Reviewing Volumes of Solids and Differential Equations (part 2 of 3)
Lesson 7 of 8
Objective: SWBAT model differential equations with slope fields, solve separable differential equations algebraically, and compute volumes of solids of revolution and cross-sectional solids.
Warm-up and Homework Review
For general ideas about implementing this and other lessons, read my Course Outline.
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
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
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
Previous lesson plan, with discussion of Free Response Question 2008 #1
Google Doc link for submitting homework answers