## The Long now project - Fall 2015

Started in 2014, the Long Now Project was created by the 9th grade Strong/Swaaley team of High Tech High. Looking at the phases of the rise and fall of civilizations, the Humanities class created a mock society and creating drawings to be represented on the 5' x 5' x 5' cube. Each side of the cube represents one of the four phases. The Physics class built the cube and defined the equations it would need to determine outcomes.

## Math integration

Coming into the 2015 school year, math class became integrated to help explore and model the equations that define the gear ratios of both the winding mechanism, the planetary gears on top of the cube, angular acceleration of the cube, the angle and time between stops, the number of rotations and more. Students modeled the equations below into the online graphing tool Desmos.

## Mathematical modeling

Our students isolated inputs and documented how the change in inputs affected or didn't affect the following equations, which were turned into functions.

- the number of rotations
- the angle and time between stops
- the tangential velocity of the ball
- the final angular velocity of the cube
- horizontal deflection of the ball

The image above represents the function for the number of rotations when mass = 8 kg.

The image above represents the function for the number of rotations when mass = 140 kg. As students observed, the line didn't move off of 2 rotations. They concluded that the mass of the weights did not affect the number of rotations.

Below is a student example of how various inputs affected or did not affect this particular desired output of number of cube rotations. Everyone completed an analysis like this for all our inputs and all of our five desired outputs.

Click below for the link to our actual Desmos graph.

Below is a student example of how various inputs affected or did not affect this particular desired output of number of cube rotations. Everyone completed an analysis like this for all our inputs and all of our five desired outputs.

Click below for the link to our actual Desmos graph.

For more information about the Long Now Project, please visit the Long Now Project Summary page on the GritLab website.