# Lesson 24

Relate Counting to Addition and Subtraction

## Warm-up: Choral Count: Backward from 50 (10 minutes)

### Narrative

The purpose of this Choral Count is to invite students to practice counting by one backwards and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students count back to find the value that makes the subtraction equation true.

### Launch

• “Count backward by 1, starting at 50.”
• Record as students count.
• Stop counting and recording at 20.

### Activity

• “What patterns do you see?”
• 1-2 minutes: quiet think time
• Record responses.

### Student Response

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### Activity Synthesis

• “Who can restate the pattern in different words?”

## Activity 1: Different Ways to Subtract (20 minutes)

### Narrative

The purpose of this activity is for students to analyze and apply both counting on and taking away as methods to subtract. Both counting on and taking away are valid methods for finding a difference. Students should begin to notice that one method may be more efficient than the other, depending on the numbers in the problem. During the synthesis, students discuss how counting on and taking away are the same and different. This allows teachers to see the mathematical vocabulary students use to describe the strategies (MP6).

This activity uses MLR8 Discussion Supports. Activity: During partner work time, invite students to restate what they heard their partner say. Students may agree or clarify for their partner.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.
• “How did Diego find the difference?” (Diego put 15 counters on the 10-frames and took away 8. The counters that are still there show the difference.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• "Look at Tyler's work. He started by putting eight red counters on his double 10-frame. Then he put on seven yellow counters. How did that help him find the difference?” (He kept adding counters until he got to 15. He knew the yellow counters were the difference.)
• 30 seconds: quiet think time
• 1 minute: partner discussion

### Activity

• 6 minutes: independent work time

MLR8 Discussion Supports

• “After your partner shares their thinking, repeat back what they told you.”
• Display the sentence frame: “I heard you say . . .”
• 4 minutes: partner discussion

### Student Facing

Yesterday, we saw Diego’s method to find the value of $$15 - 8$$.

Diego's way

Tyler’s way

Find the value of each difference using Diego’s way, then using Tyler’s way.

Diego's Way

Tyler's Way

1. $$16-3$$

Diego's Way

Tyler's Way

2. $$17-8$$

3. $$18-15$$

### Student Response

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### Activity Synthesis

• Have a student share Diego’s way for $$18- 15$$.
• Display $$18- 15 = \boxed{3}$$
• “How does this equation match their method?” (They started with 18 counters and then took away 15. They counted 3 left.)
• Have a student share Tyler’s way for $$18 - 15$$.
• Display $$15 + \boxed{3} = 18$$.
• “How does this equation match Tyler’s method?” (Tyler started with 15 counters. Then he counted on to get to 18. He had to count on 3.)
• “Which method did you like better for this expression? Why?” (Tyler's because it was a lot faster to count on 3 more than to take away 15 and count what was left.)

## Activity 2: Find the Number That Makes Each Equation True (20 minutes)

### Narrative

The purpose of this activity is for students to find the missing values that make subtraction and addition equations true. The numbers are selected to encourage students to use a ten to find the missing value and are presented as two sets: subtraction and addition. Students may notice that the first equation in Set B relates to a subtraction equation in Set A.

In the synthesis, students share methods for $$15 - 12$$. Highlight both counting on and taking away methods. Monitor for a student who found the difference between $$15 - 12$$  by subtracting 10 from 15 and then subtracting 2 more from the 5 ones that are left: $$15 - 10$$ is 5 and $$5 - 2$$ is 3. If a student does not use this method, teachers should demonstrate to students. When students break up 12 into 10 and 2 and subtract each number successively they are using their understanding of a teen number as 10 and some ones (MP7).

MLR7 Compare and Connect. Synthesis: After all methods have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “How was the same problem solved in multiple ways?” and “Why does it work to solve the same problem in multiple ways?”
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Social-Emotional Functioning, Attention

### Required Materials

Materials to Gather

### Launch

• Groups of 4
• Give students access to double 10-frames and connecting cubes or two-color counters.

### Activity

• 8 minutes: independent work time
• Monitor for students who solve $$15 - 12 = \boxed{\phantom{\frac{aaai}{aaai}}}$$ by:
• Counting on from 12 to 15
• Taking away 12 from 15
• Taking away 10 and then 2 from 15
• “Compare your thinking with other students at your table. Share the methods you used to find the missing numbers. If you disagree about an answer, work together until you come to an agreement.”
• 4 minutes: small-group discussion

### Student Facing

Find the number that makes each equation true.
Be sure you can explain your thinking in a way that others will understand.

Set A:

1. $$12 – 7 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
2. $$18 - 5 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
3. $$\boxed{\phantom{\frac{aaai}{aaai}}} = 14 - 6$$
4. $$15 - 12 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
5. $$13 - 4 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

Set B:

1. $$5 + \boxed{\phantom{\frac{aaai}{aaai}}} = 18$$
2. $$13 = \boxed{\phantom{\frac{aaai}{aaai}}} + 6$$
3. $$20 = 15 + \boxed{\phantom{\frac{aaai}{aaai}}}$$

### Student Response

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If students use the same method for each equation, consider asking:

• “How did you decide what method to use?”
• “How could you use addition to find the missing number?”

### Activity Synthesis

• Display $$15 - 12 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
• Invite previously identified students to share.
• “How is $$15 - 12 = \boxed{\phantom{\frac{aaai}{aaai}}}$$ different than all the other equations?” (All the others only subtract a one-digit number but this one is subtracting 12 so you can take away 10 and 2 more.)

## Lesson Synthesis

### Lesson Synthesis

“Today we used different methods for subtracting. What method do you like best for subtracting? Why is it your favorite method?”

## Cool-down: Unit 3, Section D Checkpoint (0 minutes)

### Cool-Down

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