Build a classic birdhouse by cutting squares from wood for the sides and bottom, triangle gables and rectangles for the roof. Check your local craft stores for pre-cut shapes, though these may be too thin to make a birdhouse for more than decorative use.
The various traditions of patchwork quilting include a treasury of geometric shapes that combine in sometimes surprising ways. Start with a small square in the center, and border it on one side and then the other with rectangles that maintain the even measure of the square. The finished square, of whatever size, is known as "log cabin," but the effect, depending on the fabrics used to make the pieces and the orientations in which squares are combined, opens wide doors for creativity.
Bathroom and kitchen tiles are sold prearranged in mats, but broken groups may be available for experimentation. Plain small squares are also available in craft stores to set into clay for experimentation or concrete to make stepping stones. Add beads and glass pieces in other shapes, or simply see how a slight or a great angle between the squares changes the overall effect.
The ancient Japanese art of paper folding has gained a resurgence in the 21st century, but without much direct attention to how the objects are formed by geometry. Start with a square of paper and fold and refold it into rectangles and triangles to make an animal or even a geometric solid, such as a cube. Unfold the finished object to inspect the geometry of the folds and understand the magic.
Return to your tangram puzzle with any one-layer cake or brownie recipe. After baking, cut the cake into the pieces of a tangram. To emphasize the lesson to other members of the family, outline each piece with frosting.