# Category Archives: Problems (math)

## Common numerator fraction division [#algorithmchat]

My future elementary teachers explore the common denominator fraction division algorithm at the end of the semester. Reading their work got me thinking about common numerator fraction division, and about what sense I could make of the symbols that result.

I tried to keep my work neat so others could follow it. If this sort of thing amuses you (as it obviously does me), then you’ll want to take a few minutes with the larger versions of these images. If it does not amuse (and I cannot begrudge anyone this), then you’ll just want to move along; there’s nothing here for you today.

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## 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 $4\cdot\left(3\cdot4\right)$

The second could be notated $\left(4\cdot3\right)\cdot4$

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?

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.

## Dear Target

Dear Target,

It seems that you and I do not agree on the meaning of 100%.

Sincerely,

Christopher

## Here’s an “unknown value problem”

This came in the mail this week. How timely.

Considering just the two bundles, that’s some expensive cream cheese. (And a seriously great price on bagels!)