Using AoPS’s “Intro. to Number Theory” to build number sense

I love the books from Art of Problem Solving.  Not just because of the subjects that the books cover, but also because the books give me a great chance to secretly review other subjects.

The Introduction to Number Theory book is amazing all by itself.  What makes me love it, though, is the opportunity it gives my younger son to build number sense.

Here’s a pretty typical example from this morning.  The problem (from the review section in Chapter 4) asks you to list the common divisors of 84 and 132.   I assume that the point of the problem is for the student to find the greatest common divisor, but instead my son lists all of the divisors and gets some great arithmetic practice.

Here’s the first part of the problem:

and here’s the 2nd half.

It is fun to watch him build up his number sense. There will be plenty of time to talk about greatest common divisor later!