Ok – I apologize for the sense this ** will not** make as I write. I’m exhausted, sweaty, bruised, covered in mud/grass, I don’t want to see a deck of cards for a LONG time and I have very little brain left (see the end of the blog for why – it’s not as bad as you’re thinking).

By the way, some of you don’t know me very well or this is your first time to my blog, so welcome to the crazy – my apologies in advance. Do not come here looking for divine inspiration and professionalism. My A.D.H.D. needs an outlet and, because I prefer to KEEP my job, I just ramble about whatever’s on my mind. So unlike other amazing bloggers you may know who overwhelm you with awesomeness, my blog is NOT written that way. You’ll love it or hate it and I’m ok with that.

Anyway, I’ve taught Algebra 2 at my current location for about 5 years. I mostly get the 10th graders who already think they’re hot snot in the intelligence arena. Quadratics, however, has always been a challenge for them. They’ve never had to REALLY THINK before and the introduction of quadratics is usually where the “fit hits the shan”. Every semester I change it up a little hoping to tame the beast, but they always freak regardless of what I do.

…until this semester… they’re kickin’ butt and taking names. And I don’t know why. So I’m gonna give you the outline/lowdown on what I did in the past and what I’m doing now. I’m only really blogging this for the 12 or so people that asked me to – I still think you’re not going to get anything out of it, but here ya go:

What I’ve done in the past:

1) Graph quadratics (standard, intercept, and vertex form)

2) Real world problems re: graphing quadratics (w/ and w/o graphing calc)

3) Factoring quadratics

4) Solve quadratics by factoring

5) Real world problems re: solve by factoring (w/ and w/o graphing calc)

6) Solve quadratics by taking square root

7) Real world problems re: square roots (w/ and w/o graphing calc)

8) Non-real numbers (imaginary/complex)

9) Solve quadratics by quadratic formula

10) Real world problems re: quadratic formula (w/ and w/o graphing calc)

11) Graph quadratic inequalities (include word problems)

12) Quadratic regression (lots of word problems)

So basically I started with the picture of a quadratic, introduced the algebra, and intertwined the algebra and the graphing and the word problems. Logically and by scaffolding, that SHOULD work and make connections to the kids, but it just didn’t (or I just SUCKED at teaching it). They weren’t used to doing many intense word problems in previous classes and I guess the combo of the two just blew their minds.

So this is what I did this semester:

1) “Fast and Furious Factoring” (or F^3).

Factoring SHOULD be a review, but most of these kids haven’t factored anything since 8th grade Algebra 1. I started with quadratics in the form x^2 + bx + c. We “muscled” through a review of about 5 of those together as a class, then they did 5 on their own and discussed their answer with a partner. THEN it was a F^3 challenge: 10 factoring problems (all the same type) and they had 3 minutes to do it. Three minutes sounds like a lot but it really wasn’t for them. They don’t like being “timed” (even though the SAT and ACT are timed) and they have issues with it. So I would loudly announce 2 minutes remaining, 1 minute remaining, 30 seconds, 10 seconds, then TIME. As students finished during the 3 minutes, they ran to bring me their papers. If they got them all right, they got a sticker (one of those old school foil stars – I was out of cool stickers). If they got ANYTHING wrong, I could tell them how many were wrong, but not which ones. But they could still correct and get a sticker AS LONG AS they got me the correct 10 within the 3 minutes. I wish you could’ve heard them. “GAAAAHHH, Ms. ApproxNorm!! This is so stressful!!” “Grrrrrr!! I thought I wasn’t gonna get done! You kept SHOUTING time at us, it stressed me out!!!” “Um, yeah, Ms. ApproxNorm. You’re annoying. No offense.” heh heh heh

So after we finished that form, we did the same pattern for the following forms, each time discussing what would have to change and WHY:

** x^2 – bx + c

** x^2 + bx – c

** x^2 – bx – c

Then all crap broke loose because after the last set of F^3, I threw in a “Double Jeopardy” round (that’s right, TWO stickers) and I mixed all 4 forms. I gave them four minutes to do 10 problems, but I just did totally random crazy junk during that four minutes. Loud stories about crazy crap that happened to me that week, out-of-tune songs, whatever I could think of to just throw them off their game. Ohhhhhhh my word, they HATED me for that. But it was crazy with a purpose they didn’t understand yet. Then I hit them with the same format, now introducing a coefficient for the quadratic term:

