Materials Needed: Paper, pencil, and probably a good eraser. You could also do this using a whiteboard or other writing surface. Math conceptsyou could explore with this challenge: algebra, arithmetic, counting, fractals, functions isometric, proportions/ratios
The Challenge: Create a visual (or audio?) of the Recamán sequence, created by a Colombian mathematician, Bernardo Recamán Santos (who seems to have very little biographical information out there??). I was first introduced through Alex Bellos and Edmund Harris’s book.
Materials Needed: Straight edge, maybe a compass, maybe a ruler. Paper, riting utensil. Math conceptsyou could explore with this challenge: algebra, circles, counting, functions, proportions/ratios, randomness, sequences
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 conceptsyou could explore with this challenge: algebra, arithmetic, combinations & permutations, counting, functions, proportions/ratios, sequences, 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 conceptsyou could explore with this challenge: angles, fractals, functions, geometry, lines, polygons, proportions/ratios, slope symmetry, vertices/intersections.
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 conceptsyou could explore with this challenge: fractals, functions, geometry, proportions & ratios, sequences
The Challenge: Create cardioid images by marking the circumference of a circle with equally spaced tick marks, then connecting them at various ratios.
Materials Needed: Paper, circle to trace (yogurt or oatmeal lid?), writing utensil, straight edge (doesn’t have to be a ruler, could just be a piece of cardboard cut straight or any other number of things. Math Concepts: sequences, modular arithmetic, angles, geometric construction, ratios, circles, functions, vertices/intersections
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 conceptsyou 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 conceptsyou could explore with this challenge: counting, functions, geometry, knot theory, vertices/intersections