There are numerous matchstick/toothpick puzzles which can be given to groups of children to prompt thinking, discussion and trials to get the correct answer.

1 matchsick used for side of a square. Matchsticks arranged in three squares in a row, then two more squares below two top left hand squares. Remove 4 to leave 2 squares...
6 matchsicks arranged in regualar hexagon, then 6 more laid from each corner to the middle. Rearrange 4 matchsticks to leave 3 equilateral triangles
1 matchstick used for a side of a square. 16 matchsticks arranged in row of four squares with one more square above right hand square. Rearrange 3 matchsticks to leave 4 squares of equal area