A dialogue where students discuss area approximations.
- Devyn
- Hey Riley, I’ve found a problem with approximating areas!
- Riley
- Fascinating! Tell me more.
- Devyn
- Remember how it works. We split the region into some number of rectangles, find the area of each of the rectangles, then add them all together.
- Riley
- Yes, and by taking more rectangles we can make that approximation better and better!
- Devyn
- Pretty much. But think about the calculations we’ve been doing. For each rectangle, we’re tracking the height and area, then adding them all together. That works for, like, 6 or 8 rectangles, but we want LOTS of rectangles to get a really good approximation.
- Riley
- How can we track this for 100 rectangles?!?!?
- Devyn
- Exactly!
- Riley
- Hmmm...