Lesson 12
Decompose to Subtract
Warmup: What Do You Know About 354? (10 minutes)
Narrative
Launch
 Display the number.
 “What do you know about 354?”
 1 minute: quiet think time
Activity
 Record responses.
 “How could we represent the number 354?”
Student Facing
What do you know about 354?
How could we represent the number 354?
Student Response
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Activity Synthesis
 “Why might you need to represent 354 in different ways?” (You might want to show the value of each digit to compare numbers. You might want to decompose to subtract.)
Activity 1: Subtract from 354 (15 minutes)
Narrative
The purpose of this activity is for students to subtract onedigit and twodigit numbers from a threedigit number using the methods that make sense to them. Each difference would require students to decompose a ten to subtract by place. They may count back or count on by place to find the difference. They may also use their understanding of place value and their experiences decomposing a ten when they subtracted within 100. In the synthesis, focus on connecting and comparing these different methods and making sense of representations that show decomposing a unit when subtracting by place.
When students use baseten blocks, number lines, or equations to find the value of each difference they use appropriate tools strategically (MP5).
This activity uses MLR7 Compare and Connect. Advances: representing, conversing.
Supports accessibility for: Attention, Conceptual Processing
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to baseten blocks.
Activity
 “Find the value of each expression in any way that makes sense to you. Explain or show your reasoning.”
 3–4 minutes: independent work time
 3–4 minutes: partner discussion
 Monitor for an expression that generates a variety of student methods or representations to share in the synthesis, such as:
 using baseten blocks
 drawing a number line
 writing their reasoning in words
 writing equations
Student Facing
Find the value of each expression in any way that makes sense to you. Explain or show your reasoning.
 \(354  7\)
 \(354  36\)
 \(354  48\)
Student Response
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Activity Synthesis
 Invite one previously identified student who used a method that did not explicitly show decomposing a ten to share.
 Invite one previously identified student to show how they decomposed a ten to subtract with baseten blocks or a baseten diagram.
 “What is the same and what is different about the ways _____ and _____ represented the problem?” (____ used baseten blocks and showed decomposing a ten. _____ showed a number line and counting back 36. They used the same numbers. They found the same difference.)
Activity 2: Decompose with Baseten Blocks (20 minutes)
Narrative
The purpose of this activity is for students to practice decomposing a unit to subtract by place. In this activity, all students use baseten blocks to find the value of each difference. Some students may be able to find the difference without blocks, but since this is the first time they decompose a unit when subtracting beyond 100, the blocks allow all students to see the work of decomposing a unit. This concrete experience will help students interpret other representations and anticipate when they may need to decompose units in future lessons. The blocks also provide a support for students as they create arguments for why they think they will decompose a unit and explain how they find the difference (MP3).
As needed, ask students to decompose a tower of ten connecting cubes into ones. Ask students how they would show the same decomposition with baseten blocks.
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students baseten blocks.
Activity
 “Now we are all going to use baseten blocks to subtract.”
 “Work with your partner to find the value of each expression. One partner will start by reading the expression and representing the larger number using blocks.”
 “The next partner will decide if they think they will decompose any units to subtract. Then they will take away blocks to show the difference.”
 “Discuss the difference and record it.”
 As needed, demonstrate with \(142  25\).
 10 minutes: partner work time
Student Facing
Work with your partner to find the value of each expression.
 Partner A: Read the expression and represent the larger number using blocks.
 Partner B: Decide if you will decompose a ten and explain. Then subtract.
 Discuss and write the difference.
 Switch roles.
 \(264  38\)

\(274  41\)
 \(336  115\)
 \(343  127\)
 \(485  266\)
 \(451  315\)
Student Response
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Advancing Student Thinking
 “Did you decompose a ten to subtract?”
 “How could you use the blocks to show that you decomposed a ten?”
Activity Synthesis
 Invite a group to share how to use blocks to find the value of \(336  115\).
 “What did _____ do to find the value of the difference?”
 Invite a group to share how to use blocks to find the value of \(343127\).
 “What did _____ do to find the value of the difference?”
Lesson Synthesis
Lesson Synthesis
“Today we saw that we can subtract by place with larger numbers, and sometimes a ten is decomposed.”
“How did you know when a ten would be decomposed when you subtracted threedigit numbers?” (I could tell when I looked at the ones place and saw I didn't have enough ones to subtract ones from ones.)
“How was this the same as when you subtracted twodigit numbers? How was it different?” (It was just like when we subtracted twodigit numbers. It's different because one of the numbers has hundreds.)
Cooldown: Subtract (5 minutes)
CoolDown
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