January 9, 2020

Measurement: Volume

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 […]
January 9, 2020

Shape: Equiangular

The term equiangular indicates that, in some figures, the angles are equal. It can be used to describe polygons, such as an equiangular pentagon.
December 3, 2019

Right Angle

Meaning: an angle that matches the corner of a (rectangular) piece of paper, or the angle at the base of a capital L or the top of a capital T.
December 3, 2019


The word dimension is related to the word measure. It is used in two ways in geometry. It is used to specify a measurement: “What are […]
December 3, 2019

Shape: Circle

"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.
November 21, 2019

Shape: Trapezoid

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.)
November 21, 2019

Shape: Quadrilateral

A quadrilateral is a polygon that has exactly four sides. (This also means that a quadrilateral has exactly four vertices, and exactly four angles.)
November 21, 2019

Measurement: Discovering formulas for area

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 […]
November 20, 2019


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 […]
November 4, 2019

Measurement: Length, width, height, depth

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, […]