What Do You Notice? Visualizing Numbers

Skills

Primary students (K-2): patterns, shapes, counting

Intermediate students (3-5): patterns, shapes, factors, multiplication

Mathematical Background

This is a fabulous way to visually show the factors of a given number. Pairs show 2 as a factor; triangles show 3 as a factor; squares show 4 as a factor. Circles are prime numbers (except for ‘1’ which is not prime.) ‘2’ and ‘3’ which are prime do not look exactly like circles since they have so few dots. But from 5 on, the primes are visible as circles. The non-circles, then, are our composite numbers.

Let’s take a look at the number ‘28’. Visually, ‘28’ is represented by 2 as a factor (pairs), 4 as a factor (squares), and 7 as a factor since there are 7 groups. Of course, ‘1’ and the number itself, ‘28’ are also factors.
I originally saw this on youcubed.org but found a lot more information and a great colorful graphic of even more numbers by clicking here.

Sample Student Responses

"I see numbers one to 28 with dots."

"Circles are prime numbers."

"The dots go up by one on each time."

"Numbers are grouped a certain way."