Rooting for NASA

A Pre-Puzzle Draft

(MathPickle, 2020)

Students can use Pythagoras to find all possible lengths of line segments on a grid. But what can you do with these line segments… Here are some pre-puzzle ideas. They’re really just universes to explore. They look beautiful but have no purpose and no solution.

If you decide to play with these pre-puzzles in your classroom I’d love to know what the students come up with. Do they have some questions that they would like to know about what’s going on?

You might think that by adding complexity to a lesson on Pythagoras that you’re going to be making life harder for yourself and your students. The irony is that 1) by introducing beauty you engage 10% – 20% of students who would otherwise be unengaged and 2) by introducing a universe worthy of exploration you engage your top students.

This video is a draft. I am choosing to display it because the creative process is sometimes difficult to perceive if you only get to see the finished puzzles. 

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!

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

MP2 Think abstractly!

Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.

MP3 Work together!

Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

MP4 Model reality!

Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.

MP5 Know the tools.

Students master the tools at their fingertips - whether it's a pencil or an online app. 

MP6 Be precise!

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!

Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist 😉

MP8 Be lazy!?!

Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?


Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos 😉 For a free poster of MathPickle's ideas on elementary math education go here.

Gordon Hamilton

(MMath, PhD)