MathClub Ideas
I was asked to suggest some ideas for a
middle school Math Club meeting and/or MathCounts training..
Here are a few that I like.

Domino tilings

Mobius strips.

KenKen

The pairing game

Matchstick puzzles

Pascal's triangle

The subtraction game

The diameter and width of a polygon

A whirlwind summary of geometry (incomplete)
Part A 
Part B 
Part C 
Sols
(Under development)