Introducing Differential Equations Through Slope Fields

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Objective

SWBAT sketch slope fields and estimate solutions graphically to basic differential equations.

Big Idea

We have sketched and computed integral functions before. Today we build on this background and introduce differential equations graphically.

Video Narrative - Lesson Overview

Warm-up and Homework Review

30 minutes
Introducing Differential Equations through Slope Fields, Lesson Plan, Warm-up and Homework Review.pdf page 1

Setting the Stage

25 minutes

Distribute the Volumes of Solids Quiz, which is 25 minutes timed.  The directions tell students to use the fnInt command on their calculators to evaluate each integral, but read these directions aloud to students as an added reminder. 

In prior years some students have wasted a lot of time working the integrals by hand, which causes them to run out of time and also weakens our ability to assess students’ ability to setup the integrals correctly.  25 minutes is enough time if students are reasonably proficient with sketching the regions, because writing the integrals from the sketched regions and evaluating the integrals with fnInt does not take a lot of time.

Closure + Homework

5 minutes
Introducing Differential Equations through Slope Fields, Lesson Plan, Closure + Homework.pdf page 1

Links

Slope fields applets

Stewart Calculus - Tools for Enriching Calculus, http://www.stewartcalculus.com/tec

University of Michigan, http://www.math.lsa.umich.edu/courses/116/slopefields.html