The purpose of this activity is for students to use their understanding that numbers can be decomposed in different ways, to subtract within 1,000. They use what they know about place value to make sense of two different ways for finding the same difference (MP7). They describe how representing the number with enough tens and ones to subtract is helpful, rather than redrawing or exchanging blocks to represent decomposing a unit. They also learn that sometimes it may be necessary to decompose a hundred and a ten to subtract within 1,000.

If students do not see that Tyler’s first step and Clare’s first step show the same number, consider asking:

• “Can you show 244, with base-ten blocks or a diagram?”
• “Which unit in your representation did Tyler decompose? Which unit in your representation did Clare decompose?”

• Display students’ work that shows Tyler’s way and Clare’s way to find the difference.
• “How were Tyler’s way and Clare’s way the same? How were they different?” (Both show decomposing a ten and a hundred to subtract. Both show the same difference. Tyler decomposed a hundred first, and then a ten. Clare decomposed a ten first, and then a hundred.)

The purpose of this activity is for students to think about the numbers and attend to the values of the digits in subtraction expressions before beginning to subtract (MP7). Students determine whether or not they will decompose to subtract by place. They also determine whether they will decompose more than one unit. Students find the values of different expressions by using any method that makes sense to them.

• Display a chart completed from students’ responses.
• Ask students to choose an expression and to explain how they know it belongs in that column.
• “When you were finding the difference, did you use the same method for all 3 expressions? How did you choose your method?” (I used the blocks when I needed to decompose, but I didn’t when I didn’t need to decompose so I just wrote equations. Since I knew before starting when I was going to decompose, I knew I didn’t need the blocks for one of them.)