# Lesson 5

Find the Difference

## Warm-up: Number Talk: Missing Value Within 10 (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for the relationship between addition and subtraction. Students who relate the pairs of equations are observing regularity in how addition and subtraction are related (MP8).

### 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

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the number that makes each equation true.

• $$6 + \boxed{\phantom{\frac{aaai}{aaai}}} = 10$$
• $$10 - 6 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
• $$8 +\boxed{\phantom{\frac{aaai}{aaai}}}= 10$$
• $$10 - 2 =\boxed{\phantom{\frac{aaai}{aaai}}}$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “Who can restate _______ 's reasoning in a different way?”

## Activity 1: Different Ways to Find the Difference (15 minutes)

### Narrative

In this activity, students analyze three different ways to subtract. They see that taking away is one way to find the difference, but that you can also count on or use known addition facts. Students further solidify their understanding that addition and subtraction are related, which sets the groundwork for a later activity when students solve subtraction problems within 10.

### Launch

• Groups of 2
• Give students access to connecting cubes or two-color counters.

### Activity

• “First you will work on your own. Think about what each student means and be ready to explain your thinking in a way that others will understand.”
• 5 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for students who can use the 10-frame with six red counters to explain the relationship between $$10 - 6$$  and  $$6 + \boxed{\phantom3} = 10$$ .

### Student Facing

Mai, Diego, and Noah find the value of $$10 - 6$$.

1. Diego says, “I can take away.” What does Diego mean?
Be ready to explain your thinking in a way that others will understand.

2. Mai says, “I can count on.” What does Mai mean?
Be ready to explain your thinking in a way that others will understand.

3. Noah says, “I can use what I know about $$6 + 4$$ to help me.”
What does Noah mean?
Be ready to explain your thinking in a way that others will understand.

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Invite previously identified students to share.
• “Who can restate what _____ just showed us?” (Diego subtracted by taking away 6 counters one at a time and saw that there were 4 counters left. Mai subtracted by thinking about addition. She counted on from 6 until she got to 10 and noticed she counted up 4. Noah knows his sums of 10. He knows 10 can be made by 6 and 4, so $$10 - 6 = 4$$.)
• “Which method do you like best?” (I know my sums to 10 so I would use that. I like counting on because I like to add more than take away.)

## Activity 2: Subtraction Number Strings (10 minutes)

### Narrative

The purpose of this activity is for students to identify patterns when subtracting (MP7). Students have access to connecting cubes and two-color counters to make sense of the problems and explain their thinking (MP1). As students subtract, they continue to develop relational thinking and notice that:

• as the subtrahend, or the number being subtracted, increases, the difference decreases.
• as the subtrahend decreases, the difference increases.

This vocabulary is not necessary to use with students. During the activity synthesis, select students who can explain each of the ideas. When students show their thinking using objects and mathematical language to explain why the concept is true, they construct viable arguments (MP3).

This activity uses MLR8 Discussion Supports. Advances: Listening, Representing

### Launch

• Groups of 2
• Give students access to connecting cubes or two-color counters.

### Activity

• 8 minutes: partner work time
• Monitor for students who can explain the pattern for Set 1 and Set 2 using 10-frames or drawings and mathematical language.

### Student Facing

Find the value of each difference in the subtraction string.
Explain what you notice.

Set 1:

$$6 - 1$$

$$6 - 2$$

$$6 - 3$$

$$6 - 4$$

What do you notice?
Why do you think this happens?
Be ready to explain your thinking in a way that others will understand.

Set 2:

$$9 - 8$$

$$9 - 7$$

$$9 - 6$$

$$9 - 5$$

What do you notice?
Why do you think this happens?
Be ready to explain your thinking in a way that others will understand.

### Student Response

For access, consult one of our IM Certified Partners.

### Advancing Student Thinking

If students start over with a new drawing or set of objects for each expression, consider asking:

• “Can you explain how you found the value of each difference?”
• “How can you use the same drawing you made for $$6 - 1$$, to find the value of $$6 - 2$$?”

### Activity Synthesis

MLR8 Discussion Supports
• Invite previously identified students to share.
• As students share, record their thinking with diagrams and equations.
• “Just like addition, there are patterns in subtraction. Understanding patterns can help you find differences.”

## Activity 3: The Value of the Difference (10 minutes)

### Narrative

The purpose of this activity is for students to find the value of differences within 10. Students are encouraged to think about how patterns in subtraction problems and knowing sums within 10 can help them find the value of the differences. Students may use take away or counting on methods. The problems are written for students to think about different methods for solving. For example, students may find the value of $$10 - 3$$ by taking away 3 to get 7, then see that they can find $$10 - 7$$ by knowing the relationship between 3, 7, and 10. Students should work in groups of 2, with a different partner than they had in the previous activity.

Engagement: Provide Access by Recruiting Interest. Provide choice. Invite students to decide which problem to start with.
Supports accessibility for: Social-Emotional Functioning, Attention

### Launch

• Groups of 2
• Give students access to connecting cubes or two-color counters.

### Activity

• “You will first find the value of each difference on your own. Then you will share your thinking with a different partner than last activity.”
• 5 minutes: independent work time
• 2 minutes: partner discussion

### Student Facing

Find the value of each difference.

1. $$9 - 6$$
2. $$10 - 3$$
3. $$7 - 3$$
4. $$9 - 5$$
5. $$8 - 6$$
6. $$6 - 5$$
7. $$9 - 4$$
8. $$10 - 7$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “Were there any expressions that helped you with another expression? How did they help you?” ($$10 - 3$$ and $$10 - 7$$. They are related because $$3 + 7 = 10$$. $$9 - 6$$, $$9 - 5$$, and $$9 - 4$$. There is a pattern. Since the number being subtracted gets 1 bigger, the difference gets 1 smaller.)

## Lesson Synthesis

### Lesson Synthesis

“Today we found differences within 10 and saw that you can use what you know about addition to find differences. To find the difference in a problem like $$9 - 5 = \boxed{\phantom{4}}$$, you can think about the sums of 9. I know that $$5 + 4 = 9$$, so $$9 - 5 = 4$$.”

“We say that 4, 5, and 9 are related. We can write both addition and subtraction equations with these numbers.”

“What are the addition and subtraction equations we can write with 4, 5, and 9?” ($$4 + 5 = 9$$, $$5 + 4 = 9$$, $$9 - 4 = 5$$, $$9 - 5 = 4$$.)

## Cool-down: Subtraction within 10 (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.