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 […]

"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.

A trapezoid is a quadrilateral with at least one pair of parallel sides. No other features matter. (In English-speaking countries outside of North America, the equivalent term is trapezium.)

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 […]

Although there are many kinds of symmetry, elementary school generally presents only reflective symmetry (or “mirror symmetry”). As a result, school materials tend to use the […]

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, […]