Calculate volumes of solids of revolution using definite integrals
I can visualize solids generated by revolution around various axes
I can identify the radius of the disk by using “upper-lower” or “further right-closer”
I can set up a definite integral to find volume using the disc method
Quick Lesson Plan
Today students will explore the disk method when revolving around other axes besides the x- and y-axis. A modified Fan and Pick protocol will be used to ensure equal participation and group interdependence. Focus is placed on proper set-up of integrals and correct input into the calculator.
To prepare for today’s lesson, print the problems on card stock and cut them up so each problem is on a separate card. There should be 7 cards all together. Each group of four will require one set of cards. We recommend directing students to only have one pencil, one calculator, and one paper per group.
In this modified Fan and Pick protocol, students are in groups of four and are each assigned a number 1-4. Each number corresponds to a specific role in the group:
1: Fan--This student fans out all cards face-down for player 2 to choose from.
2: Pick and Read--Player 2 chooses a card and reads it out loud for the group.
3: Answer (Set-up)--Player 3 completes the problem by setting up the proper integral
4: Answer (Calculate)--Player 4 is the only one who has access to the calculator and must evaluate the integral created by player 3.
1: Respond--Player 1 summarizes the results, gives feedback, corrects, and affirms.
After the first round, have students switch roles and continue with a new problem. Continue this protocol until all cards are completed.
As students are working, listen in on conversations and check for understanding. Reinforce ideas of “upper-lower” and “further right-closer” when determining the radius of each disk, especially since the “lower” and “closer” is no longer just zero.
During the debrief, have students check their work against the answer key. Encourage students to look at the set-up of the integral, not just the correct final answer to ensure that all parentheses are in the right spot.