#MathArtChallenge Day 35: Probabilistic Plants

2020-04-20 08.11.07
A watercolor plant alongside pieces of a plant labeled with numbers.

The Challenge: Today from @ayliean on twitter.

Materials Needed: Paper, pencil, something to randomize (die, coin, whatever)
Math concepts you could explore with this challenge: probability, randomness, expected value

I rolled a 6 sided die to determine how many branchings and an 8 sided die (octahedron) to determine the kind of plants on each branch. It was a little loosey-goosey, and my plant is a bit more fantastical than hers, but it was fun! #mathartchallenge

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!

1.) Make sense of problems and persevere in solving them. What is the expected length of each plant…arm? (Branch, they’re called branches, I remember now)

8.) Look for and express regularity in repeated reasoning. Under what circumstances is the plant going to continue forever? What conditions make for small plants? What conditions make for huge ones?

#MathArtChallenge Day 34: Similar Right Triangle Patterns.

The Challenge: Create a large number of similar right triangles using the technique described in this video from Mark Kaercher. Then play!

Materials Needed: Scissors, paper, ruler?
Math concepts you could explore with this challenge:  angles, geometry, lines, polygons, proportions/ratios

Continue reading “#MathArtChallenge Day 34: Similar Right Triangle Patterns.”

#MathArtChallenge Day 33: Möbius strip klein bottle

A fabric Klein bottle

The Challenge: Crochet 2 möbius strips, of opposite chirality. Then sew their edges together to get your very own Klein bottle! (A Klein bottle has no obvious inside or outside.)

Materials Needed: Crochet or knitting skills, yarn.
Math concepts you could explore with this challenge: topology

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#MathArtChallenge Day 32: Megan’s Spirals

A spiral created by connecting sequence values on a spiral chart of 1089 numbers.

The Challenge: Color a spiral of numbers. Or 3. Or fifty. (This one gets quite addictive.)

Materials Needed: A spiral chart. Two pdf versions are shown below.
Math concepts you could explore with this challenge: algebra, arithmetic, counting, functions, lines, sequences, symmetry

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#MathArtChallenge Day 31: MÖBIUS

A zippered Möbius strip.

The Challenge: If you have a math friend in your life, they’ve probably introduced you to Möbius strips. If you haven’t been introduced, my apologies, on behalf of all math teachers, for having failed you this far. Please, follow instructions below to create and then deconstruct a möbius strip.

Materials Needed: Strips of paper, possibly a zipper (note! If you choose to use a zipper, make sure it is completely detachable. Meaning that the two sides can actually separate. Some zippers are permanently connected at the bottom and will not work for this task.)
Math concepts you could explore with this challenge: knot theory, sequences, topology.

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#MathArtChallenge Day 29: Paper Roll Polyhedra

2020-04-12 14.40.31And now is a great time to explore some polyhedra if you haven’t yet done so! Here are some websites shared by Mark Kaercher that are great.

The Challenge: Make your very own paper roll polyhedra. All inspired by this tweet from Mr. Allan shared by Clarissa Grandi

Materials Needed: Paper rolls. Can be toilet paper or paper towel rolls or you can make your own!
Math concepts you could explore with this challenge: angles, geometry, polygons, polyhedra, symmetry, vertices/intersections

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#MathArtChallenge Day 28: Paper Tube Designs

The Challenge: Today, courtesy of the extraordinary Mark Kaercher:

Materials Needed: Cardboard tube (toilet paper or paper towel rolls)
Math concepts you could explore with this challenge: angles, geometry, polygons, symmetry

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Musing on the #MathArtChallenge

Hey folk. If you’re here, you’ve probably seen the #MathArtChallenge(s) that I’ve been putting on Twitter and Instagram. I just wanted to share some musing I’ve had as this has progressed, and I would love to hear any that you have as well.

The most prominent is easily that this is bringing me so much joy. Like most of you, I expect, I have moments in my day when I am overcome with dread and grief at what the world is facing in this pandemic, and I’m trying to condition myself to not wallow in that too long (if I can avoid it). One of the best ways I’ve found is to just search through the hashtag #mathartchallenge and I find so much joy that I am temporarily relieved of my existential dread.

For that reason, I’m not too bummed if there are days when only 1 or 2 people post their thinking/creations. Many of you have said that just seeing the math art challenges is a bright point in your day (and perhaps more importantly to me, many of my students have said that). My favorite challenge from the past week was almost definitely the Brunnian links and very few of you seem to have taken that up, but who cares as long as the ideas get spread and maybe someone can engage, even if thats days, weeks, months or years later. One of my actual students engaged in that one and just sent me a private video of her solution and I gotta say, I nearly burst into tears I was so happy.

Another joyful thing about it is the friendships I’m building with enthusiastic participants. Due to Katherine Seaton’s excellent challenge I’ve been introduced to her and even if it’s just a message here or there, it’s one more person I’m connected to. There are probably a dozen more people out there now who I hadn’t been as connected to as I am now, and much as I feel confident that many of you feel existential dread right now, I trust that just as many of you also crave human connection.

Back to the challenges themselves, I’m just delighted in the variety that has come up through your brilliant suggestions, and even more so that when I post one I happen to think is too simple or not interesting enough, figuring “I’m going to be doing this for a while, so I can’t be too picky”, that you all make it absolutely wonderful. Truly. I am floored that I can throw just any old thing out there, and your brilliant creativity and artistry makes it shine.

As for the ideas themselves, I’ve been operating under a few parameters as to what I will actually share:

  • If I’m using something that is decidedly a specific person’s creation, I’ve tried to ask first and if they say yes, to of course, credit them. I don’t know a single human who can lay claim to the connection between golden spirals and icosahedrons, so I didn’t worry too much about crediting that. But I do know that I was first introduced to the overlapping circles because of my brother and he through numberphile so I tried to link and thereby credit that creation. There have been a couple of requests that I haven’t yet used because I’m trying to get permission from their creators.
  • I have a list through about day 50 right now (we’re on day 28 now, as soon as I get my cat off my lap and go make it), and I have a lot of other ideas that I’ve hesitated to put out there because I want them to be accessible to as many people as possible. I guess I’d love some feedback on that. I would love to use hyperbolic crochet (crediting Daina Taimina, naturally), but I know not many people are going to have crochet needles and yarn, nor the enthusiasm to learn a whole new skill in a day. But maybe it’s worth putting out there for the few who would and for those who don’t to just play with the idea? Or Penrose tiles – I’d love to show those off and spread the idea, but it’ll be harder for everyone to play. What do you all think? 
  • I’m mostly trying to spread ideas that you all can take and share in your classes. I certainly won’t lay claim to anything except my own creations – I don’t own these ideas and you shouldn’t feel it necessary to credit me when you share them unless you’re sharing a specific image of one of my creations.

I dunno. These are just some of my musings right now. I’ll probably write again later, but for any who are following along, I guess I’d be curious as to what you’re thinking. And of course, feel free to add suggestions to the list.

#MathArtChallenge Day 27: Golden Icosahedron

The Challenge: Create your very own Golden Rectangle Icosahedron!

Materials Needed: Cardboard, markers, scissors/box cutter, string/ribbon/thread
Math concepts you could explore with this challenge: angles, geometric construction, geometry polygons, polyhedra, proportions/ratios, vertices/intersections

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