# Lesson 7

Subtract Two Digits

## Warm-up: How Many Do You See: Compose a Ten (10 minutes)

### Narrative

The purpose of this How Many Do You See is to build on what students know about place value to make sense of visual representations of two-digit numbers. When students describe how many they see by grouping tens with tens and ones with ones or composing a ten, they show how they look for and make use of base-ten structure (MP7). This will be helpful when students use base-ten representations to compose and decompose a ten during the lesson.

### Launch

• Groups of 2
• “How many do you see? How do you see them?”
• Display the image.
• 30 seconds: quiet think time

### Activity

• Display the image.
• 1 minute: partner discussion
• Record responses.
• Repeat for each image.

### Student Facing

How many do you see? How do you see them?

### Activity Synthesis

• “Which two images have the same value? How do you know?”(The first image and the second image both have the same amount. The first one shows 5 tens and 5 ones. I know Image 2 is the same because I know 2 groups of 5 is the same as 1 ten. So it's the same as 5 tens and 5 ones.)

## Activity 1: What's the Difference? (15 minutes)

### Narrative

The purpose of this activity is for students to subtract a two-digit number from a two-digit number in a way that makes sense to them. Students build on their understanding of decomposing a ten when subtracting a one-digit number from a two-digit number to subtract two-digit numbers. The synthesis is devoted to presenting and comparing techniques students use to find the difference, including diagrams and equations (MP3).

This activity uses MLR8 Discussion Supports. Advances: listening, speaking, conversing

Representation: Develop Language and Symbols. Synthesis: Make connections between representations visible. Ask students to verbalize the connection between the expression and the blocks.
Supports accessibility for: Visual-Spatial Processing, Language, Memory

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Find the value of each difference and share your method and solution with your partner.”
• 7 minutes: independent work time

MLR8 Discussion Supports

• “After your partner shares their method, repeat back what they told you.”
• Display the sentence frames:
• “I heard you say . . . .”
• “Our methods are alike because . . . .”
• “Our methods are different because . . . .”
• 5 minutes: partner discussion
• Monitor for students who use base-ten blocks to show decomposing a ten.

### Student Facing

Find the value of each difference. Show your thinking. Use blocks if it helps.

1. $$46 - 28 =\underline{\phantom{\hspace{1.05cm}}}$$
2. $$93 - 54 =\underline{\phantom{\hspace{1.05cm}}}$$

### Student Response

Some students may not use base-ten blocks to find the difference. Prompt them to show their thinking in a way that could help others understand. Ask them to write expressions to show the steps they took when appropriate. Consider asking:
• “How did you find the value of the difference?”
• “How could you use equations to show the steps you used?”

### Activity Synthesis

• Invite previously identified students to share.
• “What did _____ do to solve the problem? How can we record it?”
• 30 seconds: quiet think time
• Share responses.
• Show how to represent solving with base-ten blocks with drawings and equations.
• “How are these representations like the way _____ used base-ten blocks to find the value of the difference? How are they different?”

## Activity 2: Use Blocks to Take Away (20 minutes)

### Narrative

The purpose of this activity is for students to subtract a two-digit number from a two-digit number. In the first activity, students used any method that made sense to them to find the difference. In this activity, they use base-ten blocks to represent the starting number and subtract amounts that require a ten to be decomposed.

### Required Materials

Materials to Gather

Materials to Copy

• Using Blocks to Take Away

### Required Preparation

• Create a set of cards from the blackline master for each group of 4.

### Launch

• Groups of 4
• Give each group a set of cards and access to base-ten blocks.

### Activity

• “Now you are going to play a card game using base-ten blocks.”
• “First, each member of your group will choose a different player card, Diego, Lin, Jada, or Han.”
• “Write down the name you picked. Mix up the other cards and put them face down.”
• “Now you each have a player and your starting number.”
• “Use the blocks to represent your starting numbers.”
• 2 minutes: group work
• Guide students through the rest of the steps:
• “Take turns picking a card and read the card to the group.”
• “Listen for your player’s name and follow the directions on the card.”
• “Share your thinking while your group members listen. Write an equation to show the new number.”
• “Before picking a new card, make sure your group works together to agree on the new number.”
• “You will keep playing until all of the cards have been read. Your player‘s number should change two times.”
• 15 minutes: group work time
• Monitor for students who:
• discuss decomposing a ten using precise language
• work together to give feedback and resolve any disagreements
• compose tens when adding the ending numbers

### Student Facing

1. Choose a player card. Mix up the other cards and put them face down.

Player name: ________________________________

2. Represent your starting number with base-ten blocks.

Starting number: ____________________________

3. Take turns picking a card. Read the card to the group.
4. Listen for your player’s name. Use the blocks to show the change.
6. Write an equation to show the new number.

Equation 1: ________________________________

Equation 2: ________________________________

My player now has ____________ tens and ____________ones.

Ending number: _____________________________

7. Write an equation to show the sum of the ending numbers in your group.

### Activity Synthesis

• Invite 12 previously identified students to share with their group.
• "What questions do you have for __ about their method?"
• "How was their method the same as how you found your player's new numbers? How was it different?"

## Lesson Synthesis

### Lesson Synthesis

“Today you used different methods to subtract 2 two-digit numbers.”

“You solved in ways that make sense to you and you used base-ten blocks to take away different amounts.”

“How was subtracting a two-digit number from a two-digit number the same as subtracting a one-digit number from a two-digit number?" (It was the same because we still had to think about subtracting ones. Sometimes you have to decompose a ten if you need more ones.)

"How was it different?" (When you subtract a two-digit number, you have to think about subtracting tens too. The number you are subtracting is bigger because it's a two-digit number.)

"How did working together with a partner or a group help you understand different ways to subtract two-digit numbers?"

Math Community

“The card game required you all to work together. What are some ways your group worked together?” (We helped each other with keeping track of the blocks. We talked about our thinking. We helped each other if someone was stuck or confused.)