# Lesson 3

Relate Addition and Subtraction within 20

## Warm-up: Number Talk: Addition and Subtraction (10 minutes)

### Narrative

This Number Talk encourages students to think about the relationship between addition and subtraction to mentally solve problems. This builds on the work in the previous lesson where students used the relationship between addition and subtraction to find unknown numbers in equations. The understanding elicited here will be helpful later in the lesson when students find the value to make an equation true.

### Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$7+3$$
• $$10-7$$
• $$10-2$$
• $$10-4$$

### Activity Synthesis

• “How did thinking about addition help you subtract?” (I thought about what number I could add to the 4 to make 10. Since I know 4 + 6 = 10 then I knew 10 – 4 = 6)
• If needed, use connecting cubes to represent students’ thinking.

## Activity 1: Introduce What’s Behind My Back, 20 Cubes (20 minutes)

### Narrative

In this activity, students learn stage 3 of the What’s Behind My Back center. In this new stage, called 20 cubes, students work with 20 cubes, organized into two towers of 10 cubes. One partner snaps the tower and puts one part behind their back and shows the other part to their partner. The other partner figures out how many cubes are behind their partner’s back. Students record an addition equation with a blank to represent the missing cubes. Students may write equations with the blank as the first or second addend. Ask students to explain what each number and blank in the equation represents in the context of the center activity (MP2).

MLR7 Compare and Connect. Synthesis: Invite students to discuss connections between the different approaches. Ask, “What did these strategies have in common? How were they different?”
Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were important or most useful to pay attention to. Display the sentence frame, “To figure out how many cubes are behind my partner’s back, I can . . . .“
Supports accessibility for: Visual-Spatial Processing

### Required Materials

Materials to Gather

Materials to Copy

• What's Behind My Back Stage 3 Recording Sheet

### Launch

• Groups of 2
• Give each group 20 connecting cubes and a recording sheet.
• “We are going to play What’s Behind My Back, this time with 20 cubes.”
• “How did you figure out how many connecting cubes were behind your partner’s back last time?” (I thought about an addition expression that would make 10. I subtracted what they showed me from 10.)
• “Let’s play a round with 20.”
• Show students 2 towers of 10 cubes. Put the towers behind your back. Break off and display 8 of the cubes.
• “This time when you play, you are going to record an addition equation with a blank to represent the missing cubes, before you figure out how many are behind your partner’s back. What equation should we record?” ($$8+\underline{\hspace{.5 cm}}=20$$)
• 30 seconds: quiet think time
• Share responses.
• “How many cubes are behind my back? How do you know?” (12 because 2 more makes 10 and then here’s another tower of 10.)
• 30 seconds: quiet think time
• 30 seconds: partner discussion
• “Play with your partner. Don’t forget to record an equation each round.”

### Activity

• 10 minutes: partner work time

### Activity Synthesis

• Display 9 cubes.
• “What’s an addition equation I can write to represent the number of cubes you know and the number of cubes you need to figure out?” (9 + _____ = 20)
• “Tell your partner how you can figure out how many cubes are missing.”
• Monitor for students who talk about making a 10 and knowing there is one more 10.
• Share responses.

## Activity 2: Make the Equation True (15 minutes)

### Narrative

The purpose of this activity is for students to find the value that makes an addition or subtraction equation true, with totals of 20. Students may use whatever method makes sense to them. In the launch, students work with a new partner and fill in the unknown addend in the equations on their recording sheet from Activity 1.

### Required Materials

Materials to Gather

### Launch

• Groups of 2: different than the previous activity
• “You are going to find the number that makes each equation true. Switch recording sheets with someone who you didn’t play What’s Behind My Back with. Fill in the number that makes each equation true. Be prepared to share with your partner how you found each number.”
• 3 minutes: independent work time
• “Share your work with your partner. Choose 1 equation and explain to them how you found the number that makes it true.”
• 3 minutes: partner discussion

### Activity

• “Work in your book to find the number that makes each equation true.”
• 5 minutes: independent work time
• Monitor for students who look for ways to make 10.

### Student Facing

Find the number that makes each equation true.

1. $$4+\underline{\hspace{1 cm}}=20$$

2. $$20-\underline{\hspace{1 cm}}=4$$

3. $$6+\underline{\hspace{1 cm}}=20$$

4. $$20-\underline{\hspace{1 cm}}=10$$

5. $$\underline{\hspace{1 cm}}+3=20$$

6. $$20-15=\underline{\hspace{1 cm}}$$

7. $$20-\underline{\hspace{1 cm}}=18$$

8. If you have time:  $$\underline{\hspace{1 cm}}-5=20$$

### Activity Synthesis

• Invite selected students to show their thinking for $$\underline{\hspace{1 cm}}+3=20$$ and $$20-\underline{\hspace{1 cm}}=18$$.
• “How did thinking about a ten help them find their answer?” (They knew 20 is 2 tens so they used 1 of the tens to make the problems easier.)

## Lesson Synthesis

### Lesson Synthesis

“Today, we found the unknown number in equations that makes them true.”

Math Community
Display Math Community poster. Explain to students that norms are expectations that help everyone in the room feel safe, comfortable, and productive doing math together.

“We are going to make a list of norms for how we do math together. One example of a norm is ‘Listen as others share their ideas.’ What other norms should we set for our class?”

Share and record responses.