You will find on this site many games like Nim games (Wythoff, Kayles or others), 2-persons games (Tail and Heads, Paper scissors...) logical games, puzzles.
Arithmetic: primes, probable primes, dividers, aliquot sequences, prime decompositions, prime constellations, practical numbers, amicable pairs, perfect numbers.
Syracuse sequence or Collatz 3x+1 problem, Fibonacci sequence, Flavius Josephus, the number pi...
Cellular automatas: the game of life, cellular art.
Elementary alculations: mortgage payment calculator, triangle surface, cone and truncated cone development and volume.