Substitution Composer

Makes new shapes out of smaller shapes, and uses trial and error to substitute groups of shapes for other shapes to create new shapes in different ways. At this level, children solve Pattern Block Puzzles in which they must substitute shapes to fill an outline in different ways.


You may see this:

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Other Examples:

  • Given an outline of a hexagon shape, a child uses pattern blocks and through trial and error fills the shape multiple times. For example, once with 6 triangles and once with three rhombi.

Help your student become a(n) Substitution Composer

These activities challenge children to build the same shape in many different ways using different shape substitutions. Activities and encouragement should lead them to be systematic. As a simple example, they may make a pattern block hexagon from two trapezoids and then keep one of the trapezoids but substitute a blue rhombus and a triangle. Then they keep the trapezoid and the triangle, but substitute two more triangles for the rhombus. Ensure they do this intentionally, rather than by trial and error.

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.