Katie, at nine years old, rarely asks me to give her math problems. She always has a lot on her mind and gets plenty of problems from school and other math-related activities (interesting problems do sometimes come up spontaneously in “everyday life” and she is often willing to think about those).
Zoe, on the other hand, at almost five, often asks me to give her problems to work on. It usually sounds like this, “Mom, can you give me a math problem, but without numbers and without pluses and minuses?” I have discovered that what she means by this is that she doesn’t want a straightforward arithmetic problem like 6+7, but rather wants a “story” problem. And if she has to add/subtract numbers in the process of solving, then it’s okay.
A few days ago, Zoe used her usual formulation to ask me for a problem. I decided to try out on her some problems similar to ones I had been recently doing with my first graders in class.
First, I asked Zoe for a 4-legged animal. Inspired by a recent picture that her grandparents sent while vacationing in Florida, Zoe named the crocodile. The problem I gave her was as follows:
Some crocodiles are swimming in a lake. An underwater photographer takes their picture from below. His picture comes out with only the feet visible, and there are 20 of them. How many crocodiles are in the picture?
In class, the students would solve this problem by drawing a picture. However, we were in the car so Zoe did not have that option. She came up with many wrong answers before arriving (with some help) at the correct one. However, we had a great conversation and many laughs discussing and interpreting her proposed answers.
Zoe: I know, the answer is 10.
Me: How did you come up with that?
Zoe: Because 10 plus 10 is 20.
Me: So your crocodiles only have 2 feet each?
Zoe: Oh yeah. Well then it must be 20.
Me: 20 crocodiles and 20 feet, so how many does each one have?
Zoe: One foot! (Some laughter and silliness). Ok, then 40.
Me: Ah, now some of your crocodiles don’t have any feet! (This caused even more amusement).
We did get to the correct answer eventually, by starting with the legs of one crocodile and working our way up.
Whereas Zoe was seriously proposing her answers, she was very quick at realizing what was wrong with each one. I think she learned a lot more from our conversation than if she had just gotten the correct answer right away, and the process was definitely a lot more enjoyable for both of us.