Tree of Numbers – EKG Sequences

(MathPickle, 2014)

Student groups should work independently and then collaboratively to find when these integer sequences converge.

Neil Sloane introduced me to the first EKG sequence in 2014. Its beauty and suitability for the classroom was pivotal in setting up the Integer Sequences K-12 conference that you can read about here.

Neil Sloane thought there as yet is no proof showing the convergence of all these sequences.

If you’re sitting across the table from someone, the geometry of the situation says ‘confrontation.’ If you’re walking with somebody, you’re heading in the same direction, and the spatial dance you’re doing is a little more cooperative.

Scott Kim

Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

MP1 Toughen up!

This is problem solving where our students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

MP3 Work together!

This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

MP6 Be precise!

This is where our students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

MP7 Be observant!

One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.


Please use MathPickle in your classrooms. If you have improvements to make, please contact us. We'll give you credit 😉

Gordon Hamilton

(MMath, PhD)


Lora Saarnio