The Challenge: Create all of the possible “stars” given a certain number of vertices.

Materials Needed: Pencil/paper Math conceptsyou could explore with this challenge: angles, arithmetic, circles, combinations & permutations, lines, proportions/ratios, symmetry, vertices/intersections

I spent a long time last night and this morning thinking about whether I should post a challenge today. I live in Minneapolis. I spent a long time last night listening to pops and bangs and sirens. I know that my students are not okay. I truly hope they are safe, but I can’t imagine most of them are okay right now. There’s so much trauma and anger and fear in this city right now.

I’ve ultimately decided to post this, almost entirely based on the fact that my students have regularly shared that watching these videos is a highlight and happy part of their day during this pandemic. If I can give them even a 20 second respite to breathe, then it’s worth it. I also know that math is my refuge. I am not my students, of course, but when I am upset/angry/confused/overwhelmed doodling and sketching and doing math brings me some semblance of peace. Maybe this can do that for some of them, too.

I specifically picked something that requires NO special anything – no grid paper, just a writing utensil and something to write on.

Start with a circle of dots. Doesn’t matter if they’re evenly spaced. A good one to start with is 6 dots. Then begin connecting every other dot. Then try connecting every 3rd dot. Now try 7 dots. Connect every other dot. Continue around. Eventually, try with 11 or 12 (or more) dots. You get some pleasing doodles and some time to think and ponder and breathe.

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!

2.) Reason abstractly and quantitatively. Given k vertices, how many unique stars are possible?

5.) Use appropriate tools strategically. How do factors affect your understanding of different stars? How can you use your knowledge of factors to help you through this challenge?

Thank you Annie for all you do here.

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