Using only two moves (rotate and twist) with two ropes and four teachers, we will create a tangle (knot). (The ropes are tangled, not the teachers.) Next we "untangle" the ropes by using only those two moves. We will then explore the mathematics of the tangle and untangle.

Rational tangles were developed by John H. Conway to classify knots (a tangle is part of a knot) in the course of his work in geometric topology. This activity offers practice with operations (addition, subtraction, and reciprocation) on positive and negative fractions, as well as an opportunity to use spacial reasoning and think about inverse operations. We based our activity on that of Tom Davis; you can download a pdf of his instructions here, if you'd like to try it with your students. In addition, the file below has a few slides with a bit of background material.