Children starting school learn at their best when presented first with concrete representations of numbers rather than theoretical concepts. This is called the manipulative mode of thinking, meaning that they learn best using physical objects. Instead of trying to teach your child the number three first, show him three physical objects to begin. One example is to place three spoons in front of your toddler and then teach him the number's symbol, allowing your child to concrete the concept of the number 3.
Another math activity is to teach your children how to recognize math problems. Using index cards, you can create playing cards with simple math problems and their solutions on them. Make learning into a game by having your toddler make pairs from the cards. If your child has not developed to the point where she can recognize simple addition problems, you can have her match the pairs of symbols. As she progresses further into her development, you can create new index cards with increasingly more difficult math problems.
This activity is a fun way to teach your child to count and organize objects into groups. Make a dozen cupcakes and frost them in three different colors with your child. Add candles to one cupcake of each color. Have your preschooler count the number of cupcakes. Then, have your child count the number of cupcakes of each color, how many have candles, and how many candles are in each cupcake. Then, teach him to do simple addition and subtraction by removing cupcakes and asking him to count how many cupcakes are still on the table, the number of cupcakes left of one color, and how many cupcakes still have candles.
This activity will allow your child and his or her friends to use their muscles while learning basic counting and the concepts they will need in elementary school. Draw lily pads onto the ground in chalk close enough together that the children can leap from one to another easily. Draw around the lily pads in blue chalk to represent the lake where the frogs live. Cut out numbers from 1 to 10 and tape them into the center of your lily pads. For extra fun, add stuffed ducks, frogs and other toys to the pond. Each child will take his turn starting on the number one, then he will yell out the numbers he lands on afterward. Children should jump over each other if they can.