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 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.

• “How did you match this expression and diagram?”
• “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 look for as you matched each diagram to an expression?” (I had to look at the numbers to see where I needed to decompose a hundred or a ten. I saw that the first diagram shows no ones left over, without decomposing a ten. The second diagram shows ones left over, with decomposing a ten. The third diagram shows ones left over, without decomposing a ten.)

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 terminology and provide them with opportunities to revise their language for precision and clarity.

• “What did you do to find the value of this difference?”
• “How could you use a diagram or an equation to record how you used the blocks?”

• 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 for finding the difference the same as yours? How is it different?”
  • “What questions do you have for _____ about their steps or their representation?”