The Great Collatz Collab

Proving the Collatz Conjecture is a famous unsolved problem in mathematics. It can be understood by school students and can be explained using artistic diagrams. Introduce your students to the Collatz Conjecture by using these map (graph) drawing worksheets. The Great Collatz Collab was a project in 2022 where, using maps drawn by students all around the world, we made a giant collaborative Collatz map featuring sections from as many student maps as possible. You can view the final poster and watch the video about it below.

Graceful Trees

Can you arrange five consecutive odd numbers in a line, so that the differences between adjacent pairs of numbers are all different? What if the numbers are connected in a way other than in a line? The Graceful Tree Conjecture in graph theory says that we will always be able to arrange n evenly-spaced numbers in a tree (with n nodes) so that differences between adjacent pairs are all different. Explore this with your students!