Slope Fields (Topics 7.37.4)
Unit 7  Day 3
Learning Objectives

Create slope fields

Estimate solutions to differential equations
Success Criteria

I can create a slope field given a differential equation in terms of one or two variables

I can match a slope field to its differential equation

I can describe slope fields
Quick Lesson Plan
Overview
Today students will engage in two activities to reinforce their understanding of slope fields and estimating solutions to differential equations. The first activity involves assigning each group of four a different differential equation and having them create a slope field on poster paper using Wiki Stix. The second activity has students working in pairs where one partner makes a 3x3 configuration of slope fields and the other partner must match their partner’s configuration with their own identical set of slope field cards, by asking only yes/no questions.
Teaching Tips
Cut up the differential equations and give one to each group. Have students spread out and make their slope field on poster paper. Provide markers so they can scale their graph. We told our students to use [2,2] for both the x and yaxis, and then plot slopes at those 25 points. Students should hang their poster somewhere on the wall.
There are two variations on this activity. In the first version, students write their differential equation on their poster. During the gallery walk portion, all students must comment on at least three other slope fields by writing and posting on a sticky note. They should give feedback on their peers’ slope fields and check their work. In the second variation, the differential equations are not written on the posters. During the gallery walk, project all the differential equations and have students identify which poster corresponds to which differential equation by keeping track on a recording sheet. You could label the differential equations AI, or however many groups you have.
The second activity has students working in pairs. Pairs need to be facing each other and have some kind of divider so they don’t see each others’ cards. Each partner gets an identical set of 9 slope fields. Partner A makes a 3x3 configuration of their cards. Partner B then tries to match that configuration by asking a series of yes/no questions. (Ex: “Does the card in the upper left hand corner depend on only x?”). Over time students learn to ask better, more specific, questions and realize the value of using related vocabulary words. They also learn to notice patterns in slope fields.
You can make this activity competitive by giving a prize to the first pair that matches all their cards correctly or the pair that has the most cards in matching positions after an allotted amount of time. Furthermore, you could award a prize for the pair that matches their cards using the least amount of yes/no questions. After students finish, challenge them to think about what the solution curve would be for each slope field. Many of them are straightforward functions like sin x, cos x, and x^3.