# Lesson 3

Are the Expressions Equal?

## Warm-up: How Many Do You See: Sums within 10 (10 minutes)

### Narrative

The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see. Students see two-color counters on the 10-frame and may know that when the 10-frame is filled, it is 10. Then they may see how many are not filled and subtract that many from 10 or may see how many are filled in each row and add those together. This deepens their understanding of the structure of 10 (MP7).

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

### Student Facing

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

### Activity Synthesis

• “How does the structure of the 10-frame help you ‘see’ the total?” (I know that when the 10-frame 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.

MLR8 Discussion Supports. Synthesis: Before students share, remind students to use “sum” and “expression.”

### 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

### 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).

Representation: Internalize Comprehension. Provide students with a graphic organizer, such as a two-column table or sorting mat, to visually represent the expressions on each side of the equations.
Supports accessibility for: Visual Spatial Processing, Conceptual Processing

### Launch

• Groups of 4
• “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

• “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.

1. $$4 + 2 = 2 + 4$$
2. $$3 + 6 = 6 + 4$$
3. $$5 + 3 = 1 + 7$$

4. $$6 + 4 = 5 + 3$$
5. $$6 + 3 = 9 + 2$$

If you have time: Change the false equations to make them true.

### Student Response

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 two-color 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.
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