** ax^2 + bx + c

** ax^2 – bx + c

** ax^2 + bx – c

** ax^2 – bx – c

Then here we go again – a Double Jeopardy round. Before I started the round, I started this crazy “people of Wal-mart” story that went on and on and on… and the kids were FREAKING out. “Ms. ApproxNorm?!! Just start the round!!! Geeez!!” And JUST when they thought I was going to ramble for another 5 minutes, I said, “GO!!!!” and they all went, “AUUUUGHHH!! Ms. ApproxNorm!!!!!”

So why all the craziness?? They need to control their anxiety when under time constraints. If they can be quick and accurate under THOSE conditions, then there’s hope that the SAT/ACT won’t have such a hold on their insecurities. Or at least that’s my idea. 🙂

For the FIRST time, no one failed my “First Round Factoring” Quiz. Or my 2nd… or my 3rd. Blew my mind.

2) Solve Quadratics by Factoring

I actually left this as a challenge for my students while I was at a meeting. I left a hand-written sheet (no, I’m not proud, but was out of ink) to complete after a quiz where I’d showed them about the zero product property, I worked a few problems for them, and then challenged them to teach each other how to do it before I got back. I didn’t expect them to even put any effort into it. But I got back and they said, “Ms. ApproxNorm… where was the challenge?” Yeah – my kids addressed ME in a #childplease moment. So that was that. Two objectives down.

3) Solve Quadratics by Square Roots (and unexpectedly, by Quadratic Formula)

This usually takes me an entire block to teach all the different crazy ways they might have to do this. From x^2 + 7 = 15 to (x – 4)^2 = 28, kids have historically STRUGGLED with this topic (which to me is a “no brainer”). Both my Alg2 classes picked this up in no time whatsoever, so I was completely caught off guard. So I thought, “Ok, I can stop class 40 minutes early and let them be bored after they finished homework. Nope – I was about to take this good luck for a spin and see where we went with it. So within the same class I started the next topic – solve by quadratic formula. Now I know what you’re thinking. “Girl, you haven’t covered non-real numbers.” Yeah, I know that. I stuck to the ones that would only have real solutions and hoped it wouldn’t come around and bite me in the butt later. They rocked that too (thanks to a jingle they learned in Algebra 1).

**again, this is KILLING me to just do algebraic manipulation. BUT I’d tried the other way 10 different times with the same results, so in my mind I’m thinking, “Let me show them how to use all the tools in the toolbox first (algebraic stuff) and THEN we’ll build a treehouse (real world stuff).” I’ve never done this approach before and it made me feel like a total “drill ’em and kill ’em” LOSER. But to be honest, the kids were entertained (mostly because of the competition, challenge and the fact that I’m goofy as heck) and they were doing GREAT. Plus, as freakin’ clumsy as I am in real life, you HAVE to show me how something works before you expect me to APPLY it.

4) Non-real numbers, graphing quadratics (sort of) and quadratic formula (again).

Ok – at first this was a halting point. They could do all the algebraic manipulations, but they couldn’t understand how the HECK people came up with that crazy imaginary number, i. THANK GOD for @gwaddell’s presentation at TMC12! (Link will go here) Once I showed them how the non-real numbers were related to the reflected parabola’s intercepts and the “shared” line of symmetry, they were GOOD TO GO. So non-real numbers were non-problemo and FOR FUN, they wanted to go back to quadratic formula and use their new “knowledge” on solving quadratics w/ non-real solutions. Who the heck ARE these alien children????

So now we’ve covered all the tools of the trade and know what quadratics look like algebraically – let’s see what these suckers look like in 2-dimension function world.

5) Graphing quadratics.

Do your kids freak about the different forms, finding the vertex, etc.? Mine do too… or at least they DID. The kids were amazing. “Ok, Ms. ApproxNorm, well DUH. Vertex form allows you to start with the vertex, intercept form allows you to start with the intercepts (and then we find the vertex on the symmetry line which is half-way, so no big deal). And then you’ve got this standard form – finding the vertex is related to quadratic formula, so what’s the big deal? #MsApproxNormPLEASE” I’m FLOORED. I did an exit pass to check to see if I was crazy, but no – THEY GOT IT.

