## 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:

## #MTBOS My Favorite: Graphfree

HUGE HUGE HUGE hat tip to @jreulbach and @MrsDavisAlg2 for introducing me to My Favorite. If you make any of your own worksheets, tests, or warmups and if those include graphs, this is going to be YOUR favorite favorite as well (I guess you could check out the other favorites from the ExploreMTBoS blogging initiative, but I’ll know that this one is secretly still your favorite)

Let me preface by saying that I love Desmos. I love introducing teachers and students to it for the first time. So intuitive and the graphs are so pretty…until you try to put them in Word. Then the graph is too big or the font is too small and you can’t label and the grid lines aren’t where you want them and you can’t see the gridlines when you copy on the copier and yes, there are some workarounds and hacks but at 8:30 the night before I’m giving a test I just want to painlessly insert a readable graph. I actually got pretty good at using wordart to graph stuff (please don’t even mention the horrible graphs that come out of the Microsoft Math add-on), but still, it was time-consuming and not perfect.

Enter: graphfree.com

(If I was one of those annoying websites with sound, I’d have a chorus of angels singing right now)

This is EXACTLY what I needed.

The above graph took me a minute, maybe two at the most. The program is fairly intuitive (there’s also a great user guide and videos), so I’m just going to point out some things you may not notice at first glance.

Hint: To make labels, under the calculator, there are three tabs. Choose “set custom note texts” and type your labels. Once you “Create Plot” you can drag the labels around the graph. Note: The location resets every time you “Create Plot” so wait until you have your final version of your graph before you drag them around.

Hint: (I just found this one out this week!) You can make a custom quickset with all of your settings. Look at the very bottom (below the three tabs below the calculator), you’ll see “apply custom quickset” and “create custom quickset.” I like -8 to 8 on my axes with black gridlines, so I set that as quickset. Now I just click that when I open the page and it’s magic!

Did you say you wanted to make some inequalities?

Hint: Again, below the calculator, there is a tab for “set shading options” Here you can tell it shade above/below any of your functions, and also shade right/left/above/below vertical or horizontal lines. Note: it does not graph the actual line for the right/left/above/below shading. I added the vertical line by choosing the “implicit” plot type and entering x = 4. Alternatively, there is an “asymptote” plot type that will give you a dashed line.

The asymptote is what I used for the axis of symmetry:
Hint: Use the scatterplot type to add specific points to the graph.

There’s also polar:

And Cartesian in radians in terms of pi!  (this option is found under “Grid Type”)

And slope fields for you Calculus folks (under “plot type”):

And even number lines! (Hint: make sure both the plot type and the grid type is set to Number Line)

The only thing that’s a little tricky is getting it into your Word document. You can either use the snipping tool OR right click, copy image, then in Word select “paste special” then “device independent bitmap”. I like to set the pixel image size to about 200 x 200; I usually don’t have to resize it once I paste it. For more details about how to insert the image, see the user guide here.

Seriously, spend 10 minutes reading the user guide and watching the videos and you will be a Graphfree expert.

Bonus hint: you can also not plot any function to make a blank coordinate grid for worksheets and tests!

I told you it was going to be your FAVORITE favorite!!!!

## When to Throw in the Towel

tl;dr: What should one do if, after a week of lessons, a majority of your students are still struggling on a concept that you’re not even sure is all that important?

This week was a really rough week in Algebra II. My goal was to have them be able to graph a parabola given in 3 different forms, then at the end of the week, also show how we can use completing the square to transform standard into vertex form, maybe do some applications of quadratics as well. This is what happened:

Day one: I want to update the chart I used last year, so I made this NTM:

(here’s the file, although after reading this post you probably won’t want it!) Ok, so this took us the entire class period. And it was horrible.
“hey guys, to find the y-intercept, what do we know about a point on the y-axis?”
“….”
one meek voice: “(0, 8)?”
“Yes! So what should the x-coordinate be?”
“0?”
“Yes! So if I know the x is zero, how could I find y?”
“0?”
“Ok, that’s our x, what should we do with that to find y?”
“…”
“Ok, if I give you any x value, how could we find the y-value?”
“….”
(barely containing my frustration at both the students for not knowing and myself for being such a crap teacher that I haven’t even gotten this point across in the first semester of Alg II) “Well, we put it in for x. Because see how the equation equals y? This is how we can find any ordered pair if we know one of the coordinates! So plugging in zero for x in any equation always gives us our y-intercept!”

