**The Challenge**: Today from Ann Marie Ison

*Materials Needed*: Pencil & grid paper*Math Concepts: *Arithmetic sequences, modular arithmetic

Skip to content
# Category: Counting

## #MathArtChallenge Day 44: Spirolaterals

## Bonus #MathArtChallenge: Y-Labyrinths

## #MathArtChallenge Day 37: Pascal’s Triangle Patterns

## #MathArtChallenge Day 32: Megan’s Spirals

A spiral created by connecting sequence values on a spiral chart of 1089 numbers.
## #MathArtChallenge Day 23: Brunnian Links

## #MathArtChallenge Day 19: Alternating knots

An alternating knot with 4 crossings.
## #MathArtChallenge Day 18: Celtic Knots

## #mathartchallenge Day 10: Arrays

A rainbow array of butterflies (4×6)
## #MathArtChallenge Day 4: Hyperbolic Geometry

5 differently colored origami hyperbolic planes
## #MathArtChallenge: Day 2 Looping Colors

A looping line, with created spaces alternating blue and red in color.

**The Challenge**: Today from Ann Marie Ison

*Materials Needed*: Pencil & grid paper*Math Concepts: *Arithmetic sequences, modular arithmetic

**The Challenge: **Using a hexagonal grid, create a labyrinth using “Y” shapes.

*Materials needed: *hexagonal/isometric grid (you can print from the internet or obtain from a compass), writing utensil, randomizer (die, coin, etc.) *Math Concepts you could explore with this challenge*: 2D, combinations & permutations, counting, isometric, probability, randomness

**The Challenge**: Start by making (or use mine below) a Pascal’s Triangle. Then shade in some sequence of values. I suggest starting with even/odd numbers, and then perhaps multiple of 3, 4 etc.

*Materials Needed*: Pascal’s triangle. You can print one or you can create your own!*Math concepts* *you could explore with this challenge: *algebra, arithmetic, combinations & permutations, counting, functions, proportions/ratios, sequences, symmetry

**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

**The Challenge**: Build a set of 3, 4, or even 5 Brunnian links.

*Materials Needed*: Your call. Joey already did the 3 link one with straws. I used crocheted yarn. Shoelaces?*Math concepts* *you could explore with this challenge: *Combinations & Permutations, counting, knot theory, vertices/intersections

**The Challenge**: Draw an alternating knot. Then see if there’s any way to draw a looping line that cannot be turned into an alternating knot.

*Materials needed*: Pencil & eraser, or whiteboard, or markers?*Math concepts* *you could explore with this challenge: *counting, graph theory, knot theory, vertices/intersections.

**The Challenge**: Create a Celtic knot, and do some wondering about why you got the number of links that you did. Can you predict how many links you’ll get? (I wrote another blog post on this a while ago, but only go there if you need more examples, because I reveal a lot of the good stuff in it: Knots, Links, & Learning)

*Materials Needed*: Paper, pencil. If you have grid paper, that might help, and here is some special grid paper you can use courtesy of Justin Aion.

Day18 11×15 Celtic Knot Grid

Day18 MAC 16×22 Celtic Knot Grid

(or you can just rotate grid paper 45 degrees like I do in the video below)*Math concepts* *you could explore with this challenge: *arithmetic, combinations & permutations, counting, knot theory, proportions/ratios.

**The Challenge**: Create an array with materials around your house. What do you notice? What do you wonder?

*Materials needed*: Go wild. Anything can work here: origami butterflies, shoes, paperclips, cereal, pencils… *Math concepts* *you could explore with this challenge: *arithmetic (multiplication), counting, proportions/ratios, sequences, symmetry

**The Challenge:** Fold your very own Hyperbolic Plane from a simple piece of paper!

*Materials Needed*: A square piece of paper. Youtube instructional video below!*Math concepts* *you could explore with this challenge: * Algebra (how many folds per stage?), angles, counting, exponents, functions, geometry, Hyperbolic planes, proportions/ratios, sequences, symmetry, topology, vertices/intersections

**The Challenge: **Draw a long, looping, self-intersecting line that meets back with itself at the start. Avoid having any 3 lines cross at the same intersection (although after a bit it may be fun to play with this). Then, select a color, and start coloring in the spaces created by your line’s intersections.

Can you color it such that you end with every section alternating colors?

*Materials Needed: *writing utensil, writing surface*Math concepts* *you could explore with this challenge*: counting, functions, geometry, knot theory, vertices/intersections