Geometry is a huge part of mathematics, although it often gets passed over in the school curriculum. Here are some great games and puzzles that help build geometric intuition. Some support more formal mathematical study as well.
Make two-and three-dimensional shapes from drinking straws. The three-dimensional shapes are particularly eye-catching. (Small hands will require some help with those.) You can also create towers using the straws – the most stable are built from triangles.
Pentominoes are a terrific source of fun and games. They can also be used to study a wide variety of mathematical properties.
For K-3 students, I would recommend five-piece tangrams instead of the classic seven-piece puzzles.
If you have a compass and straight-edge, make your own Magic Egg, then see what kinds of birds you can hatch from your egg.