Lesson 13

• 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

• “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “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.)

The purpose of this activity is for students to interpret base-ten diagrams that represent decomposing a unit when subtracting by place (MP2). Students analyze a base-ten diagrams that show decomposing a hundred into 10 tens. They make connections between representing with base-ten blocks and base-ten diagrams and between decomposing a hundred and decomposing a ten.

• Groups of 2
• Give students access to base-ten blocks.
• “Mai found the value of \(336-52\) using base-ten blocks. She started recording her thinking with a base-ten 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.

• “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

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?”

• 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.)

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 base-ten 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.

• Groups of 2
• Give students access to base-ten blocks.

• “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 base-ten diagrams and explain their steps clearly.

If students only use base-ten 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?”

• 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?”