Lesson 6
Represent Numbers with Expressions
Warmup: 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
Teachers with a valid work email address can click here to register or sign in for free access to Student Response.
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
Launch
 Groups of 2
 Give students access to baseten blocks.
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 baseten 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.
 5 hundreds + _____ tens + 6 ones = 5 hundreds + 5 tens + 16 ones
 1 hundred + 1 ten + 17 ones = 1 hundred + _____ tens + 7 ones
 4 hundreds + 15 tens + 3 ones = _____ hundreds + 5 tens + 3 ones
 4 hundreds + 3 tens + 7 ones = 3 hundreds + _____ tens + 7 ones

7 hundreds + 8 tens + 4 ones = 7 hundreds + 7 tens + _____ ones
 6 hundreds + 9 ones = 5 hundreds + _____ tens + 9 ones
 2 hundreds + 9 tens + 17 ones = _____ hundreds + 7 ones
 3 hundreds + 1 ten + 5 ones = 2 hundreds + 10 tens + _____ ones
Student Response
Teachers with a valid work email address can click here to register or sign in for free access to Student Response.
Advancing Student Thinking
If students create equations that are not true, prompt students to make the known side of the equation with baseten 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 baseten blocks, draw place value diagrams to record their explanation.
 Consider asking:
 “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 Threedigit 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).
Advances: Speaking, Conversing
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.

letters for matching expressions: __________________
new expression:

letters for matching expressions: __________________
new expression:

letters for matching expressions: __________________
new expression:

letters for matching expressions: __________________
new expression:
Student Response
Teachers with a valid work email address can click here to register or sign in for free access to Student Response.
Advancing Student Thinking
If students find matches that are not equivalent or do not explain their matches, consider asking:
 “How could you use baseten 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?”
 If time, consider asking:
 “What other expressions could you write to match these expressions?”
Lesson Synthesis
Lesson Synthesis
“Share your work from the cooldown with your partner. Then we will share with the class.”
Cooldown: Think of a Time (5 minutes)
CoolDown
Teachers with a valid work email address can click here to register or sign in for free access to CoolDowns.