## Thursday, June 26, 2014

### 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.

## Monday, June 23, 2014

### Class Consensus

I taught a five-day summer camp last week to prepare our incoming juniors and sophomores for the PSAT/NMSQT.  One of the greatest things about it, for me, was that the other teacher (English) and I have very similar approaches to teaching; that is, make the kids do the work and talk as little as possible.  We split the kids into groups quite a bit (half did math with me and half did English with her and then we'd switch); when we reconvened, we'd often shrug and say, "Well, that was easy."  We got to teach some pretty motivated kids (especially considering it was summer), and they were good at taking ownership for their own instruction.

That said, there were still times when I'd have an internal panic attack that went something like, "WHAT AM I GOING TO DO WITH THESE KIDS FOR THE NEXT HOUR AND TWENTY-FIVE MINUTES?"  Because it wasn't really "normal" school where I have to get through Section 4.1 today, please and thank you.

So, this little idea came from trying to stretch out what was supposed to be a 15-minute activity into a 30-minute activity.  Honesty is the best policy?

Last summer I attended a PD session on literacy.  Apparently, some stuff really stuck, such as this idea which (I think) the instructor called "Class Consensus." I've done this with some reading passages with moderate success.  But how I never thought to use it with math exercises is beyond me.

This is how it went down:  I gave each student a "Mini-PSAT Test," consisting of seven past PSAT questions.  They were given ten minutes to work this test on their own.  After the ten minutes, they compared their answers with their partner and were asked to reach unanimous consent.  Then, the group of two joined another group of two, and the new group of four was asked to also reach unanimity.  Then the groups of four made groups of eight.  At this point, I had written on the board the numbers 1-7: