The Challenge: Create a Mondrian artwork (maybe with a goal of getting the lowest score?) Here’s a Math Pickle article to get you started.
Materials Needed: Writing utensil and paper. (This would be fun with chalk on a sidewalk!)
Math concepts you could explore with this challenge: arithmetic, geometry, proportions/ratios
The Challenge: Create an illusion using isometric lines.
Materials Needed: Isometric Grid paper You can print some or you can create some (that just takes a bit of patience), pencil and ERASER. This challenge is best done as an exercise in erasing, changing and play. You can see in my time lapse below just how much erasing I did and I’ve done this kind of thing many times before. Be gentle with yourself.
Math concepts you could explore with this challenge: Angles, geometric construction, geometry, isometric grids, perspective
(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: 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 cube by connecting 3 rhombi (see below). Then use lines parallel to those of the rhombi to embellish the cube.
Materials Needed: writing surface, writing utensil, straight edge, colors
Math concepts you could explore with this challenge: geometric construction, isometric grids, lines, perspective, polygons, polyhedra, 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
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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