TABLE 6-2 Space and Shapes in Three Dimensions

Steps/Ages (Levels of Thinking)


A. Perceive, Say, Describe/Discuss, and Construct Objects in 3-D Space

B. Perceive, Say, Describe/Discuss, and Construct Spatial Relations in 3-D Space

C. Perceive, Say, Describe/Discuss, and Construct Compositions and Decompositions in 3-D Space

Step 1 (Ages 2 and 3)

Thinking visually/holistically

See and describe pictures of objects of all sorts (3-D to 2-D).*

Understand and use relational language, including “in,” “out,” “on,” “off,” and “under,” along with such vertical directionality terms as “up” and “down.

Represent real-world objects with blocks that have a similar shape.

  • Combine unit blocks by stacking.

Thinking about parts

Discriminate between 2-D and 3-D shapes intuitively, marked by accurate matching or naming.



Step 2 (Age 4)

Thinking visually/holistically

Describe the difference between 2-D and 3-D shapes, and names common 3-D shapes informally and with mathematical names (“ball”/sphere; “box” or rectangular prism, “rectangular block,” or “triangular block”; “can”/cylinder).

Match 3-D shapes.

  • Uses relational words of proximity, such as “beside,” “next to” and “between,” “above,” “below,” “over,” and “under.”


Thinking about parts

Identify faces of 3-D objects as 2-D shapes and name those shapes.

  • Use relational language involving frames of reference such as “in front of,” “in back of,” “behind,” “before.”

Identify (matches) the faces of 3-D shapes to (congruent) 2-D shapes, and match faces of congruent 2-D shapes, naming the 2-D shapes.

  • Represent 2-D and 3-D relationships with objects.

Combine building blocks, using multiple spatial relations.

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