Slope Field Activity

I’m getting ready for Twitter Math Camp's calculus working group (ah!).  We’ve been asked to bring some activities to share with the group, so I’ve been frantically searching my blog this afternoon for stuff I can contribute.  I was typing up a list when I realized I don’t have a whole lot for the second semester of Calc AB.  I imagine a lot of that has to do with the fact that we’re in review mode for half the semester, but still.

However, I did realize that there was one pretty good lesson on slope fields that I didn’t blog about.  I probably didn’t write about it because I stole it 100% from my APSI instructor last summer.  Nevertheless, I’m not feeling that trepidation currently.  This magic should be shared.

• On the board, draw or project a blank Cartesian plane along with a differential equation.  There should be at least as many integer coordinates as there are students:

• Give each student a card with a coordinate on it.  {If you're as Type-A as I am, here are cards you can print for up to 35 students.  And if you're REALLY Type-A, you can print them on card stock, laminate them, and cut on the solid lines.  I love laminated cards.  Laminated cards make me feel like I just insured a valuable asset. Moving right along...}

• Each kid figures out the slope of the tangent line at the given point and draws a tiny line segment with that slope at the given point.

• When everyone is finished, they’ve all contributed to a graph that looks something like this:

My class's actual slope field;
not perfect, but whose slope field is?

For this example, we discussed questions like:

• What's the pattern for the slope to be zero? Why?
• What is the slope doing to the left of y=x?  Why?
• What about to the right? Why?

And I mean that was pretty much all they needed in the way of instruction.  Not that it's all that complicated to begin with, but this was a nice, everyone-get-up-and-contribute type of lesson.

Again, I can take zero credit for this.  But I thought it was worth sharing.