## 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
1. Review concept of Riemann sums.
2. Provide this graph to students: https://www.desmos.com/calculator/mxfrxbs7sn
3. Have students work in groups of two to estimate the total length of boards needed to support the roller coaster.
4. 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

1. How many meters of track will Mickey and Sofia need for constructing their roller coaster if straight tracks were connected every 8 meters?
2. 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