3D Array Structurer

Has an abstract understanding of the rectangular prism volume formula. Shows a propensity for multiplicative comparisons, coordinates multiplicative and additive comparisons flexibly. With linear measures or other similar indications of the three dimensions, multiplicatively iterates cubes in a row, column, and/or layers to determine the area. Constructions and drawings are not necessary. In multiple contexts, children can compute the volume of rectangular prisms from its dimensions and explain how that multiplication creates a measure of volume.


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Other Examples:

  • Children determine that they need 24 blocks to fill a rectangular prism based on a 3 x 4 x 2 net of the prism.

Help your student become a(n) 3D Array Structurer

Activities help children understand and use a formula for the volume of rectangular prisms, V = l * w * h, because it is a meaningful way to figure out, for example, the number of cubes in a bottom layer of a container as length times width and then the number of cubes in the entire container–that number times the height. Discussions of these concepts and of spatial structuring in the children's solutions keep the formula from being only "rote."

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.