I am parent to a 4-year-old son who is mathematically precocious. An example of what I mean (since I'm sure guys like Gauss were proving theorems at 4):
- He multiplies and divides small numbers easily, like knowing that if there are 3 kids and 12 Halloween treats then everyone gets 4
- He understands the idea of prime numbers as those numbers of candies which can't be equally divided among his cousins
- He has figured out by himself the prime numbers up to ~20
- He is a LEGO fanatic and uses math as necessary - he can calculate that he needs nine 2x4 LEGO bricks to cover a 6x12 plate before he starts.
- He asked me what 12 times 12 is, then he announced that the carpet in the doctor's office has 144 squares.
I'm wondering how to help him engage more with math since he seems to enjoy it and is good at it. He's not ready yet for "Martin Gardner junior" style questions like "How many balance weighings would it take to identify the one low-weight gem among 9?" And I'm not sure I want to start him on things like memorizing addition and multiplication tables since that's not very relatable to the real world.
What kinds of concepts, questions, techniques, books, activities, etc. should I be introducing him to?