The Challenge: Represent a pattern of permutations

Materials Needed: ??? There are so many options here. I used paint, but you could draw, use yarn, legos… anything. Math conceptsyou could explore with this challenge: combinations & permutations, counting

Here is mine, based on the permutations of 12345. See the planning docs below.

Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

3.) Construct viable arguments and critique the reasoning of others. Once you have finished – how do you know that you’ve accounted for each of the possibilities?

8.) Look for and express regularity in repeated reasoning. Can you create a generalized formula for how many permutations there are for a given number of things?

3 thoughts on “#MathArtChallenge Day 54: Permutations”

I don’t understand the notation. When I saw the picture, I thought it was like a braid where each string followed one number through various permutations. But the lines on your planning pages connect different numbers. How are you deciding which color line goes where?

Fair. Each row tells me which position the string should go to next. So 12345 sends the string directly below, whereas 12354 would send the string in the fourth position to the fifth position, and the string in the fifth position to the fourth position. Does that clear it up?

There are probably cleaner ways to do it, but this one made sense to me at the time.

I don’t understand the notation. When I saw the picture, I thought it was like a braid where each string followed one number through various permutations. But the lines on your planning pages connect different numbers. How are you deciding which color line goes where?

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Fair. Each row tells me which position the string should go to next. So 12345 sends the string directly below, whereas 12354 would send the string in the fourth position to the fifth position, and the string in the fifth position to the fourth position. Does that clear it up?

There are probably cleaner ways to do it, but this one made sense to me at the time.

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Ah, I see what you’re doing now. Thanks!

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