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• #### Index 371-386

TABLE 6-1 Space and Shapes in Two Dimensions

 Steps/Ages (Level of Thinking) Goals A. Perceive, Say, Describe/Discuss, and Construct Objects in 2-D Space B. Perceive, Say, Describe/Discuss, and Construct Spatial Relations in 2-D Space C. Perceive, Say, Describe/Discuss, and Construct Compositions and Decompositions in 2-D Space Step 1 (Ages 2 and 3) Thinking visually/holistically Recognition and informal description (including at least circles, squares, then triangles, rectangles). Recognize shapes in many different orientations and sizes. Trial-and-error geometric movements (informal, not quantified). Use relational language, including vertical directionality terms as “up” and “down,” referring to a 2-D environment. Informally recognizes area as filling 2-D space (e.g., “I need more papers to cover this table”). Solve simple puzzles involving things in the world. Create pictures by representing single objects, each with a different shape. Thinking about parts Shapes by number of sides (starting with restricted cases, e.g., prototypical equilateral triangle, square). Step 2 (Age 4) Thinking visually/holistically Recognition and informal description at multiple orientations, sizes, and shapes (includes circles and half/quarter circles, squares and rectangles, triangles, and others [the pattern block rhombus, trapezoids, hexagons regular]). Recognize shapes (to the left) in many different orientations, sizes, and shapes (e.g., “long” and “skinny” rectangles and triangles). Match shapes by using geometric motions to superimpose them. Use relational words of proximity, such as “beside,” “next to,” and “between,” referring to a 2-D environment.

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