Lesson 13
Decompose Tens or Hundreds
Warmup: Which One Doesn’t Belong: Blocks and Blocks (10 minutes)
Narrative
Launch
 Groups of 2
 Display the image.
 “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
 1 minute: quiet think time
Activity
 “Discuss your thinking with your partner.”
 2–3 minutes: partner discussion
 Share and record responses.
Student Facing
Student Response
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Activity Synthesis
 “Which images could show a way to decompose a hundred? Explain.” (B because 10 tens is the same as a hundred. A is close, but I think it shows composing a hundred.)
 “Which images do not show a way to decompose a hundred?” (C because 10 ones are not the same as a hundred. D because it could show a ten as 10 ones.)
Activity 1: Subtract with Baseten Diagrams (15 minutes)
Narrative
The purpose of this activity is for students to interpret baseten diagrams that represent decomposing a unit when subtracting by place (MP2). Students analyze a baseten diagrams that show decomposing a hundred into 10 tens. They make connections between representing with baseten blocks and baseten diagrams and between decomposing a hundred and decomposing a ten.
Advances: Reading, Writing
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to baseten blocks.
 “Mai found the value of \(33652\) using baseten blocks. She started recording her thinking with a baseten diagram.”
 “Take a minute to look at Mai’s diagram. What did she do in Step 2?”
 1 minute: quiet think time
 “Talk to your partner about Mai’s representation. Explain what she is doing in each step.”
 1–2 minutes: partner work time
 “What does Mai do in her first step?” (First, she draws 336 with 3 hundreds, 3 tens, and 6 ones.)
 “What does Mai do next?” (Next, she breaks apart a hundred into 10 tens.)
 “What should Mai do next to find the difference? Show your work on Mai’s diagram.”
 1–2 minutes: independent work time
 “Share your thinking with your partner.”
 Display sentence frames:
 “First, I . . .”
 “Then, I . . .”
 “The difference is . . .”
 Invite a student who describes crossing out tens first then ones and a student who describes crossing out ones first then tens to share their steps and the difference.
Activity
 “Work with your partner to match each expression to one of the diagrams. Then find the value of each difference.”
 3–5 minutes: partner work time
Student Facing
Mai used baseten blocks to find the value of \(33652\). Then, she started making a diagram to show her work.
Explain what Mai did in Step 2. Show what Mai should do next to find the difference.
Step 1
Step 2
Write each expression next to the matching diagram. Then find the value of each difference.
\(244  28\)
\(256  64\)
\(244  64\)

Student Response
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Advancing Student Thinking
If students match an expression to a diagram that doesn't show the same value, consider asking:
 “How does the diagram show each number in the expression?”
Activity Synthesis
 Invite students to share the expression that matches each diagram.
 “What did you have to pay attention to as you matched each diagram to an expression?” (I had to look at the numbers that were being subtracted. I looked for where there were more tens or more ones drawn when there weren’t enough tens or ones.)
Activity 2: Decompose a Ten or Hundred (20 minutes)
Narrative
The purpose of this activity is for students to subtract by place and record their thinking. Students decompose either a ten or a hundred as they subtract. They should have access to baseten blocks, but can represent their thinking in any way that makes sense to them. Throughout the activity, as students share their thinking with their peers, listen for the way they use place value vocabulary and provide them with opportunities to revise their language for precision and clarity.
Supports accessibility for: Language, Attention, SocialEmotional Functioning
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to baseten blocks.
Activity
 “We are going to practice subtracting by place. Show your thinking in a way that will make sense to others.”
 5 minutes: independent work time
 4 minutes: partner work time
 Monitor for students who use baseten diagrams and explain their steps clearly.
Student Facing
Find the value of each difference. Show your thinking. Try Mai's way for one expression.
 \(245  28\)
 \(352  71\)
 \(364  182\)
 \(293  147\)

Share how you found the value of one of the expressions to your partner. Use the sentence frames to help explain:
 “First, I . . .”
 “Next, I . . .”
 “Then, I . . .”
 “Last , I . . .”
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
If students only use baseten blocks to solve and do not show their thinking with a diagram, equations, or words, consider asking:
 “How could you record how you used the blocks with a diagram or with equations?”
Activity Synthesis
 Invite previously identified students to share how they found the value of each difference.
 After each student shares, consider asking:
 “Did _____ decompose to subtract? Why? How can you use their diagram to tell?”
 “How is _____’s method the same as how you found this difference? How is it different?”
 “What questions do you have for _____ about their steps or their representation?”
Lesson Synthesis
Lesson Synthesis
“Today we decomposed tens or hundreds to subtract by place.”
Display \(534  41\) and draw a baseten diagram to represent 534.
“Kiran wanted to take away by place and use a baseten diagram to keep track of his thinking. First, Kiran drew 534 as 5 hundreds, 3 tens, and 4 ones. What could Kiran do next? Explain.” (He could take away 1 one because he has enough to subtract. He could cross out 1 hundred and draw 10 tens, because he needs more tens to subtract.)
Cooldown: More Subtraction (5 minutes)
CoolDown
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