Manipulatives gone wild!

Things have taken a turn for the worse for last week’s Peeps.

These crocodiles came to school today to kick off some probability work. I’ll report back on that shortly.

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Peeps math with Tabitha

After the Peeps photo session last week, I test drove my images with Tabitha (six years old).

Me: Which are there more of in this picture? Purple Peeps or pink?

Tabitha: Purple.

Me: How do you know?

T: It goes all the way to the top.

Piaget would be proud. Tabitha’s focus is on one dimension, rather than on overall quantity. So let’s test that hypothesis. Does she really believe that’s all that matters?

Me: What about in this picture?

T: Purple.

Me: But they both go to the top in this one.

T: This one (purple) has full rows, and this one (pink) has holes.

Me: Interesting. You know what I see? I see that if you moved that last bunny on the bottom row up to the next row, you’d have two rows of three and an extra bunny, while the purple has three rows of three.

T: Yeah.

Me: OK. One last one. What about this picture?

T: Purple.

Me: Because it goes to the top?

T: Yeah.

Me: Look carefully, though.

T: Pink.

Me: Why?

She proceeds to count 9 pink bunnies. I correct her and have her count over. She again counts 9 pink bunnies. I show her that if you move the two top purple bunnies into the second row, you would fill that row. She is uninterested and we move on to other things.

Math Peeps at Play

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.