**The Challenge:** Make yourself a MathArtChallenge sketchbook

*Materials Needed*: Paper (10 or so sheets), scissors.*Math concepts* *you could explore with this challenge: *topology

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# Category: 3D

## #MathArtChallenge Day 49: No tape/staple Sketchbook

## #MathArtChallenge Day 47: Origami Cube with Windows

## #MathArtChallenge Day 46: Origami Firework – Yami Yamauchi

gif of origami firework
## #MathArtChallenge Day 42: Origami Octahedron

An origami octahedron.
## #MathArtChallenge Day 40: Flexagons

Several Flexagons.
## #MathArtChallenge Day 39: Flowered Dodecahedron

A flowered dodecahedron.
## #MathArtChallenge Day 38: Chirality

## #MathArtChallenge Day 35: Probabilistic Plants

A watercolor plant alongside pieces of a plant labeled with numbers.
## #MathArtChallenge Day 33: Möbius strip klein bottle

A fabric Klein bottle
## #MathArtChallenge Day 31: MÖBIUS

A zippered Möbius strip.

**The Challenge:** Make yourself a MathArtChallenge sketchbook

*Materials Needed*: Paper (10 or so sheets), scissors.*Math concepts* *you could explore with this challenge: *topology

**The Challenge**: Fold an origami cube with windows. Possibly make multiple. (This could be a great collaborative activity for a class!)

*Materials needed:* 12 pieces of paper, cut to rectangles with a 1:2 ratio.*Math concepts* *you could explore with this challenge: *angles, geometry, origami, sequences, symmetry, vertices/intersections

(You may have picked up on this, but I tend to do the more involved things on the weekends when I have a bit more time. This one was HONESTLY pretty reasonable until the last step, which took me about 5 finicky minutes to get together. YOU CAN DO THIS. And it is SO SATISFYING when it’s finally together.)

**The Challenge**: Fold yourself an origami firework.

*Materials Needed:* 12 congruent paper squares, patience.*Math concepts* *you could explore with this challenge: *angles, orgiami, symmetry, vertices/intersections

**The Challenge**: Fold you own octahedron from 6 square pieces of paper.

*Materials Needed*: 6 square pieces of paper.*Math concepts* *you could explore with this challenge: *angles, geometric construction, geometry, origami, symmetry, vertices/intersections

**The Challenge**: Make you very own flexagon. Inspired today by this from @ayliean. Instructions from her below.

*Materials Needed: *Strips of paper, cloth, or some other foldable strip. *Math concepts* *you could explore with this challenge: *graph theory, polygons, sequences, symmetry, topology

**The Challenge**: Suggested by Clarissa Grandi, to cut out and construct this flowered dodecahedron. Mine below followed by links to instructions.*Materials Needed:* A set of these papers printed and cut from cardstock. (there are other sized pieces available at the links below. *Math concepts* *you could explore with this challenge: *geometric construction, geometry, polygons, polyhedra, symmetry, vertices/intersections

**The Challenge**: Play with chirality. Chirality refers to the rotation of a specific object. The knots above have opposite chirality.

*Materials Needed*: This is wide open. Spinning video? Knots? Twisted candy? Be creative!*Math concepts* *you could explore with this challenge: *knot theory, pespective, topology, vertices/intersections

**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? *

**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

**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.