Area Between Curves Partner Task

We are starting my favorite unit of the year tomorrow....area and volume! 

Not only is it the culminating moment in the course- our very last unit- but it's also just plain FUN! I'm replacing half their test with a performance task, having them build 3D models of anything possible, and just spent way too much money on honeycomb party decorations on Amazon Prime. You'd think by now my husband would just expect weird and seemingly non-math related items to be shipped to our house regularly, but evidently I'm still surprising him. 

To start off tomorrow, I wanted to get the kids working in partners and visualizing what is actually going on when we find area between curves. We can do a lot with technology, but this one time where I want them to develop the idea by hand. Each group will be given a different set of functions and a different interval on which to graph them. They will then develop the formula for area between the curves with their partner. We can hang them all up and compare our methods to determine area. 

Area Between Curves Partner Task

I'm worried about the "big idea" here...once they have that, we can get into the more complicated and interesting things we'll explore this unit. I'm excited to build some models of 3D solids with known cross sections, spend some time playing with honeycomb decor, and revisit my Volumes Performance Task from last year. This will be a unit where I will definitely miss being in a science classroom (I know, I was spoiled), but I'm so excited to get started. Let the fun begin!