# Lesson 16

Subtract Within 1,000

## Warm-up: True or False: Equations Based on Place Value (10 minutes)

### Narrative

The purpose of this True or False is to elicit strategies and understandings students have for composing or decomposing numbers in different ways. These understandings will be helpful later when students decompose tens and hundreds when they subtract. In this activity, students look for and make use of structure of base-ten units (MP7) when they explain why statements are true or false.

### Launch

• Display one statement.
• “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategies.
• Repeat with each statement.

### Student Facing

Decide if each statement is true or false. Be prepared to explain your reasoning.

• 2 hundreds $$+$$ 3 tens $$+$$ 4 ones $$=$$ 2 hundreds $$+$$ 3 tens $$+$$ 14 ones

• 2 hundreds $$+$$ 3 tens $$+$$ 4 ones $$=$$ 1 hundred $$+$$ 13 tens $$+$$ 4 ones

• 1 hundred $$+$$ 13 tens $$+$$ 4 ones $$=$$ 1 hundred $$+$$ 12 tens $$+$$ 14 ones

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “How could we change the first statement to make it true?” (You could change 3 tens to 2 tens on the right side. You change the left side so it has 14 ones too. You could change the left side so it has 4 tens.)

## Activity 1: Jada’s Thinking (15 minutes)

### Narrative

The purpose of this activity is for students to interpret and connect different representations for methods that decompose to subtract by place. They also make sense of Jada's choice to use a number line to find the value of $$402-298$$ and critique her reasoning . Students then find the value of the difference in any way that makes sense to them to explain why they agree or disagree with Jada's reasoning (MP3).

This activity uses MLR8 Discussion Supports. Advances: listening, conversing

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Display Lin’s diagram.
• “Take a minute to make sense of Lin’s subtraction.”
• 1–2 minutes: quiet think time
• “Discuss Lin’s work with your partner.”
• 1–2 minutes: partner discussion
• Share and record responses.
• Highlight that a ten was decomposed and discuss student ideas about the numbers being subtracted.

### Activity

• “Jada and Lin both found the value of $$582 - 145$$. Work with your partner to compare Lin and Jada's work. Then complete Jada's work to find the value of $$582 - 145.$$
• 3–5 minutes: partner work time
• “Jada found the value of $$402 - 298$$ with a different method. Work with your partner to make sense of Jada's thinking. Discuss if you agree or disagree with Jada’s reason for why she chose this method.”
MLR8 Discussion Supports
• Display sentence frames to support partner discussion:
• “I agree because . . .”
• “I disagree because . . . ”
• 7–8 minutes: partner work time
• Monitor for students who share why they agree with some (or all) of what Jada says and those that disagree and use a diagram to show decomposing to subtract by place.

### Student Facing

Lin’s diagram:

1. Discuss how Jada’s equations match Lin’s diagram.
2. Finish Jada’s work to find the value of $$582 - 145.$$

1. Jada is thinking about how to find the value of $$402 - 298.$$

1. Jada says she knows a way to count on to find the difference. She showed her thinking using a number line.

2. Jada says you can’t decompose to find the value of $$402-298$$ because there aren’t any tens. Do you agree with Jada? Use base-ten blocks, diagrams, or other representations to show your thinking.

### Student Response

For access, consult one of our IM Certified Partners.

If students say they agree with Jada’s thinking about decomposing to find the value of $$402-298$$, consider asking:

• “What parts of Jada's reasoning do you agree with and why?”
• “Can you use base-ten blocks to show how she could subtract by place?”

### Activity Synthesis

• “How does Jada’s method for finding the value of $$402-298$$ work?”
• Record student explanation using a series of equations. ($$298+2= 300$$, $$300+100 = 400$$, $$400+2 = 402$$, $$2+100+2 = 104$$)
• “Why do you think Jada used this strategy?” (She thought you couldn’t decompose. She noticed 298 is close to 300 and 402 is close to 400.)
• “Do you agree with Jada that you can't decompose 402?” (I agree that there are no tens so it’s hard to subtract ones right away. I disagree that you can’t decompose. You can decompose a hundred first to get tens, then decompose tens to get ones.)
• Display the sentence frames to support the whole-group discussion.
• If time, select previously identified students to share how they decomposed to find $$402-298$$.

## Activity 2: Find It Your Way (20 minutes)

### Narrative

The purpose of this activity is for students to choose methods flexibly for finding the value of differences. Students might subtract by place, count on, or make an easier problem. There is no right answer to which method should be used for each problem. Students should choose a method that makes sense to them and justify their choice (MP3).

Engagement: Provide Access by Recruiting Interest. Provide choice. Invite students to decide the order of the problems to complete the task. They can choose to work through in any order.
Supports accessibility for: Social-Emotional Functioning, Organization

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• “We’ve learned how to decompose units to subtract by place and different ways to represent that. We’ve also learned other methods for subtracting. We use them when they make sense to us or when they make sense for the numbers in an expression.”

### Activity

• “Find the value of each expression using a method that makes sense to you. You’ll have a chance to share your work with others.”
• 6 minutes: independent work time
• Monitor for expressions that most students find the same way and expressions that many students find in different ways.
• “Find a partner who found the value of _____ the same way as you.”
• 1–2 minutes: partner discussion
• “Now find a partner that found the value of _____ in a different way than you. Share your thinking.”
• 2–3 minutes: partner discussion
• Repeat for additional expressions as desired.

### Student Facing

Find the value of each expression in a way that makes sense to you. Show your thinking. Organize it so it can be followed by others.

1. $$535 - 214$$

2. $$700 - 589$$

3. $$683 - 398$$

4. $$918 - 608$$

5. $$735 - 457$$

6. $$602 - 487$$

### Student Response

For access, consult one of our IM Certified Partners.

If students use the same method for each problem, ask students to think about how they could use Jada’s way to find the value of $$701 - 599$$. Consider asking:
• “What do you notice about the numbers in this expression that makes it easier to use Jada’s way?”
• “What other expressions do you see where you might try Jada’s way?”

### Activity Synthesis

• Have 3–4 students share a method or representation that someone they talked to shared.
• “What methods or representations do you want to try more?”

## Lesson Synthesis

### Lesson Synthesis

“In this unit, you added and subtracted within 1,000, composing and decomposing units when necessary. What are you most proud of learning? What do you still need to work on?”

## Cool-down: Find the Difference Your Way (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.

## Student Section Summary

### Student Facing

In this section of the unit, we learned many different ways to subtract three-digit numbers using what we know about place value. We used base-ten blocks, diagrams, and equations to show subtracting hundreds from hundreds, tens from tens, and ones from ones. We learned that when you subtract by place, you may decompose a hundred, a ten, or both. We learned that it is helpful to look closely at the numbers in an expression to plan how to decompose or to choose a method that helps us use friendly numbers or the relationship between addition and subtraction.

Base-ten Diagram for $$256-64$$

Unit Form for $$726-558$$
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