Understanding base-2 numbers (and other bases) is another good idea, though it's more suitable for a ten year old. Game: represent numbers using progressively

Understanding base-2 numbers (and other bases) is another good idea, though it's more suitable for a ten year old. Game: represent numbers using progressively more exotic representations: Base 10 Base 5 Base 2 Unary Then Fibonacci base (http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibrep.html http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci... ) Then Invent a place-value system using product of primes (inspired by fundamental theorem of arithmetic) Etc. This is a very "digital" set of exercises and it's very focused on counting. Logic will take care of itself.