## Friday, November 25, 2022

### The Rectangle: an appreciation

[A recently rediscovered post from 11 years ago]

Only the Triangle gets a course to itself, but, as a tool for teaching math concepts in general, the Rectangle (including the special case of the Square) is, as it were, unparalleled.  Rectangles are, of course, the basic constituent of Singaporean bar modeling, substituting for x and y in word problems that might otherwise require algebra:

Mr. Lim read 10 pages from his book on Monday. Mr. Smith read three times as many pages as Mr. Lim. Their friend, Mr. Samy, read 15 pages more than Mr. Smith. How many pages did Mr. Samy read from his book?

Rectangles are also a good way to visualize multiplication:

5 × 9:

74 × 368:

including the commutative law of multiplication:

And the distributive law:

a (b  + c) = ab + bc:

And equivalent fractions:

And the factoring or multiplying out of quadratics:

And the area of triangles:

And the area under a curve:

Indeed, so versatile is the unassuming rectangle that I'm sure I've missed a number of other areas for which it is a powerful conceptual building block.