Challenge preschoolers to use their critical thinking to solve triangle puzzles. Give each child seven toothpicks. Ask children to see how many triangles they can make out of their toothpicks. It's possible to make three by forming two triangles right next to one another, then placing the last toothpick over the gap between them. Some preschoolers will be able to figure this out and some won't, but they'll all learn to experiment by moving the toothpicks around in different formations.
Make palm trees using brown and green triangles. Give each child about 10 brown triangles and 20 green triangles cut from construction paper. Each triangle should be about an inch high. Show children a picture of a palm tree and ask them to form the triangles into the shape. Pass out large pieces of white paper and glue so children can glue their pictures together. To make the trunks, children should overlap their brown triangles. The straight sides of each triangle should point down, with the points facing up. Children can then overlap several green pieces to create branches, with the triangle points facing out away from the center of the tree.
Tangrams are games that challenge you to use smaller shapes to make larger images. Cut out a few dozen triangles for each child. Use different sizes and colors of paper. Have children experiment with moving their triangles into different formations to see what they can create. They may discover that they can create larger triangles, squares, and rectangles, or they may form different objects such as houses. When children have decided on one creation that they like, pass out paper and have children glue their triangle tangrams onto the paper.
Preschoolers likely don't realize that unlike squares or circles, triangles can have many possible variations depending on the angles and lengths of the sides. Teach preschoolers about this concept by cutting up hundreds of skinny rectangles. Create pieces that are anywhere from one inch to five inches long and a quarter of an inch thick. Spread out all the pieces and explain that a triangle must have three sides and three points. Let children experiment with making triangles out of them.