Reviewing Volumes of Solids and Differential Equations (part 2 of 3)

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SWBAT model differential equations with slope fields, solve separable differential equations algebraically, and compute volumes of solids of revolution and cross-sectional solids.

Big Idea

Today we continue reviewing volumetric solids and differential equations, focusing on slope field questions from the AP exam.

Lesson Overview

Warm-up and Homework Review

15 minutes

For general ideas about implementing this and other lessons, read my Course Outline


Today’s Warm-up

                                 None – check your homework answers right away…



Last Night’s Homework Review

Note:  last night’s homework solutions appear in the “In The Classroom” file


The primary source of student questions on last night’s homework will be from problems assigned from your textbook in parts F and E.


Resources:  In The Classroom file

Setting the Stage

15 minutes

For this section, spend whatever time you need to finish the AP free response question 2008 #1 that we started in yesterday’s lesson.  Revisit the Investigation section of yesterday’s lesson for my commentary on teaching this problem.  


Resources:  AP FRQ 2008 #1 question, scoring rubric, and pipecleaner model


28 minutes

Based on your observations of students’ work, decide how today’s class time will best be spent in preparing students for the upcoming test on solids of revolution, cross-sectional solids and differential equations.  One option is to review slope fields by presenting students with some released AP exam questions that focus specifically on differential equations with slope fields.  Lin McMillan and James Rahn compiled several released AP questions involving slope fields in the Slope Field AP Problems (McMillan Rahn) file, so you might work through some of these in class.  Note that tonight’s homework sheet uses questions #16-19 so do not solve these problems in class today!  Decide how you want students to complete problems while in class:


1)   Individually, perhaps if most students have moderate proficiency, and to make the focus on preparing for individual completion of these types of problems on the upcoming test

2)   Small groups, perhaps if many students are still weak with slope fields, and you feel students would benefit more from a collaborative environment in attaining mastery prior to the test. 


Resources:  Slope Field AP Problems (McMillan Rahn) questions – all

Closure + Homework

2 minutes
Reviewing Volumes of Solids and Differential Equations (part 2 of 3), Lesson Plan, Closure + Homework.pdf page 1
Reviewing Volumes of Solids and Differential Equations (part 2 of 3), Lesson Plan, Closure + Homework.pdf page 2