Informally, volume is the amount of (three-dimensional) “stuff.” The volume of a body of water is how much water there is. The volume of a sculpture […]

The number line is not just a school object. It is as much a mathematical idea as functions. Unlike the Number Line Hotel, hundreds charts, Cuisenaire rods, and base ten blocks, the number line is not just a pedagogical aid used only to help children learn; mathematicians refer to it, too.

"Circle" is a familiar word to most children very early, but with little more than an informal sense of "round." We sit "in a circle" without much thinking about how round it is, and without picturing the geometrical object associated with the word.

Area formulas Students who have the informal notion that area is the “amount of 2-D ‘stuff'” contained inside a region can invent for themselves most of […]

Length, width, height, depth Outside of the mathematics class, context usually guides our choice of vocabulary: the length of a string, the width of a doorway, […]