for students as they create arguments for why they think they will decompose a unit and explain how they find the difference (MP3).

As needed, ask students to decompose a tower of ten connecting cubes into ones. Ask students how they would show the same decomposition with base-ten blocks.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students base-ten blocks.

### Activity

• “Now we are all going to use base-ten blocks to subtract.”
• “Work with your partner to find the value of each expression. One partner will start by reading the expression and representing the larger number using blocks.”
• “The next partner will decide if they think they will decompose any units to subtract. Then they will take away blocks to show the difference.”
• “Discuss the difference and record it.”
• As needed, demonstrate with $$142 - 25$$.
• 10 minutes: partner work time

### Student Facing

Work with your partner to find the value of each expression.

• Partner A: Read the expression and represent the larger number using blocks.
• Partner B: Decide if you will decompose a ten and explain. Then subtract.
• Discuss and write the difference.
• Switch roles.
1. $$264 - 38$$
2. $$274 - 41$$

3. $$336 - 115$$
4. $$343 - 127$$
5. $$485 - 266$$
6. $$451 - 315$$

### Student Response

If students add ones to their representation without taking away a ten when they show a decomposition, ask the group to explain their steps. Consider asking:
• “Did you decompose a ten to subtract?”
• “How could you use the blocks to show that you decomposed a ten?”

### Activity Synthesis

• Invite a group to share how to use blocks to find the value of $$336 - 115$$.
• “What did _____ do to find the value of the difference?”
• Invite a group to share how to use blocks to find the value of $$343-127$$.
• “What did _____ do to find the value of the difference?”

## Lesson Synthesis

### Lesson Synthesis

“Today we saw that we can subtract by place with larger numbers, and sometimes a ten is decomposed.”

“How did you know when a ten would be decomposed when you subtracted three-digit numbers?” (I could tell when I looked at the ones place and saw I didn't have enough ones to subtract ones from ones.)

“How was this the same as when you subtracted two-digit numbers? How was it different?” (It was just like when we subtracted two-digit numbers. It's different because one of the numbers has hundreds.)