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 and critique her reasoning. Students then find the values 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.

• “How does Jada’s method for finding the value of  work?”
• Record students’ explanations, using a series of equations. (, , , )
• “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 she can’t decompose 402?” (I agree that there are no tens, so it’s hard to subtract ones right away. I disagree that she can’t decompose. Jada can decompose a hundred first to get tens, and then decompose tens to get ones.)
• Display the sentence frames to support the class discussion.
• If time, select previously identified students to share how they decomposed to find .

The purpose of this activity is for students to flexibly choose methods for finding the values 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 then justify their choice (MP3).

• “How could you use Jada’s way to find the value of ?”
• “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?”

• Invite 3 or 4 students to share a method or a representation that someone they talked to shared.
• “What methods or representations do you want to use more?”