Use different colored balls to teach abstract concepts. Very young children can sort the balls by color and size. Older children can learn basic counting concepts from them. Use the balls to create sequential patterns, then have the child repeat the pattern or work out which color would come next in the pattern. Use the balls to teach the concept of odd and even.
Cut letters about 4 inches high out of sandpaper, and glue them to green painted cardboard. Have the child run his fingers over the number while you say its name. The sandpaper will help his fingers follow the pattern of the number.
Use a small bead stand to teach an understanding of math. The bead stand should have four wires strung across it, each with 10 beads that can move from left to right. Each string of beads should be in different colors. Use this to teach the children how to count to 10, then how adding 1 more makes 11, or by using all four strands, you can demonstrate how 4 plus 30 equals 34. Have the children count by 5 or 10 on the beads as well.
Create a spindle box by making 10 cardboard rows across a cardboard box so that you have 10 different compartments. Write a large number on each compartment, starting with 0 and ending with the number 9. Cut a dowel up so that you have 45 pieces. Have the child put one dowel piece in the number 1, two in the number 2, three in the number 3 compartment, on until the appropriate number of dowels are in each marked compartment. Show the child that there are no dowels in the compartment marked 0. This will introduce him to the concept of zero, as well as to associate the proper quantity with each number.