Consider these two division problems:
Problem A: 22 cookies. Each kid gets 10 cookies. How many kids can get a full share? How many are left over?
Problem B: 22 cookies. There are 10 kids. How many cookies does each kid get? How many are left over?
These are not copied verbatim from Tabitha’s third-grade homework this week, but the numbers and context are the same. (Forgive me; I didn’t think about the potential for large-group discussion until the homework went back to school.)
The point is this: One of these problems was very easy for Tabitha, and the other was very challenging.
Do you know which is which?
We talked about this on Twitter today. (Click through for some really outstanding discussion….seriously.)
I have written about the two major types of division problems before, and they are relevant here.
Problem A was a snap for Tabitha. She skip counts well, and she is a whiz with place value. How many 10s in 268? Why 26 of course! This is the sort of thing I’m talking about.
So Problem A above is a piece of cake for her. This problem—for Tabitha—is very clearly asking How many tens are in 22? For her, this isn’t really even a question worth asking. Each kid gets one ten. There are two tens. QED.
Problem B doesn’t submit to this strategy in an obvious way. It requires her to keep track of 22 things as they get shared among 10 kids. One for you, one for you, one for you, etc. That’s taxing work, and so it’s a much harder problem for her.
When we discussed this problem together the other night, I made the argument that you use up 10 cookies each time you give everybody one cookie. I wanted to help her see how her strategy from Problem A would be useful in Problem B, while respecting that—for her—the sameness of these two problems is not at all obvious.
What’s the moral of the story? Let me know your thoughts in the comments.