Lesson 3
Are the Expressions Equal?
Warmup: How Many Do You See: Sums within 10 (10 minutes)
Narrative
Launch
 Groups of 2
 “How many do you see? How do you see them?”
 Flash the image.
 30 seconds: quiet think time
Activity
 Display the image.
 “Discuss your thinking with your partner.”
 1 minute: partner discussion
 Record responses.
 Repeat for each image.
Student Facing
How do you see them?
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 “How does the structure of the 10frame help you ‘see’ the total?” (I know that when the 10frame is filled it is 10. I can see how many are not filled and subtract that many from 10, or I can see how many are filled in each row and add those together.)
Activity 1: Sort Addition Expressions (20 minutes)
Narrative
The purpose of this activity is for students to sort addition expressions by their value. Students find the value of each sum on their own and share their method with a partner, moving students towards fluency.
During the synthesis the teacher introduces an equation with addition expressions on both sides of the equal sign.
Advances: Speaking, Conversing
Required Materials
Materials to Gather
Required Preparation
 Each student needs their addition expression cards from a previous lesson.
Launch
 Groups of 2
 Give students their addition expression cards.
 “Sort the cards into groups with the same value.”
 Display an addition expression card, such as \(2 + 5\).
 “I know the value of this sum is seven. It is a sum that I just know. I will start a pile for sums of seven.”
Activity
 “Work with your partner. Make sure that each partner has a chance to find the value before you place the card in a group. If you and your partner disagree, work together to find the value of the sum.”
 12 minutes: partner work time
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 “What sums have a value of seven?” (1 + 6, 6 + 1, 2 + 5, 5 + 2, 3 + 4, 4 + 3)
 Display \(4 + 3 = 3 + 4\).
 “What do you notice about this equation?” (Each side has a 3 and a 4, but in a different order. Each side equals 7.)
Activity 2: Are Both Sides Equal? (15 minutes)
Narrative
The purpose of this activity is for students to determine whether equations are true or false. Students may use a combination of computation and reasoning about the commutative property to determine whether each equation is true or false. The synthesis focuses on how students can use the structure of the expressions to determine if they are equal without finding their values (MP7).
Supports accessibility for: Visual Spatial Processing, Conceptual Processing
Required Materials
Materials to Gather
Launch
 Groups of 4
 Give students access to connecting cubes or twocolor counters.
 “We just found expressions that were equal to each other. Look at this equation.”
 Display \(4 + 2 = 6 + 1\).
 “Is this equation true or false? How do you know?” (False. \(4 + 2 = 6\), but the other side of the equal sign is 1 more than 6.)
 30 seconds: quiet think time
 1 minute: partner discussion
 Share responses.
Activity
 Read the task statement.
 “You will work on these problems independently. I will let you know when it is time to share with a partner.”
 4 minutes: independent work time
 “Share your thinking with a partner. Find a different partner for each problem. If you and your partner do not agree, work together to agree on the answer.”
 3 minutes: partner discussion
Student Facing
Determine whether each equation is true or false.
Be ready to explain your reasoning in a way that others will understand.
 \(4 + 2 = 2 + 4\)
 \(3 + 6 = 6 + 4\)
 \(5 + 3 = 1 + 7\)
 \(6 + 4 = 5 + 3\)
 \(6 + 3 = 9 + 2\)
If you have time: Change the false equations to make them true.
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
If students circle true for an equation where the value to the left of the equal sign is the same as the first number on the right of the equal sign, consider asking:
 “How did you decide this equation is true?”
 “How can you use twocolor counters to represent both sides of the equation? Can you use these counters to decide if the equation is true?”
Activity Synthesis

“Which equations could you tell were true or false without finding the value of both sums?” (Problem 1. That’s the add in any order property. Problem 2. You can see that the number you are adding to 6 is different on each side of the equal sign. Problem 5. \(6 + 3\) is 9. The other side of the expression is 9 and some more.)
Lesson Synthesis
Lesson Synthesis
Display \(6 + 3 = 9 + 2\)
“Today we worked with equations that have expressions on both sides of the equal sign. What would you tell someone who said this equation was true because \(6 + 3 = 9 \)?” (This side of the equal sign is 9 and the other side is 11. 9 does not equal 11.
Cooldown: Equal Expressions (5 minutes)
CoolDown
For access, consult one of our IM Certified Partners.