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9.4 TeachingStudents in grades 3-5 can explore shapes with more than one line of symmetry. For example: In how many ways can you place a mirror on a square so that what you see in the mirror looks exactly like the original square? Is this true for all squares? Can you make a quadrilateral with exactly two lines of symmetry? One line of symmetry? No lines of symmetry? If so, in each case, what kind of quadrilateral is it? NCTM Standards 2000, page 168Use a set of pattern blocks and a small rectangular mirror to devise and write a set of activities so that students can discover which pattern block pieces have line symmetry. Extend your activity to include some shapes formed by joining two or more pattern block pieces to form a new polygonal shape. 9.4 Concepts Make a tetrahedron from four identical paper or cardstock equilateral triangles. Using a wire such as an unbent paperclip, or a thin rod such as a knitting needle, as an axis of rotation, pierce the tetrahedron to determine the number and location of different axes of rotation. Describe your results so that a reader can reconstruct your process for determining the axes of rotation for a tetrahedron. 9.4 Concepts Read the following quote about line symmetry from the Standards 2000. Illustrate the ideas in this statement with diagrams accompanied by a narrative that explains the observations that can be made by looking at figures with symmetry. Looking at line symmetry in certain classes of shapes can also lead to interesting observations. For example, isosceles trapezoids have a line of symmetry containing the midpoints of the parallel opposite sides (often called the bases). Students can observe that the pair of sides not intersected by the line of symmetry (often called the legs) is congruent, as are the two opposite pairs of angles. Students can conclude that the diagonals are the same lengths, since they can be reflected onto each other, and that several pairs of angles related to those diagonals are also congruent. Further explorations reveal that rectangles and squares also have a line of symmetry containing the midpoints of a pair of opposite sides (and other lines of symmetry as well) and all the resulting properties. NCTM Standards 2000, page 237 |