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From an early age, children make sense of the shapes they see in the world around them.

## Learning Benefits

Hover over each Learning Benefit below for a detailed explanation.
Shapes
Measurement
Geometry

Young children "do" math spontaneously in their lives and in their play. We've all seen preschoolers exploring shapes and patterns, drawing and creating geometric designs, taking joy in recognizing and naming specific shapes they see. This is geometry — an area of mathematics that is one of the most natural and fun for young children.

Preschoolers' intuitive knowledge of geometry frequently exceeds their numerical skills. By building on strengths and interests that are already present, you can foster enthusiasm for math and provide a logical context to develop number ideas.

In a preschool classroom you might see a scene like this: A teacher challenges Michelle and Debbie to use their bodies to make a shape together. The girls sit down facing each other and stretch their legs apart. With feet touching, they create a diamond. Another child takes a look, sees the diamond shape, and says: "If we put someone inside, we can make two triangles." Immediately, they ask Ray to scrunch in and lie across the middle.

It works! A diamond can be divided into two triangles. Michelle notes that there's a shape that has six sides, and she wants to try making one of those. Another child may even know that the shape is called a hexagon. After a brief discussion, Michelle gets five other children together. Then, under her direction, they all lie down on the floor and create a six-sided shape.

Preschoolers are learning to make mental images — pictures they can carry in their minds. Young children tend to form static images — "still" mental pictures they can refer to. Older children are learning to form dynamic images that they can move or change. For example: Five-year-old Brian eyes the gerbil cage, trying to figure out if it will fit in the back of his mother's car. He thinks so, and later that day he finds out he's right. Building children's geometric imaginations is an important part of exploring spatial relations and experiencing mathematics.

By age six, children often have stable yet limiting ideas about shapes. Four-year-old Tina tells her mother, "That's not a square. It's too big. A square looks like this." Her friend Charlie adds, "Triangles have to be this way. That's not a triangle. It's too upside down." Broaden your child's understanding by pointing out a variety of examples — squares that are many sizes and triangles that are "long," "skinny," "fat," and turned in many directions. You can also encourage deeper thinking about shapes not just through hands-on activities and discussions, but through picture books such as The Greedy Triangle by Marilyn Burns.

Mapping the World
What can preschoolers understand about place and movement mathematically? Is it reasonable to think that your young child could actually make and use maps? Consider this:

• Many three-year-olds can build simple but meaningful maps with landscape toys such as houses, cars, and trees. Some can even replicate a room in miniature using blocks, toys, and other props.
• Many older preschoolers know about relative distances between landmarks. For example, without having been specifically told, four-year-old Andrea may know that there is a greater distance between her house and Grandma's than there is between her house and the stop sign on the corner.
• Many children can also place locations based on a route. Let's say you take a walk to the store with your child. You leave your house, turn right, go down the street one block, turn right again, and walk one more block to the store. Back at home, stand in front of the house with your child and ask him where the store is. Without ever having walked the route "as the crow flies," your child points diagonally in the direction of the store.
• When challenged to learn a route through a playhouse that had six rooms, four-year-olds who examined a map beforehand learned a route more quickly than those who did not.

Geometry can be the most fun and naturally engaging aspect of mathematics to explore with your child. As children learn about the structure of shapes and space, they are building on what they already know. But we must all keep in mind that children learn these ideas most effectively through active engagement with toys, blocks, puzzles, manipulatives, drawings, computers — and, of course, you!