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: Find a smaller circle you can trace. Then trace large circle to use as a guide. Finally, trace a bunch of smaller circles in a ring to create a torus (more commonly known as a donut).
Materials Needed: Paper, writing utensil(s), circles/compass. The circles can be whatever, but rigid is helpful and even better if they’re empty (masking tape is great!)
Math concepts you could explore with this challenge: circles, geometric construction, proportions/ratios (to get interlocking tori, there are restrictions on the possible ratios between the circles)
The Challenge: Use something like a die or a coin to get random outputs. The probabilities don’t need to be equally spread! Assign a design to each output, and then get to designing. I have two examples for you below.
Materials Needed: Honestly, whatever you want. There are endless possibilities on this one. Some examples: paper & pencil (like above and in the video below), yarn (friend ship bracelets or crochet), legos… See the examples of other people’s work below!
Math concepts you could explore with this challenge: Probability, probability distributions, randomness
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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