One of the earliest math concepts to acquire is sorting. Color, shape, amount...
I literally stumbled over this one morning. I had placed a square on the floor with red tape. I didn't mention it or point it out to the kids. In fact, I had another activity in mind. One I can no longer remember. But before I got to the activity, every child had found a red object in the room and placed it in the square. What a lesson in classification!
Another day I tried a green square. Once again, just taping it down and walking away. Within minutes, it was full of green items, including 2 kids wearing green!
Grasping a tong is a new skill for most preschoolers. Hesitate before you jump in to show them how it works. Lessons are better retained when a child goes through problem solving on the way. Along with the fine motor muscle development, the use of tongs requires motor planning and spatial awareness. Use it as a color sort or block building. Kids love to transfer items from one place to another and this way is always a hit.
A great introduction into geometry. Vocabulary acquisition of higher math concepts begins in preschool. Research shows that children who are exposed to mathematical vocabulary as preschoolers are better prepared for higher math in later educational settings.
"Can you stack the triangle on the circle?"
"Is the rhombus bigger than the cone?"
"Are there more blocks on the table or the floor?"
Then follow up with some one--to-one correspondence.