3D Row and Column Structurer

Able to coordinate flexibly filling, packing, and building aspects of volume. Shows a propensity for additive comparisons (e.g., "this one has 12 more") but may show some nascent multiplicative comparisons (e.g., "this one is four times as big"). Initially counts or computes (e.g. number of rows times number of columns) the number of cubes in one layer, and then uses addition or skip counting by layers to determine the total volume. Eventually moves to multiplication (e.g. number of cubes in a layer times number of layers).


You may see this:

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Other Examples:

  • Counts or computes (row by column by height) the number of cubes in one row, and then uses addition or skip counting to determine the totals.
  • Computes (row times column times height) the number of cubes in one row, and then multiplies by the number of layers to determine the total.

Help your student become a(n) 3D Row and Column Structurer

Activities help children continue to develop spatial structuring–organizing objects in space such as cubes into rows, columns, and layers. Here, children might make one row of cubes in the bottom of a container, then skip count or multiply to figure how many rows will make one layer on the bottom. They then can skip count to figure out how many layers. Such thinking leads to, but is just as or more important than, learning a formula such as V = l * w * h.

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.