# Lesson 6

Represent Numbers with Expressions

## Warm-up: True or False: Place Value (10 minutes)

### Narrative

The purpose of this True or False is to elicit the strategies and understandings students have for explaining why an equation is true based on place value. These understandings will be helpful later when students need to find ways to make equations true by attending to place value.

### Launch

• Display one statement.
• “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategies.
• Repeat with each statement.

### Student Facing

Decide if each statement true or false. Be prepared to explain your reasoning.

• 5 hundreds + 2 tens + 7 ones = 527
• 4 hundreds + 12 tens + 7 ones = 527
• 5 hundreds + 7 ones + 2 tens = 527

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “What other ways could we write an expression that has a value of 527?”

## Activity 1: Make Equations True (20 minutes)

### Narrative

The purpose of this activity is for students to use their understanding of place value to find the number that makes each equation true. Students must consider how units may be composed or decomposed to find the unknown number (MP7). The number choices intentionally emphasize the types of compositions and decompositions students may use to add and subtract within 1,000. The synthesis focuses on the equations that involve composing or decomposing two units.

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• 5 minutes: independent work time
• “Take turns sharing your thinking with your partner. Show or explain how you know your equation is true.”
• 3 minutes: partner discussion
• For finding the number that makes 2 hundreds + 9 tens + 17 ones true, monitor for students who:
• explain by using base-ten blocks or place value diagrams
• explain how they noticed when they would need to compose or decompose more than one unit

### Student Facing

Find the number that makes each equation true.

1. 5 hundreds + _____ tens + 6 ones = 5 hundreds + 5 tens + 16 ones
2. 1 hundred + 1 ten + 17 ones = 1 hundred + _____ tens + 7 ones
3. 4 hundreds + 15 tens + 3 ones = _____ hundreds + 5 tens + 3 ones
4. 4 hundreds + 3 tens + 7 ones = 3 hundreds + _____ tens + 7 ones
5. 7 hundreds + 8 tens + 4 ones = 7 hundreds + 7 tens + _____ ones

6. 6 hundreds + 9 ones = 5 hundreds + _____ tens + 9 ones
7. 2 hundreds + 9 tens + 17 ones = _____ hundreds + 7 ones
8. 3 hundreds + 1 ten + 5 ones = 2 hundreds + 10 tens + _____ ones
If You Have Time: Make your own equation with a missing value for your partner.

### Student Response

For access, consult one of our IM Certified Partners.

If students create equations that are not true, prompt students to make the known side of the equation with base-ten blocks, consider asking:

• “How can you compose or decompose units to show the equation is true?”

### Activity Synthesis

• Invite previously identified students to share their method for finding the unknown number for 2 hundreds + 9 tens + 17 ones = _____ hundreds + 7 ones.
• For students who use base-ten blocks, draw place value diagrams to record their explanation.
• “How do you know both sides of the equation are equal?”
• “Did you compose or decompose units? Did you compose or decompose more than one time?”

## Activity 2: Card Sort: Expressions with Three-digit Values (15 minutes)

### Narrative

The purpose of this activity is for students to use their understanding of place value to find and create matching expressions. The activity encourages students to write expressions that show the same value by composing or decomposing hundreds, tens, and ones. Although students may find the value of each expression to find matches, monitor for the ways they reason why two expression match or do not match by using what they know about hundreds, tens, and ones (MP7).

MLR8 Discussion Supports. Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frames for all to see: “I noticed _____, so I matched . . . .” Encourage students to challenge each other when they disagree.
Engagement: Develop Effort and Persistence. Chunk this task into smaller, more manageable parts. Instead of giving all 12 expressions, start with 4 (be sure that there are matches) and check in with students to provide feedback and encouragement on their thinking and effort. Ask students about their strategy, or about how they were able to determine the expressions that were the same. Look for thoughts on place value and combining some of the parts, not always just basic addition.
Supports accessibility for: Conceptual Processing, Attention, Organization

### Required Materials

Materials to Copy

• Match Expressions Cards 2.9

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.

### Launch

• Groups of 2
• Give each group a set of cards.

### Activity

• “Work with your partner to find three expressions that have the same value.”
• “Record the letters of the matching cards and write your own expression that has the same value.”
• 10 minutes: partner work time

### Student Facing

Group the cards into sets of expressions that have the same value. Record the letters of the matching cards. Write an expression that represents the same value.

1. letters for matching expressions: __________________

new expression:

2. letters for matching expressions: __________________

new expression:

3. letters for matching expressions: __________________

new expression:

4. letters for matching expressions: __________________

new expression:

### Student Response

For access, consult one of our IM Certified Partners.

If students find matches that are not equivalent or do not explain their matches, consider asking:

• “How could you use base-ten blocks or diagrams to show your thinking?”

### Activity Synthesis

• Display cards C, H, and J.
• “Do these expressions match? Explain.”
• “What other expressions did you write that match these expressions?”