5 minutes later, for the next form:
“So, how would we find the y-intercept?”
“….”

I kid you not. Every. single. class. period. In retrospect, I think I should have had one example of each form under each category and worked through it, rather than just doing it as scratch work on the board. But I thought seeing it all together with the graph would make more sense. I was wrong.

Also, I thought this was going to be so easy that I might as well talk about where the graph is increasing/decreasing and positive/negative to fill in time. (Note: we had already done positive/negative when talking about quadratic inequalities).  In case you didn’t know it already, talking about where a graph is increasing in terms of x and not y is one of the hardest concepts in math. Ask me how I know.

Day 2:

Onto the back (which I had planned to have finished yesterday! Ha!)

They were in partners and I let them work on each section for 3-5 minutes, then we talked about it. They were doing not horrible, but some didn’t know where to start. Again, in retrospect, I should have put “how to find the vertex” on the front, not “axis of symmetry” because they would tell me there were no instructions for the vertex. (I mean, yeah, except for the box at the bottom of the graph that had “vertex” and an example of each equation, but c’mon, that was all the way at the bottom.)  We had about 7 minutes left at the end of class, just enough time for them to cut out their dominoes for tomorrow. The right side was homework.  (The bottom was homework the previous night, because they didn’t do so hot on their unit circle test, either. So far this semester has not been off to a great start.)

Day 4: “Ok, I think we maybe need to see the big picture of all these equations again.” So on the back of our worksheet, we did an example together of each of the three types. Then I set them loose on the front again. It was horrible. We have no idea what these numbers are. The x-intercepts are (-1, 0) and (4, 0)? That must mean the vertex is at (-1, 4)! Oh, the vertex is x = 5 and y = 3? Oh, that must mean the x-intercept is 5 and y-intercept is 3. Or the vertex is just x = 5. I went around putting out fires and got most of them through it, but I doubt they would be able to do it again on their own (ok, maybe 15% could).

So this bring us to where we are today: Not much farther in our knowledge of parabolas than we were on Tuesday, perhaps even less (or at least more confused). Also, may I remind you that this is Algebra II, so we’ve already seen these in Algebra I, and I have many, many, many more topics to cover this semester. These extra forms aren’t even in the course of study; I just thought it would be a nice review of parabolas by themselves (we’ve already had a whole chapter on transforming famous parent functions) and practice in seeing the same thing different ways and being able to see why some forms may be better than others.

My question is: do I throw in the towel?

I honestly think it would take at least two more days of practice for them to even be able to attempt a quiz on this. And what could I do differently during those two days that would help them improve? Other than, here is yet another example step-by-step. And I still want to cover completing the square and maybe some applications (as in, where is the ball at its maximum, how long in flight, etc…stuff they’ll see on tests and in other courses). Should I just say, this just wasn’t a good week of lessons. Let’s work on changing standard to vertex because we like vertex form and that’s the only type of graphing that will be on the quiz. Should I try the applications on Monday, which would give them more practice about finding y-intercepts, vertices, and x-intercepts? Should I just forget that last week happened entirely and start the polynomials chapter?

Any advice would be greatly appreciated. Leave it in the comments, or better yet, tweet me (@mathymeg07) so I can pick your brain even more.

## #MTBoS A Day in Meg’s Life

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I’m optioning the movie rights as we speak.

(This is part of the Explore MTBoS Blogging Initiative. Please join in!)

