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

Thinking about parts

Describe and name shapes by number of sides (up to the number they can count).

Describe and name shapes by number of corners (vertices).

Move shapes using slides, flips, and turns.

  • Use relational language involving frames of reference, such as “to this side of,” “above.”

  • Compare areas by superimposition. For rectangular spaces

  • Tile a rectangular space with physical tiles (squares, right triangles, and rectangles with unit lengths) and guidance.

Move shapes using slides, flips, and turns to combine shapes to build pictures. For rectangular spaces

  • Copy a design shown on a grid, placing squares onto squared-grid paper.

Relating parts and wholes

Sides of same/different length.

  • Right vs. nonright angles.

Predict effects of rigid geometric motions.

Combine shapes with intentionality, recognizing them as new shapes.

  • In an “equilateral triangle world,” create pattern block blue rhombus, trapezoid, and hexagons from triangles.

Step 3 (Age 5)

Thinking visually/holistically

Recognition and informal description, varying orientation, sizes, shapes (includes all above, as well as octagons, parallelograms, convex/concave figures).

 

 



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