Work with preschoolers on counting orally before introducing numbers. Kids can toss a ball to a partner, stack blocks or drop seeds in dirt while counting aloud. Show children number cards and have them perform jumping jacks, toe touches or arm circles the correct number of times. Make two sets of number cards and let kids play a matching game. Encourage children to play hopscotch or "I Spy" to build number recognition skills. Preschoolers can form numbers out of play dough or yarn, or write numbers in sand, salt or shaving cream.
Start by making a pattern and having children copy you or add to your pattern. Later, children can create their own patterns. Preschoolers can line up different sizes or colors of blocks or toys to make patterns. Kids can stamp sponge shapes onto paper or glue on different types of pasta or beans in a pattern. The CoolMath website suggests threading colored pieces of cereal onto a piece of yarn to make a pattern necklace.
Help preschoolers identify shapes in the environment by talking about the shapes of food containers, household objects or street signs. Kids can cut pictures out of old magazines and sort them by shape to make collages. Show children how to make three-dimensional shapes using straws connected by pipe cleaners or toothpicks connected by balls of play dough. Bend wire clothes hangers into different shapes, then let kids use them to blow bubbles, as suggested by Michigan's Family FUNdamentals for Literacy and Mathematics.
Pre-K kids may be too young to measure with standard units of inches, feet or centimeters. Instead, preschoolers can measure length by lining up pencils, shoes, toy cars or other objects. Children can sort items into groups by size or arrange dolls, plastic animals or block towers from shortest to tallest. Help kids measure and compare weight using a rocker balance or a scale. The concept of volume is difficult for preschoolers to grasp, so provide plenty of opportunities for children to explore this idea. Kids can pour water, rice or sand from one container to another container of a different size or shape. Explain to children that although the shape of the material changes, the amount of material stays the same.
Create a graph as a whole class using a pocket chart on an easel or by taping grid lines onto the floor. Preschoolers can help make a graph that displays the number of letters in their names, eye colors, shoe sizes or number of family members. Graph children's favorite pizza toppings, ice cream flavors or story characters. Kids can sort candies or cereal into groups, then graph the number of each color. Take a nature walk and record tally marks for the number of birds, squirrels, bugs or other animals the children saw. Return to the classroom and graph the results.
Introduce older preschoolers to addition and subtraction through the use of number stories. Give children numbers of objects and have them act out a number story. For example, say "Kendra has six feathers, and Michael has two feathers. How many feathers do they have together?" Alternatively, kids can illustrate number stories above a written math problem. Children can sort dominoes under number cards by counting both sides of the domino and adding them together. Kids can stack connecting blocks or unit cubes together, then break them into two pieces. Kids write down the number of blocks in each piece, then count them all together to find the sum.