Explore relationships among shapes, such as congruence, symmetry, similarity, and self-similarity. Students make a collection of natural shapes, including a wide variety of three-dimensional shapes such as fruits and vegetables, shells, flowers, and leaves. They describe the symmetry found in these shapes. Students find objects that exhibit self-similarity, i.e., that contain copies of a basic motif which is repeated at smaller sizes of the same shape. Examples of such objects arefeathers, the shape of a coastline, chambered nautilus shells, and plants which branch out such as cauliflower, broccoli, Queen Anne's lace, and ferns.
Students use scale models of cars and airplanes to study similarity.
They recognize that figures that have the same shape but different sizes are similar. Students look for lines in the classroom, identifying pairs of lines that are parallel, that intersect, or that are perpendicular. Students use the computer language Logo to describe the path made by a turtle as it goes around different geometric shapes. Students make a chart or bar graph showing how many squares, rectangles, triangles, etc., they find in their classroom. Students classify shapes according to whether they contain right angles only, all angles smaller than a right angle, or at least one angle larger than a right angle.