It has been a little difficult to find a good plan for math with the boys for this school year. They are attending the local schools and I don’t want to send them off to school tired or mentally burnt out, but I still would like to do a little math with them.

I’ve decided to look at the nuts and bolts of problem solving in math. Not academically, but rather just by talking through problems. This plan came from looking at problem #13 from the 2015 AMC 10a with them this weekend:

Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have?

There are many different ways to solve this problem. What was interesting to me was that they had a really hard time knowing where to start. The trouble getting started led to a long and pretty interesting (to me anyway) conversation about how to solve problems. That conversation made me want to explore problem solving in more depth with them this year.

Today was our first attempt. My younger son worked on 5 problems from a MOEMs test and my older son worked at 5 problems from the 1985 American Junior High math exam. After them were finished, they each picked on to talk about in a movie. Here are those conversations:

This video is my younger son talking through a problems from an old MOEMs exam – the problem is a mix of number theory and pre-algebra. The interesting idea for me in this problem is how a kid approaches an algebral-like problem before having had algebra:

This video is my older son taking about problem 23 from the 1985 AJHME – this problem is a counting problem + a little arithmetic. The interesting things for me in this video where (i) why my son thought the “trap answer” was wrong, and (ii) how he identified a pattern that helped him solve the problem.