## Parabolas Post Mortem

FINALLY.  I am FINALLY done with parabolas in Algebra II.

I spent most of last Sunday afternoon trying to take all the suggestions from my last post and put it together into some sort of lesson and this is what I came up with:

I went in on Monday feeling like Super Teacher.  I mean, I hate to brag, but check out #14. Taking a side!  And figuring out what the most important point of a parabola!  And all the other problems, where we find something in the graph and then relate it to the equation!

And then first period hit:

The thing was, 98% of them were tryingReally hard. But the questions!  I think when I had to answer “So it says find the value of y when x = 1. Should I plug in 1 for x or for y?” is when I had my complete George Michael collapse. I don’t know how to fix this. I can’t fix this AND teach one of the most packed curriculum in high school math. I was actually considering doing even more application problems without a graph the next day until my Best Teacher Friend (I hope everyone has a BTF as good as mine at their school) talked me out of it.  You have to meet them where they are, right? So, after finishing it up on Tuesday and discussing it, we went on to:

OKAY I WILL SHOW YOU AGAIN STEP BY STEP HOW TO DO EACH OF THESE.

(file here, with some bonus homework on pg 2)

Me: “OK, we found the x-coordinate of the vertex. How are we going to find the y-coordinate?”
At least three students: “PLUG IN ZERO!”
Me: “I’m glad you finally remembered that about finding the y-intercept, but now I need to find the how high the point will be on the axis of symmetry. So I know the x, but I need to find the y….how could I do this?”
Everyone: “….”
Me: “OK, well, guys, we’re going to plug it into the equation. Remember if we know one coordinate, we can always find the other by plugging it in?”
Student: “Whoa. That never would have occurred to me to do that.”

Wait, what? We’ve done this for a week and you just did a whole application worksheet where 1/2 of the questions were, “we know this x, let’s plug it in to find y” and it never would have occurred to you?!?!?!

I don’t want you to get the wrong impression; I’m not saying these kids are stupid or dumb. It’s just I don’t know how to get them to connect anything.

Ok, wait, I’m getting into a “Sometimes I Wish I Had Never Found the MTBoS Because I Used to Think I Was A Fairly Good Teacher and I went Home at a Normal Time and I Can’t Continue to Be Student-Centered if the Students Aren’t Prepared to Bring Anything to The Table” Funk so let’s focus on something that sort of worked!

We were still (!) struggling with characteristics of a graph. So I made this worksheet and put it into dry erase pockets:

(file here) Here is one thing that I found that helped teach increasing/decreasing:

At what time does the parabola change direction? Draw a vertical line and label it with the x-value.” (also label +/- infinity)

As you’re drawing from left to right, are you doing down or up? Ok, so we’re decreasing on this interval and let’s read it from left to right, (-infinity, 3).”

Repeat with the right side. This seemed to help (a) “but aren’t we started at the top which is positive infinity?” (b) “we’re decreasing to -5” (c) answering are we increasing/decreasing on a certain segment seemed better than where are we increasing/decreasing.

I did a similar thing for positive/negative, calling back to Dolphin Dave being underwater or above water and drawing the waves on the x-axis:

The success rate on the quiz was lower than I expected after doing some formative assessment on the last two problems on the handout, but better than it was before this activity. I think doing this as a separate lesson on day 1 would have helped. Or just waiting until Precal, which is when we normally focus on this.

Anyway, we started the study guide and worked on it Thursday:

The quiz grades were actually really good–lots of As and Bs, only a smattering of Ds and Fs. But the level of the quiz was definitely lower than what I’ve given in the past. I don’t know what to do about that.

I would also like to apologize to the 10% of my students that got this on the first day. I actually had two of them say that this was so easy, why were taking a quiz on just this? I’m sorry we had to spend two weeks on this. I know you’ve been bored out of your mind but you’ve still been working hard and helping your friends and thanks. (I did tell them this, but in a nice way about “some of us found it really hard…”). I don’t know what to do about them either (and please don’t tell me “find some differentiated activities for them to do” because I just cannot handle one more thing at this moment in my teaching.  I’m really just saying I don’t have the answers to anything.)

But I do know one thing.

I am done with parabolas.

Category: Alg II | Tags:

## 8 comments on “Parabolas Post Mortem”

• Thanks! It’s always better when you know someone else is in the same boat, even if it’s sinking. 🙂

2. Cute story. 🙂 Thanks for following up and I’m glad it’s over with an increased level of success for those kids.

• Thanks! I’m just glad it’s over (in case I didn’t emphasize that enough in the post. 🙂 )

3. It sure made me feel better to read your post. We are about to face our new more strenuous college and career readiness state exam this spring and I don’t think most of our students are anywhere ready for it because the rigor of the questions is so far above what most of them see capable of at this point. I just hope that we aren’t the only ones

4. I also feel your pain. I have had your blog post in my email since you posted as I was also in the middle of quadratics. It has been 6 weeks & we are still not finished. I am so sick of factoring as are some students, but 75% still cannot do simple factoring from Algebra 1. I know they will need the idea for Trig & College Alg, but finally decided to move on to quadratic formula. Discovered about 10 students tried to substitute x in for “b” when “b” was equal to “1”. Still cannot get them to relate “x” is the same as “1x”. I also appreciate the 25% that always do their practice & help their peers, but I feel that we are not moving forward at all. We did the whole graphing & graph characteristics first then tackled solving quadratics.

• YES substituting in x!!! And I too feel so sorry for that 25%, but can’t feel I can move faster with so many lagging behind.

The good news is, solving polynomials has been going a little better. They actually liked it today. 🙂

5. A few thoughts. The first is that, honestly, I think most ALG2 kids just aren’t ready for this type of thing. I’m lucky enough to work at an independent school, so I teach what I want, how I want. A lot of the stuff you’re covering I don’t get into until PREC (domain, range, increasing, decreasing) or CALC (concavity). Which is where I feel that fits better anyway, as they’re doing that type of analysis on all the 12 basic functions anyhow.

So I really focus on the “what matters” parts of parabolas in ALG2. And that’s the y-int, the x-int(s), and the vertex. Those are where the interesting things happen anyway. The “we found h but don’t know how to find k” part of the vertex is something I remember them struggling with last year.

I just wrote my curriculum for next week and I’m trying something new for the vertex. I’m going to make them expand vertex form and compare it standard form. Then it’s pretty easy to see that b=-2ah and c=ah^2+k. Their skills are good enough that they can easily isolate h & k and now they can find the vertex from standard form without needing f(h)! Of course, they’ll still need to plug h into the formula for k, but I’m hoping that comes more naturally to them than plugging h in where x usually goes. Also, I’m going to show them that plugging it back into the quadratic yields the same answer for k and that it SHOULD occur to them to plug it in. But they’ll have a work-around, if they want.

We’ll see. Maybe the idea will fail horribly, I dunno.