## Volumes of Cross-Sectional Solids (part 4 of 4), Lesson Plan, Investigation.pdf - Section 4: Investigation

*Volumes of Cross-Sectional Solids (part 4 of 4), Lesson Plan, Investigation.pdf*

Volumes of Cross-Sectional Solids (part 4 of 4)

# Volumes of Cross-Sectional Solids (part 4 of 4)

Unit 7: Applications of Integration

Lesson 12 of 14

Lesson 12 of 14

## Objective: SWBAT verify or correct the accuracy of other students’ pipe cleaners models for volumes of cross-sectional solids.

## Big Idea: We spent a full period building 3D models of cross-sectional solids. Today students analyze and correct other students’ models and work.

Subject(s):

Math, Precalculus and Calculus, Integrals, AP Calculus AB, solids, cross, volumes of solids, calculus, AP Calculus, calculus ab

*60 minutes*

3

#### Setting the Stage

*4 min*

**Have students take out their Volumes of Cross-Sectional Solids sheet that we gave them 2 days ago, and talk through one or two of these examples to summarize the process for drawing and labeling the picture, writing the area expression for the cross-section, and integrating to obtain the volume.** Although we distributed this sheet on the 2^{nd} day of this set of 4 lessons, for some students this sheet will make more sense now that we have spent more time with cross-sectional solids. Students may refer to this sheet throughout class today as they check the mathematics in other groups’ pipe cleaners projects.

*expand content*

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- UNIT 1: Back to School
- UNIT 2: Limits and Derivatives
- UNIT 3: Formalizing Derivatives and Techniques for Differentiation
- UNIT 4: Applications of Differentiation, Part 1
- UNIT 5: Applications of Differentiation, Part 2
- UNIT 6: The Integral
- UNIT 7: Applications of Integration
- UNIT 8: Differential Equations
- UNIT 9: Full Course Review via Motion
- UNIT 10: The Final Stretch - Preparing for the AP Exam

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- LESSON 1: Easy as ABC - Areas Between Curves
- LESSON 2: Areas Between Curves - dx or dy?
- LESSON 3: Variable Limits of Integration and the Fundamental Theorem of Calculus
- LESSON 4: Catch-up Day - ABC and FTC
- LESSON 5: Volumes of Solids of Revolution (part 1 of 4)
- LESSON 6: Volumes of Solids of Revolution (part 2 of 4)
- LESSON 7: Volumes of Solids of Revolution (part 3 of 4)
- LESSON 8: Volumes of Solids of Revolution (part 4 of 4)
- LESSON 9: Volumes of Cross-Sectional Solids (part 1 of 4)
- LESSON 10: Volumes of Cross-Sectional Solids (part 2 of 4)
- LESSON 11: Volumes of Cross-Sectional Solids (part 3 of 4)
- LESSON 12: Volumes of Cross-Sectional Solids (part 4 of 4)
- LESSON 13: Applications and Problem Solving with Volumes of Solids (part 1 of 2)
- LESSON 14: Applications and Problem Solving with Volumes of Solids (part 2 of 2)

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