# Mathbreakers Labs

## Expanding how we play with numbers

#### What can you do in a 3D math game world?

For the past year and a half we developed the Mathbreakers video game with an eye on the 2nd-6th grade math topics — negatives, operators, and fractions being the primary concepts. We’ve tested and refined the virtual gadgets and machines we use to teach these topics, which can be a long process! While running our Kickstarter campaign, we had the idea to try to build new gadgets and game features to show off the possibilities of our game *beyond* the elementary school level.

### Introducing Mathbreakers Labs

It works like this: first, we meet a math enthusiast who is excited about teaching or expressing a particular topic. They show us something cool in math, and then we work together to figure out how to make it work in Mathbreakers. Charlie, Vivian and I would work together to build a working demo of the concept in Mathbreakers in just three days. Then, we mix a quick video showing off the new features! Now here we are, 3 weeks into it and we have 4 experiments done! You can view them all at mathbreakers.com/labs.

#### Turing Machines

We first did a two-parter — state machines and turing machines — with math tutor Pepe Swer. We represented state machines using trains, tracks, and stations; the train has cars which represent input, and it travels on a track which resembles a logic flow chart. To make our system Turing equivalent we also added a Queue to the train as the caboose.

#### Set Theory

Next we came up with a cool representation of Set Theory basics with our friend Jon Hull. This involved building sets out of suitcases and then combining them in union/difference/subtraction machines. The best part is that you can nest sets inside each other, whether or not they’re empty, to infinity! (Well, ok, not infinity, but that’s a limitation of the computer, not of our logic.)

#### Radians & Tau

Our most recent lab was a Tau Day celebration level that teaches radians in a unique way. You can squash numbers into lengths of material and then roll them up to become the perimeter of a circle. These radian objects can be used in new machines to build discs that you can walk around on and use to solve puzzles. For fun, we also made fractal trees that grew four branches out of each successive node at an angle determined by what radian “seed” you give it.

We have been building these experiments to show what sorts of things Mathbreakers could be capable of in the future. Our dream is to let students play with numbers, whether they are learning to count or studying calculus!

Head on over to our Kickstarter page and donate now if you would like to support Mathbreakers and see more awesome math toys.

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