The Infinite Chocolate Trick, Tangrams, and Area on the Coordinate Plane

With 2 months to go in this semester, it'll be time this week to begin the work on the last big project in my Applied Math class where the kids use tangrams to study area, the distance formula, and linear equation writing. Usually I hook the kids with a day of playing tangrams to practice the spatial reasoning, but before that, I played this video of "The Infinite Chocolate Trick," where the user supposedly breaks off a chocolate bar, moves the pieces around, and winds up with an extra piece of chocolate, which if its true, would mean extra surface area just materialized out of nothing.

I didn't know how much the chocolate video would pull them in, but I'd declare it was a huge success! Kids were jumping out of their seats to come to the smartboard and try to explain their hypothesis on where the chocolate was coming from, several theories were floating around the room, and kids were asking me to play the clip over and over so they could try and catch what was happening. It set up so well for the essential question, someone actually REMEMBERED it today without me even asking. :)

For the next layer of the learning I started class with a Do Now of a triangle, circle, and rectangle on a coordinate plane, but with the relevant sides laying horizontal or vertical so the lengths could be determined just by counting units.

After we reviewed the solutions, I had to students focus on the example projects above the whiteboard and asked, "Looking at the projects up there, why do you think we started with these specific problems today?"

A student jumped right into, "So that we can prove that area of a shape is the same even if you move the pieces around..." Granted, that wasn't really why we started with that specific Do Now (I was setting up the distance formula), but I was glad that EQ stuck with her!

The official essential question for this unit is:

"How can you prove that the area of a given polygon is constant, no matter how its parts are arranged?"

Practically, the kids will be thinking, "Can I show that the area of my tangram goose (or sailboat, candle, fox, etc) is the same as the square my shapes came from?"

This project covers:
Area on the coordinate plane
Distance formula
Linear equation writing
Parallel and perpendicular lines/equations
Spatial reasoning
Using tools appropriately (measuring with a ruler, setting up their grid paper)

Here are some examples of previous years' work:

Instruction/example handout

An example of a kid who had all the required elements, but it WASN'T pretty.

If you've listened to either of the podcast episodes about our statistics based project based learning unit, you'll remember I was very frustrated with how little buy in my students showed behind what I thought was a highly relevant, meaningful project. This one is less relevant, so I wanted to make an extra effort to start with a strong hook and have an experience to draw from when the kids seemed to be lost on the connection or purpose of our work in this unit.