## Riemann Roller Coaster

**Type:** Mini-lesson

**Theme:** Calculus

**Grades:** 7, 8, 9, 10

**Learning Target:** Students will use Riemann sums to estimate board length of a roller coaster.

Instructions

- Review concept of Riemann sums.
- Provide this graph to students: https://www.desmos.com/calculator/mxfrxbs7sn
- Have students work in groups of two to estimate the total length of boards needed to support the roller coaster.
- Ask, "What if the horizontal distance was halved?

Alternatively, have students estimate arc length.

If you would like students to work with the Pythagorean Theorem, provide them the following graph: https://www.desmos.com/calculator/ixvwdhx18y

- How many meters of track will Mickey and Sofia need for constructing their roller coaster if straight tracks were connected every 8 meters?
- Considering this would not be a smooth smooth ride. Estimate how many meters of track would they need for a smooth ride?

Students will paste their work into a shared PowerPoint.

Exit Ticket

CCSS Math Practice

- I can use appropriate tools strategically.

NGSS Crosscutting Concepts