Review Topics 8.4-8.12
Quick Lesson Plan
As a final review before the Unit 8 test, students are asked to demonstrate their understanding of the learning targets around areas and volumes. Students will work in groups to craft solutions to given problems and then critique the work of others in a fun and revealing Gallery Walk.
Depending on your school setting, you may be able to distribute chalk to each group, assign a section of sidewalk, and simply let them begin working. A large window can also become the canvas for a group’s work. Other options include whiteboards or chart paper --- make the best choice for your environment!
The functions assigned to each group are identical, so their sketches, points of intersection, and calculations of the area of Region S should also be identical. This makes the evaluation of Question 1 easy for the teacher, but also allows students to check their work with other groups at the start of the activity.
Question 2 requires students to revolve the region around an axis: groups A - D work with a horizontal axis, groups E - H work with a vertical axis. Note that students are asked only to write an integral expression. Check for correct integrands, limits of integration, and inclusion of important details (pi and choosing dx vs. dy).
Question 3 evaluates understanding of finding volumes using known cross sections. Groups will work with various geometric shapes: rectangles, half-circles, quarter-circles, squares and triangles. Stronger students are more likely to have success with Set H.
When work concludes, have each group post their directions near their work so “visitors” in the gallery can see how they approached the problems. Allow groups to wander through the gallery and post constructive criticisms on Post-It notes as they pass each solution.
Finding areas of regions and the volumes associated with those regions (either by revolving the region around an axis or using the region as a base for given cross-sectional areas) is standard fare for the AP test each year. As the last major topic in the AB calculus curriculum, the calculation of areas and volumes utilizes numerous calculus concepts. Student work on these questions will clearly communicate to the AP Readers the scope of their understanding and extent of their mathematical skills.
Peer-to-peer conversations during this activity can alleviate many persistent misconceptions and careful questioning by the teacher may resolve other specific areas of confusion. For some students, direct instruction and correction may be needed to best prepare students for the Unit 8 test.