Geometry and art sometimes go hand in hand. Have students choose a real-world object. It can be just about anything that can be broken down into geometrical shapes: a fire hydrant, a desk, a chair, a coffee mug or anything else. Have students draw a picture of an object using only the geometrical shapes you've studied, for example, triangles, rectangles and circles. This will vary depending on the grade level. Let students color their picture using pencils or markers. For older students, have them calculate the surface area of each geometrical shape and add up those figures.
Geometry is present in abstract designs as well. This project works for any grade level. Give each student a large sheet of white paper with a large octagon drawn or printed upon it. Give each students a ruler, a pencil and an eraser. Have students draw straight lines linking any two corners of the octagon. The result will be a crystal-like design with a high degree of symmetry. Have students color the resulting miniature triangles in different colors. Hang the designs on the wall or a bulletin board.
This project teaches the application of lines, angles and shapes and is appropriate for older elementary students. Have students design a map of a town or neighborhood. List elements that must be included, such as a set of parallel and perpendicular streets, a pizza parlor shaped in a triangle, a school shaped in a rectangle and anything else that seems applicable. Let students color in their maps. Once the map complete, students must write three to five sets of directions from one place to another.
This project works well for kids of any age. Have students choose one of the shapes you've been studying. Students must make a list of at least 10 objects that contain this shape. Have students write a story from the perspective of the shape, taking into account the different roles they play. For example, the autobiography of a triangle might include details of how happy he is to dig in the garden as a spade, but unhappy when he is eaten as a slice of pizza.