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 trying. Really 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)
I am not kidding about this exchange on the last problem:
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?”
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.