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
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 every graph be 2 colored? As you add intersections, how many new spaces are created? Can you create a function to describe the relationship between the number of intersections and the number of enclosed spaces?
2.) Reason abstractly and quantitatively. How many new spaces does each crossing create?
6.) Attend to precision. Ensure that a 2-coloring is correct by methodically working through your design.