If you don't have the budget for brand-name building toys, you can let your children build geometric models out of straws and modeling clay. Show children how to roll a small piece of clay into a ball and stick a straw into it, then keep adding balls and straws as the vertices and edges of a two-dimensional shape or three-dimensional solid. Children create flat polygons like a square or pentagon by laying straws out on a table and then connecting them with clay.
Plastic construction bricks with raised bumps provide an automatic visual cue about the dimensions of the top surface of a shape. Introduce elementary school students to the geometrical concept of dimensions by guiding them to build rectangular prisms out of construction bricks. Students can then count the bumps along the length and width and the number of block layers in the height to find the dimensions of the prism. Some students may find this activity easier to understand if you start with rectangles before moving on to rectangular prisms.
Inflate brown paper lunch bags, fill them with crumpled newspaper and tape or staple the tops shut to create inexpensive items that children can shape or combine into various geometric solids. Older elementary school students will have fun trying to mimic shapes you create, such as forming a pyramid by squeezing the top of the bag or patting the stuffed bag into a sphere. If desired, you can use tape loops with the sticky side out to connect individual shapes into larger combinations, creating a pyramid out of spheres or a large cube out of small cubes.
Pipe cleaners are easy for children to manipulate into new shapes and connect to create geometric sculptures. Guide children through the process of twisting the ends of pipe cleaners together to form zigzags, branching tree shapes or geometric solids. If children have trouble twisting the ends of a pair of pipe cleaners together, show them how to leave about 1/2 inch of each pipe cleaner sticking out past the intersection and twist the protruding ends like the key to a wind-up toy.