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11.3 TeachingStudents need to understand that the perimeters of pairs of similar shapes are proportional to their corresponding side lengths but that their areas are proportional to the squares of the corresponding side lengths. NCTM Standards 2000. Page 245Design a sequence of pattern block activities, using no formulas, to help middle school students discover that figures enlarged by scale factors of 2, 3, or 4, have areas that increase by factors of 4, 9, and 16 respectively. Use diagrams to illustrate your activities. 11.3 Concepts Draw a small rectangle in the center of a sheet of paper. Place a point A inside the rectangle. With point A as the projection point and using a scale factor of 3, draw the image of the rectangle. Put a point B on the perimeter of the original rectangle. Using it as the projection point and a scale factor of 3, draw the image of the original rectangle. Put a projection point C outside the original rectangle and find a third image of the rectangle with projection point C and a scale factor of 3. Compare the three images for the three projection points and discuss their similarities and differences. 11.3 Concepts Suppose you were told to reduce a 12-inch by 12-inch photo by 1/3. This could mean to reduce the dimensions by 1/3 or to reduce the area of the photo by 1/3. For each case determine the new dimensions to the nearest tenth of an inch. If a copy machine allows you to reduce an image by settings in whole numbers from 100% to 50%, determine the machine setting for both of these cases to the nearest whole number percent. Explain your procedures. |