The Challenge: Build yourself a wobbler. Wobblers are 2 circle (or 2 ellipse!) constructions that have a constant center of mass. Or rather, a center of mass that doesn’t move up and down as the wobbler rolls. Thus, resulting in a satisfyingly continuous “wobble”.
Materials Needed: cardboard, ruler, boxcutter or scissors
Math concepts you could explore with this challenge: algebra, angles, circles, geometry, proportions/ratios, symmetry, vertices/intersections
I first heard about this from Matt Parker’s “Things to Make and Do in the 4th Dimension”, (which is an excellent read for anyone interested, and the link above even has some printable templates for both a circular and an elliptical wobbler) – he attributes this to A.T Stewart in 1966.
To build, cut out 2 congruent circles from cardboard (or something cardboard like).
Then cut a slit that is ~29.3% the length of the radius in each circle, and use that to connect.
Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!
1.) Make sense of problems and persevere in solving them. Can you calculate the size of the cut needed for any give wobbler? Including those for ellipses?
5.) Use appropriate tools strategically. What surface is best to demonstrate the wobbler? What speed of roll?
6.) Attend to precision. Experiment with how much precision is needed. How does your accuracy with the cutting affect the wobbling of the wobbler?