The Challenge: Explore a toppling sand pile.
Materials Needed: Paper, pencil, and probably a good eraser. You could also do this using a whiteboard or other writing surface.
Math concepts you could explore with this challenge: algebra, arithmetic, counting, fractals, functions isometric, proportions/ratios
The Challenge: Create a self-repeating pattern – a fractal. You may choose your own design, or perhaps you recreate some of the ones from Ron Eglash’s survey studying the fractal formation of African villages. I did both of these looking at the applet at his website.
Materials Needed: paper and pencil, likely, but you can probably get more creative than that, too! Maybe using sculptural materials?
Math concepts you could explore with this challenge: angles, fractals
The Challenge: Today’s math art challenge is to play the chaos game, and was inspired while I was perusing the excellent Power in Numbers by Talithia Williams. Her chapter on Fern Hunt indicated one of her research interests as Chaos Theory – something that always grabs kids attention, and leads to one of the more fascinating probability related math-art creations.
Materials Needed: randomizer (die, coin, etc.), paper, pencil, possibly graphing software.
Math concepts you could explore with this challenge: fractals, probability, randomness
The challenge: Create a Hilbert curve.
Materials needed: Paper and pencil. Grid paper is helpful.
Math concepts you could explore with this challenge: exponents, fractals, geometry, sequences, symmetry, tessellations
The Challenge: Make a chair fractal (That link will take you to the originators blog post about it. Seriously, go. It’s GREAT.)
Materials Needed: paper, pencil
Math concepts you could explore with this challenge: fractals, geometry, symmetry
The Challenge: Draw a polygon. Then mark the midpoint of each side. Connect the midpoints of each side to make a new polygon. Repeat. (Don’t sleep on the quadrilaterals here. They do something rather surprising and beautiful!)
Materials Needed: Paper & pencil or online graphing software like Geogebra or Desmos
Math concepts you could explore with this challenge: angles, fractals, functions, geometry, lines, polygons, proportions/ratios, slope symmetry, vertices/intersections.
(Props to Kate Nowak who suggested this.)
The Challenge: Create as many iterations of the Dragon Fractal as you can. See below for my attempts and videos to help.
Material Needed: There are a couple options here:
-Paper and marker (sharpie?). Maybe grid paper, preferably paper that is thin enough to see through (notebook paper is normally thin enough)
-Strips of paper to fold it
-Whiteboard marker and whiteboard/window
-??? I bet you have better ideas than I do.
Math concepts you could explore with this challenge: fractals, functions, geometry, proportions & ratios, sequences
The Challenge: Draw a large shape. Then place a large circle inside that shape, touching at least one edge of the original shape. Then draw the next largest circle you can, and repeat drawing the next largest circle you can. (See video below for examples.)
Materials Needed: Writing utensil, paper.
Math concepts you could explore with this challenge: : Ratios, radius, tangency (tangent circles), proportions, area, perimeter, fractals, geometry
The Challenge: Draw as many connected triangles as you can. Goal is to have as many vertices with 7 triangles as possible.
Materials Required: Writing surface, writing utensil
Math concepts you could explore with this challenge: angles, counting, exponents, fractals, functions (exponential), triangles, geometry, graph theory, hyperbolic geometry, lines, polygons, sequences, intersections/vertices
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