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 conceptsyou could explore with this challenge: arithmetic, combinations & permutations, counting, knot theory, proportions/ratios.
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 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 conceptsyou could explore with this challenge: arithmetic (multiplication), counting, proportions/ratios, sequences, symmetry
The Challenge: Make two different sizes of origami butterflies and then see what you notice and wonder about your pieces!
Materials Needed: At least two different sizes of square paper. (Can be obtained from non-square paper if you ask nicely.) Math conceptsyou could explore with this challenge: angles, proportions/ratio (particularly between length, area, volume)
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 conceptsyou could explore with this challenge: : Ratios, radius, tangency (tangent circles), proportions, area, perimeter, fractals, geometry
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: 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 conceptsyou 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: 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