## Monday, May 5, 2014

### A Question That Builds Understanding Of "Power"

Is this a power of something?

How could you change the picture so that it's a power?

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When I posed this question to students, the first answer that I got was "Yes! It's a power of three!" quickly followed by "No it isn't!"

The next thing the kids came up with was "Yeah! It's the first power of 54!" This was expected. As part of our work on powers in the past week kids had worked with power patterns, and realized that any number can come at the start of one of these patterns.

Then I asked kids to pair up and to find a way to change this picture so that it was a power of something. Here were some of the answers that the kids gave when we came back:

...a power of 3.

("That could be the 1,274 power of one," B said.)

...a power of 2.

It took us a surprisingly long time to get to this:

Here's what I like about this task:
• It works out the language of "power" without worrying about which power it is.
• It's not calculation heavy, and I think that heavy calculations can get in the way of learning the language.
• It's a nice open question that allowed for a lot of different approaches.
We did this as part of a Quick Images activity, which I learned about from the TERC curriculum. (Video with 1st Graders here.) That's a fun game on its own: flash a dot-image for a second, then ask kids to write down what they saw and how many dots there were in total.

#### 4 comments:

1. I like this activity. I hope you don't mind me posting a link to it on the MathThinking Blog.

Also, the dot activity is really nicely structured as part of a math talk. Sally Keyes from the Silicon Valley Math Initiative did some work with our teachers on this last summer. See http://instructionalactivities.com/activity/math-talk for a summary.

1. Of course! I'm so glad that you like it.

The TERC curriculum calls these number talks "10 Minute Math," and they've got a bunch of them.

http://investigations.terc.edu/curric_features/CRandTMM.cfm

2. Have you used number talks? I'm considering using some power-based dot patterns with my 8th graders in a number talk...they've already learned exponents but I'd love to give them the opportunity to see exponential structure somewhere they don't expect, and share that with their classmates

1. That sounds cool! Maybe mix up the exponential dot patterns with the non-exponential ones, ask them whether each one is a picture of a power?

For laughs, you could also toss in a single dot, a blank slide, a half-filled in dot, and a cube of dots.