Tuesday, Jan 12th

5:30 Alarm goes off. Hello, She & Him!
5:40 Alarm goes off. Oh, hi, again, She & Him.
5:50 Alarm goes off. You again, She & Him?
6:00 Alarm goes off. JEEZ LOUISE I’M GETTING UP ALREADY. WHY ARE YOU SO JUDGE-Y, SHE & HIM?
6:00 – 6:30: Get Pretty.
6:30 Mr Craig is out of town, so I have to make my own breakfast, ugh. (By “make my own breakfast, I mean, “get out a breakfast cookie from the pantry and pour a glass of water” but these tasks are what I have Mr Craig for, right?)
6:45 Off to school
7:00 School! I do some quick MTBoS research to come up with an easy game to play in Alg II while doing a trig practice worksheet. Then reprint my gradesheet AGAIN because they keep adding new students (without telling me, of course. It’s a fun game called “watch your attendance numbers/spot the difference!”).  I also check email, write a quick bellringer for Algebra II, and write my daily quote and learning targets on the board.
7:30: Bell rings to allow students to come into the classroom part of the building. I take up my high-five patrol at my door. Guys, I don’t know how Glenn kept this up for an entire year. Next year, I’m only doing it on Fridays.
7:45: First period. The game goes well! I modified Ghosts in the Graveyard with Mrs D’s choose-a-color-to-grade. (Assigned numbers to each person in group and roll die to see which person’s worksheet will get checked.)  Our sign language interpreter also came to observe me because one of my students with a hearing impairment is doing well in my class versus her previous math classes and they wanted to see what I may be doing differently.  A nice compliment, but I’m not sure I have any sort of magical powers.
8:47: Second period, same as first.
9:44 PreAP Precal. I get to teach function tranformations!  Yippee!!  It’s also Trig Tuesday–a four-question trig value quiz they’ll have from now until the end of the semester. They are finally super quick with their values and I don’t want them to lose that knowledge!
10:41: Fourth period, Alg II. Because of lunch, this class is longer than all the rest (an hour and five minutes versus 52 minutes (this is also a “long period” day. MWF we have 47 minute classes and a 30 minute study hall)). This class period makes me long for hour classes; it’s nice to have room to breathe!
11:46: Lunch. It’s supposed to be 23 minutes (!) but fortunately the math department has planning 5th period, so we usually stretch it out to a half hour. No matter how busy my day is, I never miss lunch with my colleagues! They are the best. I am a creature of habit; my lunch is always pack of peanut butter crackers, a scoop of trail mix, and a peanut butter chocolate chip granola bar.
12:15: Planning. I find my function transformation speed dating cards for tomorrow, enter in grades, email a teacher assignments for a homebound student, go to the restroom, and start working on modifying the Precal study guide that I’ll hand out tomorrow.
1:11: PreAP Precal
2:08: PreAP Precal
3:00 School’s over!  Take my 10 minute twitter-and-apple break. Finish the precal study guide, make copies, then decide to go ahead and make the key, then find the mistake I should have corrected before making the copies. When will I ever learn?
3:50: Leave school
4:05: Get home, turn the fireplace on and play some Two Dots.
4:30: Mr Craig gets home
5:00: Go out to dinner. We are not cooks at all so usually go out to eat. Last night we used a gift card for Bonefish–I’m kind of in love with their mango salsa over mahi.
6:30: Back home, relax with a little more Two Dots (I may be slightly addicted to that game)
6:45: Search for an activity for my students to do when they finish trig worksheet. Can’t find exactly what I want, so I spend 20 minutes creating my own Odd Man Out worksheet. (Which I determined today has 2 wrong problems out of 10. I guess the answer is, no, I will never learn. But the linked file is fixed!)
7:30 Watch 2 episodes of Making a Murderer with Mr Craig, miss the last 30 minutes because I fell asleep.
9:30 Get unpretty, read a little bit of Girl with A Gun.
10:15: Lights out!

Category: Uncategorized

## 2016 Resolutions #MTBoS12Days

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But to expand that a little more…

Goal #1: To become more efficient at school. I worked too many long days this semester and a few weeks it became sleep, eat, school, repeat. I need to streamline some tasks and remember that perfection is the enemy of good!

Goal #2: To keep trying to stay fit. The #500in2015 challenge really pushed me, but since I’m a slow trotter, I didn’t have time to do any other type of exercise. This year, to keep myself accountable and have a challenge to work towards, I started the #160in2016 challenge: Exercise in any form (walking, running, biking, yoga, ballet, strength training, unicycling) for 160 hours during the year. If you want to join in for accountability and motivation, sign up at bit.ly/fitbos16. You can set your own goal–we have goals ranging from 104 to 200.  (I got 160 by 30 minutes x 5 days x 50 weeks = 125, so 150 would be a stretch goal, and then 160in2016 just sounded nicer.)

Goal #3: 100 Hours of Creativity. In the past, I loved making handmade cards and I hate to brag, but I was pretty good at it! Then we moved to new house with a view and all I want to do is sit on the porch bedswing and read. But I fear as though my creative side is turning to mush, so I’d like to get back to creating something.

Goal #4: Read 52 books and participate in modernmrsdarcy’s book challenge (thanks for the link, Pam!)

Maybe I’ll find the next ICPBy award winner from the challenge!

Goal #5: Take time to enjoy my husband, my dog, and my family.

Wishing you all a wonderful, healthy, goal-achieving 2016!