Deepening Student Understanding of Area and Volume by Focusing on Units and Arrays

Abstract

When we teach elementary school students about area, surface area, and volume, we are teaching ideas that help them measure the physical world. In biology and chemistry, the surface area to volume ratio sets a limit to the size of cells, and is also a factor in the rate at which chemical reactions occur. Volume is important in measuring density, and in calculus, understanding area and volume is critical for understanding the construction of Riemann sums that are used to model accumulation of various quantities. In addition to these applied uses in science, technology, engineering and mathematics (STEM) fields, by teaching students these ideas, we are also giving them tools with which to understand other mathematics. For example, beyond serving as a measure of space, area can be used as a model for multiplication of real numbers and multiplication of expressions with variables.