# Lesson 13

Decompose Tens or Hundreds

## Warm-up: Which One Doesn’t Belong: Blocks and Blocks (10 minutes)

### Narrative

This warm-up prompts students to compare four images of base-ten blocks. This gives the teacher an opportunity to hear how students describe the blocks and how they use “compose” or “decompose” to describe their understanding of equivalent forms of a hundred and a ten. This will be helpful as students decompose hundreds and tens to subtract and interpret base-ten representations in the lesson activities.

### Launch

• Groups of 2
• Display the image.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

### Activity

• 2–3 minutes: partner discussion
• Share and record responses.

### Student Facing

Which one doesn’t belong?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “Which images could show a way to decompose a hundred? Explain.” (B because 10 tens is the same as a hundred. A is close, but I think it shows composing a hundred.)
• “Which images do not show a way to decompose a hundred?” (C because 10 ones are not the same as a hundred. D because it could show a ten as 10 ones.)

## Activity 1: Subtract with Base-ten Diagrams (15 minutes)

### Narrative

The purpose of this activity is for students to interpret base-ten diagrams that represent decomposing a unit when subtracting by place (MP2). Students analyze a base-ten diagrams that show decomposing a hundred into 10 tens. They make connections between representing with base-ten blocks and base-ten diagrams and between decomposing a hundred and decomposing a ten.

MLR5 Co-Craft Questions. Keep books or devices closed. Display only the images, without revealing the question, and ask students to write down possible mathematical questions that could be asked about the situation. Invite students to compare their questions before revealing the task. Ask, “What do these questions have in common? How are they different?” Reveal the intended questions for this task and invite additional connections.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• “Mai found the value of $$336-52$$ using base-ten blocks. She started recording her thinking with a base-ten diagram.”
• “Take a minute to look at Mai’s diagram. What did she do in Step 2?”
• 1 minute: quiet think time
• “Talk to your partner about Mai’s representation. Explain what she is doing in each step.”
• 1–2 minutes: partner work time
• “What does Mai do in her first step?” (First, she draws 336 with 3 hundreds, 3 tens, and 6 ones.)
• “What does Mai do next?” (Next, she breaks apart a hundred into 10 tens.)
• “What should Mai do next to find the difference? Show your work on Mai’s diagram.”
• 1–2 minutes: independent work time
• Display sentence frames:
• “First, I . . .”
• “Then, I . . .”
• “The difference is . . .”
• Invite a student who describes crossing out tens first then ones and a student who describes crossing out ones first then tens to share their steps and the difference.

### Activity

• “Work with your partner to match each expression to one of the diagrams. Then find the value of each difference.”
• 3–5 minutes: partner work time

### Student Facing

Mai used base-ten blocks to find the value of $$336-52$$. Then, she started making a diagram to show her work.

Explain what Mai did in Step 2. Show what Mai should do next to find the difference.

Step 1

Step 2

1. Write each expression next to the matching diagram. Then find the value of each difference.

$$244 - 28$$

$$256 - 64$$

$$244 - 64$$

### Student Response

For access, consult one of our IM Certified Partners.

If students match an expression to a diagram that doesn't show the same value, consider asking:

• “How does the diagram show each number in the expression?”

### Activity Synthesis

• Invite students to share the expression that matches each diagram.
• “What did you have to pay attention to as you matched each diagram to an expression?” (I had to look at the numbers that were being subtracted. I looked for where there were more tens or more ones drawn when there weren’t enough tens or ones.)

## Activity 2: Decompose a Ten or Hundred (20 minutes)

### Narrative

The purpose of this activity is for students to subtract by place and record their thinking. Students decompose either a ten or a hundred as they subtract. They should have access to base-ten blocks, but can represent their thinking in any way that makes sense to them. Throughout the activity, as students share their thinking with their peers, listen for the way they use place value vocabulary and provide them with opportunities to revise their language for precision and clarity.

Action and Expression: Develop Expression and Communication. Provide students with alternatives to writing on paper. Students can share their learning by creating a video using the base-ten blocks, or writing out their steps and explaining on video.
Supports accessibility for: Language, Attention, Social-Emotional Functioning

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “We are going to practice subtracting by place. Show your thinking in a way that will make sense to others.”
• 5 minutes: independent work time
• 4 minutes: partner work time
• Monitor for students who use base-ten diagrams and explain their steps clearly.

### Student Facing

Find the value of each difference. Show your thinking. Try Mai's way for one expression.

1. $$245 - 28$$
2. $$352 - 71$$
3. $$364 - 182$$
4. $$293 - 147$$
5. Share how you found the value of one of the expressions to your partner. Use the sentence frames to help explain:

• “First, I . . .”
• “Next, I . . .”
• “Then, I . . .”
• “Last , I . . .”

### Student Response

For access, consult one of our IM Certified Partners.

If students only use base-ten blocks to solve and do not show their thinking with a diagram, equations, or words, consider asking:

• “How could you record how you used the blocks with a diagram or with equations?”

### Activity Synthesis

• Invite previously identified students to share how they found the value of each difference.
• After each student shares, consider asking:
• “Did _____ decompose to subtract? Why? How can you use their diagram to tell?”
• “How is _____’s method the same as how you found this difference? How is it different?”
• “What questions do you have for _____ about their steps or their representation?”

## Lesson Synthesis

### Lesson Synthesis

“Today we decomposed tens or hundreds to subtract by place.”

Display $$534 - 41$$ and draw a base-ten diagram to represent 534.

“Kiran wanted to take away by place and use a base-ten diagram to keep track of his thinking. First, Kiran drew 534 as 5 hundreds, 3 tens, and 4 ones. What could Kiran do next? Explain.” (He could take away 1 one because he has enough to subtract. He could cross out 1 hundred and draw 10 tens, because he needs more tens to subtract.)

## Cool-down: More Subtraction (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.