Shape Composer

Composes shapes with anticipation (“I know what will fit!”). Chooses shapes using angles as well as side lengths. Rotation and flipping are used intentionally to select and place shapes. In the“Pattern Block Puzzles” below, all angles are correct, and patterning is evident. May begin substituing shapes, although not as comprehensive across shapes and tasks and as intentional as is a sign of those at the "Substitution Composer" level.

Practice-based Research: Seeing shapes as composed of various parts is central to early mathematics. This idea is connected to other mathematical topics—number, addition, fractions, and measurement.


You may see this:

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Other Examples:

  • Given an outline of a dinosaur originally made with pattern blocks, a child intentionally chooses shapes that will fill the puzzle and rotates and flips the shapes into place.

Help your student become a(n) Shape Composer

These activities provide shape puzzles without any internal guidelines and larger areas than those of earlier levels so children have to figure out how to fill the space by carefully composing shapes.

Practice-based Research: Carefully observe the level at which children are working. Shape Composers can combine shapes to make a new shape, such as using two triangles to make a rhombus, with growing anticipation: “I know what will fit.”  They focus more on composing regions of puzzles than merely on determining placements of specific shapes one by one. Although difficult to tell the difference, children who have fully attained this level do focus on composing shapes to make new shapes, going beyond just "finishing a puzzle" (Bofferding & Aqazade, 2022, Clements & Sarama, 2021).

Special Thanks To

Institute of Education Sciences
The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through grant numbers R305K050157, R305A120813, R305A110188, and R305A150243. to the University of Denver. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.