Initial Composite 3D Structurer

Understands cubes as filling a space but does not use layers or multiplicative thinking. Moves to more accurate counting strategies. Relates number of cubes to cubic units as measured by capacity. Given a graduated cylinder marked in cubic-inch units, child understands that sand filled to the 10 in the cylinder would fill a box that holds ten, 1-inch cubes. Begins to visualize and operate on composite units such as rows or columns (what we call a 1x1xn core). Iterates to pack the space completely, accounting for “internal/ hidden” cubes. Decomposes space, allowing for accurate use of units and subunits. Recognizes when a box is half full, visualizes remaining rows or columns.


You may see this:

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Other Examples:

  • Counts unsystematically but attempts to account for internal cubes.
  • Counts systematically, trying to account for outside and inside cubes.
  • Counts the numbers of cubes in one row or column of a 3D structure and using skip counting to get the total. 

Help your student become a(n) Initial Composite 3D Structurer

Activities help children start to develop spatial structuring–organizing objects in space such as cubes into rows, columns, and layers. Challenge childen to organize their counting, such as counting in rows and then keep counting or making such rows.

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.