Use the images from the "The Very Hungry Caterpillar" such as apples, pears and plums and other foods and make several copies of each image. Glue the image of one apple on a blank index card and the image of two pears on another index card and so on. You can also mix different foods on each card. Continue to do this for 10 to 20 cards. On the other side of the index card, use a marker to write the number corresponding to the number of images on the other side. Children can count the number of foods on the index card and see the number on the other side.
Make addition flashcards by cutting out images of different foods that the caterpillar eats along its journey. Instead of using numbers for adding or subtracting, use the images of the foods in the story. On one of the index cards you can have an image of two plums plus one plum. The kids can count the number of plums and conclude that there are a total of three. On another card, you can have three apples plus one apple. The kids can count the number of apples and conclude that there are a total of four apples.
Write random numbers such as 9, 6, 8, 4, 3 and 5 down a piece of paper and make several copies. Beside each number, draw the head of a caterpillar. Kids draw circles to complete the body of the caterpillar based on the number beside the caterpillar's head. For example, they would draw three side-by-side circles beside the head that has the number three beside it. Likewise, you can can cut small colored circles from construction paper that the kids can glue on the paper.
Draw a caterpillar on a piece of paper. Erase some lines that you've drawn so that you can write numbers and draw dots for connecting in certain places on the drawing. Likewise, you can use tracing paper to trace some parts of the caterpillar that you've drawn and write numbers for connecting. Kids can complete the image and practice counting by connecting the numbered dots. After they've connected the dots, they can color the picture of the caterpillar.
Cut out different images of food that the caterpillar in "The Very Hungry Caterpillar" eats. Make several copies of each of the foods. Make sure that you make enough for this activity. Give your child a paper plate. Practice counting with your child by saying something like, "The caterpillar ate five pies. Can you put five pies on your plate?" The child looks for pictures of pies and should be able to place five of them on the plate. You can continue this game using all the different pictures of food.