Give the knotted rope to another student or group of students. When you receive a knotted rope from another group of students, try to figure out what the two knots were that the knot you received was made from. When a group succeeds in decomposing a knot, the decomposition should be compared to the drawing that was made. If the knot is decomposed differently than the drawing shows, both groups will need to get together and talk about the result. Any knots that cannot be decomposed during the class period can stand as open problems in the classroom.
Open problems are the lifeblood of mathematics.
The knot decomposition puzzles can be made even more challenging if more than two knots can be summed to make the puzzle. If students try to decompose the knots on the knot diagram into smaller knots, they will meet with quite a bit of difficulty. After much experimentation with the aid of computers, no one has succeeded in decomposing these knots, but this does not mean that there is not a decomposition waiting to be discovered. Identification of the ultimate building blocks of the universe is one of the quests of particle physics. Amino acids are the building blocks of the proteins in all living things.