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6. to identify a shape from visual clues• gradually reveal a shape, asking students to identify at each stage possible names for the shape. 7. to empirically derive (from studying many examples) “rules” and gen¬eralizations• From tiling and measuring many rectangles, students see that “b x h" is a shortcut for adding the number of tiles.8. to identify properties that can be used to characterize or contrast dif¬ferent classes of figures• Ask, “Opposite sides equal describes . . .”• Explore the relationship between diagonals and figures by joining two cardboard strips. A square is generated by the end points when . . . (the diagonals are congruent, bisect each other, and meet at right angles). Change the angle and , the diagonals determine ... (a rectangle). Noncongruent diagonalsgenerate ...
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