A few weeks ago I asked the boys what math they wanted to do for the summer. They decided on a summer project that they could work on together rather than the separate algebra / prealgebra math we did during the school year. Not the easiest task in the world given the 2.5 year age difference, but I ended up settling on a slow walk through Art of Problem Solving’s “Introduction to Counting and Probability.” Some parts of the book might be pretty challenging (and skipped for now!), but it looks like we’ll have a fun summer of basic combinatorics.

I got a nice surprise right off the bat and it showed quite directly the value of all of the work we’ve been doing with Fawn Nguyen’s material. Particularly the visual patterns:

http://www.visualpatterns.org/

The first section in the book discusses counting lists of numbers. One of the slightly complicated problems was counting the numbers in this list:

3 2/3, 4 1/3, 5, 5 2/3, . . . , 26 1/3, 27

My older son’s solution had a really nice grouping strategy that surprised me and clearly showed Fawn Nguyen’s influence:

Definitely going to be a fun summer!