I have test driven these photographs and questions with a 6-year old, an 8-year old, a 43-year old and a classroom full of 19—40 year olds. Good conversations were had with all populations. I turn them over to you. Use them for the forces of good, not evil.
Associative and distributive properties
How many Peeps in this picture?
Do you see 4 boxes of 12?
Or do you see 12 sets of 4?
The first could be notated
The second could be notated
That these two are equal is an instance of the associative property of multiplication.
There are, of course, other ways to view these guys, and to notate how you see them. The mathematics doesn’t live in the Peeps, it lives in the interactions we have around the Peeps.
Careful discussion and notation will demonstrate the associative property and/or the distributive property in each of the pictures below.
Which is more?
In each of the following images, are there more purple Peeps or more pink Peeps? Of special importance is this question: How can you know without counting?
Here is the full set of Peeps photos for easy downloading (.zip).
In the meantime, these guys are still hanging around my office. Got any other arrangements you’d like to see?
I know, for instance, that I wish I had a fifth box so I wouldn’t have repeated 4’s in that first picture.