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| 10.2 Concepts NCTM’s Standards 2000, page 244, notes that formulas for the area of parallelograms, triangles, and trapezoids can be developed by using the formula for the area of a rectangle, along with an understanding that decomposing a shape and rearranging its component parts without overlapping does not affect the area of a shape. Show with diagrams and explanations how this can be done. 10.2 Teaching The basic concept involved in calculating area, determining the number of units required to cover a region or surface, is often poorly understood by children, in part because formulas are introduced too soon. Design an activity for students to determine the areas of figures by using grid paper, colored tiles, or unit squares cut from construction paper. Draw sketches of figures for this activity and include some for which students need to approximate the area by cutting or sketching parts of the basic unit to cover a region. Write a few questions to help students see that the number of unit squares needed to cover a figure is the measurement called area. 10.2 Concepts Studies have shown that school students often confuse the concepts of area and perimeter. One mnemonic device for helping students remember that perimeter is the distance around the boundary or “rim” of a figure is to point out that the word “rim” is included in “pe-rim-eter”. Devise an activity using string and colored tiles or grid paper to determine the areas and perimeters of a few figures. Write questions that will help students discover that it is possible for two figures to have the same area but different perimeters, and the same perimeter but different areas. |