Wednesday, September 7, 2011

The Rectangle: an appreciation

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.

1 comment:

FedUpMom said...

Oh, I like the distributive law demonstration. I'll show that to Older Daughter.

She was totally confused about when to apply the distributive law -- I finally told her "it's the distribution of multiplication over addition", and that seemed to help.