Calculus · Week 34 · Applications of Integration
Volumes: Cross Sections and Disks
The same base region can build different solids, and each classmate's picture of a slice helps everyone see how volume is a sum of cross sections.
- Students will
- Students find volumes of solids with square and semicircle cross sections and a solid of revolution using disks, all on the same base.
- SEL skill
- Restate how a partner pictures a slice before sharing your own view
- What it looks like
- Students practice social awareness by asking how a partner pictures a slice and restating that view before sharing their own.
- Content focus
- Volumes with cross sections and disks
- Format
- Collaborative analysis
Social awareness
Social awareness means understanding how others see things, like listening to how a partner pictures a slice of a solid. More social awareness activities
What you get
A teacher guide with what to say, step by step, plus student pages and a supports page for students with diverse learning needs, including those with IEPs. Print or Project it, or assign it in Google Forms and Google Docs for Google Classroom. Your first 10 activities are free.
Standards
- AB 8.7: AP Calculus AB, Unit 8, Topic 8.7
- AB 8.8: AP Calculus AB, Unit 8, Topic 8.8
- AB 8.9: AP Calculus AB, Unit 8, Topic 8.9
- Standard for Mathematical Practice: MP7 Look for and make use of structure
- CA Mathematics Framework (2023): Taking Wholes Apart, Putting Parts Together
- Traditional course: Calculus
More social awareness activities for Calculus
- Squeeze and Infinity Social awarenessThe squeeze theorem, infinite limits, and limits at infinity, comparing a classmate's method with your own.
- Smooth or Sharp? Differentiability Social awarenessEstimating derivatives and seeing where a graph is smooth, cornered, or too steep, by looking from both sides.
- Motion: Position, Velocity, Acceleration Social awarenessReading the signs of velocity and acceleration to tell a motion story.
- Concavity and the Second Derivative Social awarenessConcavity, points of inflection, and seeing a classmate's method as another valid view.
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RoseThread Connect activities are drafted with the help of AI and shaped by educators. Students never have to share anything personal. Our five SEL skills are informed by CASEL's SEL Framework; RoseThread Learning is not affiliated with or endorsed by CASEL. AP and Advanced Placement are trademarks of the College Board, which was not involved in making and does not endorse RoseThread Connect.