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.
For the Collatz activities (Draw a Collatz Map and Draw a Collatz Super Map): pen/pencil, may also need scrap paper.
Curriculum Topics Covered
Following an algorithm, using mental or written arithmetic skills, solving simple equations (for ‘working backwards’ in Draw a Super Collatz Map).
Classroom activities to download are Draw a Collatz Map and Draw a Collatz Super Map files. Each file includes associated Teacher Notesto give you ideas for questions to ask students and further investigations to do alongside the activity worksheets.
Draw a Collatz Super Map worksheet has been designed on the assumption that students have completed the Draw a Collatz Map worksheet first.
THE GREAT COLLATZ COLLAB
Entries for the Great Collatz Collab are now closed and the finished poster can be viewed here: bit.ly/collatzcollab
Watch the video about the project on Matt’s second channel, featured at the bottom of the page.
Think Maths are posting a printed copy of the poster to all schools who submitted. If you emailed Think Maths when you submitted, you have been emailed to arrange this and to give you some information about which of your students’ pieces were featured.
If you are a participating school and did not receive an email, please email email@example.com to arrange this. Include your full school postal address and ensure you email by January 13th 2023 in order to receive a print.
Links to Collatz ONLINE:
There are lots of excellent YouTube videos on the Collatz Conjecture linked below that can give your students a greater background and excite them about the topic.
- Veritasium’s The Simplest Math Problem No One Can Solve summarises the progress that has been made by mathematicians to try to prove the conjecture, and features some artistic representations of the Collatz directed graph (what we are calling a ‘super map’). Suitable for older secondary students. https://youtu.be/094y1Z2wpJg
- Numberphile’s Uncrackable? The Collatz Conjecture introduces the Collatz Conjecture and focuses on the directed graphs or trees (what we are calling a super maps) that can be drawn. Suitable for KS3 upwards. https://youtu.be/5mFpVDpKX70
- Numberphile’s Collatz Conjecture in Colour introduces the Collatz Conjecture and focuses in more detail on one particular artistic representation of the Collatz directed graph (what we are calling a ‘super map’). Suitable for KS3 upwards. https://youtu.be/LqKpkdRRLZw
We’ve linked below to some example visualisations of Collatz.
- This diagram is a Collatz directed graph (what we are calling a ‘super map’). This is the type of map Think Maths created in the Great Collatz Collab: https://commons.wikimedia.org/wiki/File:Collatz-graph-20-iterations.svg
- This excellent interactive allows you to see the directed graph for varying orbit lengths. Orbit length is how many numbers you go through in a path from the outer most number down to 1. https://www.jasondavies.com/collatz-graph/
- This blog has various artistic visualisations of Collatz: https://vsudbrack.github.io/codes/2021-01-02-Collatz_conjecture.html