Lesson 16
Subtract Within 1,000
Warmup: True or False: Equations Based on Place Value (10 minutes)
Narrative
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
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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 \(402298\) 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
 Give students access to baseten blocks.
 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.”
 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:
Jada’s equations:

 Discuss how Jada’s equations match Lin’s diagram.
 Finish Jada’s work to find the value of \(582  145.\)

Jada is thinking about how to find the value of \(402  298.\)

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

Jada says you can’t decompose to find the value of \(402298\) because there aren’t any tens. Do you agree with Jada? Use baseten blocks, diagrams, or other representations to show your thinking.

Student Response
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Advancing Student Thinking
If students say they agree with Jada’s thinking about decomposing to find the value of \(402298\), consider asking:
 “What parts of Jada's reasoning do you agree with and why?”
 “Can you use baseten blocks to show how she could subtract by place?”
Activity Synthesis
 “How does Jada’s method for finding the value of \(402298\) 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 wholegroup discussion.
 If time, select previously identified students to share how they decomposed to find \(402298\).
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).
Supports accessibility for: SocialEmotional Functioning, Organization
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to baseten blocks.
 “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.

\(535  214\)

\(700  589\)

\(683  398\)

\(918  608\)

\(735  457\)

\(602  487\)
Student Response
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Advancing Student Thinking
 “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?”
Cooldown: Find the Difference Your Way (5 minutes)
CoolDown
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Student Section Summary
Student Facing
In this section of the unit, we learned many different ways to subtract threedigit numbers using what we know about place value. We used baseten 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.
Baseten Diagram for \(25664\)
Unit Form for \(726558\)