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, […]

Informally: When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect […]

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 […]

Any counting number, other than 1, can be built by adding two or more smaller counting numbers. But only some counting numbers can be composed by multiplying two or more smaller counting numbers.

Reducing ambiguity by agreement In general, nobody wants to be misunderstood. In mathematics, it is so important that readers understand expressions exactly the way the writer […]

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.)

How to build mathematical vocabulary: Understand it well yourself (see glossary), and use it naturally (and correctly) in communication when you need it, in a rich enough context so that students can “figure out” the meaning from context, just as you might expect them to figure out the meaning of a new word that occurs in the middle of a story.

"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.

Children are extraordinary linguists! They acquire half their adult vocabulary and nearly all their adult grammar by the time they are 5 years old, mostly informally […]