6) Welcome to the Jungle, er Real World

So here we go… GAME TIME. Did my “method to the madness” work? Or will it bite me in the butt? Let’s see…

So we talk about the h(t) = -16t^2 + v0t + h0 formula, where it comes from, what the “pieces” mean… and then I intro’ed their first “real world” problem. “Some rogue former student with a grudge is holding Ms. ApproxNorm by her ankle from the top of a water tower. She is literally HANGING 168 feet above the ground. Assuming no superhero (or boyfriend musician *cough* GAVIN *cough*) swoops in to save her, how long until she becomes a red spot on the pavement below?” –> I realize this is gross and morbid… and gross. But the kids LOVE this and it works for me, so back off. 🙂

Anyway, I honestly cringed inside and thought, “Ok – THIS is going to kill them. You’re about to see where you ROYALLY screwed up, Hedgiepoo.”

But it didn’t happen… They got it. I changed it so I was shot in the air and they got it. I was thrown to the field from the press box of the football field and they got it. I shot myself from a cannon. I was dropped by the CIA from a stealth bomber and they got it. Sometimes I was caught, sometimes I wasn’t. Didn’t matter.

THEY GOT IT.

I’m not finished with quadratics (midterms and all), but this is just NOT the norm for what I’m used to in Alg2. Is it good? Is it bad? They all had the same teachers as every other sophomore before them. So what’s different?? I refuse to think any of this has to do with my awesome teaching skills (because let’s face it – I have none). But maybe the “tools in the toolbox” method actually WORKED?????

Holy cheeze-its – that would be AHMAHZHANG if I finally found the solution to the biggest zit I’ve ever faced in Algebra 2.

But only time will tell if it was the right decision. I hope I didn’t screw ’em up. I know a lot of you will disagree with my layering, but I SWEAR I’ve tried it every other way over the last 11 semesters. I’m still not 100% convinced THIS was right.

I guess we’ll see.

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For the NONE of you that care, I started doing athletic training a few weeks ago. Hardest and most physically demanding thing I’ve ever done, but HOLY CRAP it’s also the most amazing and rewarding thing I’ve ever done.

But I’d invest in band-aids, Epsom salt and Icy Hot prior to starting. 🙂

I wrote this blog after we played “Poker”. Every suit represented a task (burpees, situps, butterfly kicks, pushups, jokers were suicide runs). Our trainer shuffled the deck (seven times at MY request). Whatever suit he pulled was the task we had to do – whatever card he pulled represented the number of times we had to do it (aces were 11, in case you wondered). So, for example, he pulled the 10 of hearts (which is torture because hearts = burpees and WE ALL HATE BURPEES) so we had to drop and immediately give him 10 burpees. Then he pulled the 8 of clubs, so we had to drop and give him 8 military-style pushups). I’ve never felt so “useful” and so challenged in my life. “Ms. ApproxNorm?! He pulled a heart? What’s the probability it’s a low number?” Dammit – WHY did I tell these people I taught math??? But it was amazing. We had to go until we went through the ENTIRE deck (which took about 27 minutes). No workout is ever the same but ALL are completely brutal. The day before, we did our “usual” warm up (run 400 meters, 50 jumping jacks, 20 squats, 20 lunges, 20 pushups, high knees for 10 meters, butt kicks for 10 meters, punter’s kick for 10 meters, karaoke slides for 10 meters, run 200 meters),then we did had to do 12 rounds of 20 squats, 15 sit ups (all the way back up), 10 pushups rotated and completed within less than 2 minutes (so you could catch your breath before doing another round). HOWEVER, I’ve gotten more from this in a few weeks than I’ve gotten from randomly going to the gym over the last few years. I have muscles in places I didn’t know EXISTED, hahahaha.

It’s a great way to clear your head and get all the “grrrrrr” out of your life. If you have a CrossFit-type gym in your area, I HIGHLY recommend it. It’s WORTH the cost, trust me.

And that’s all I’ve got to say about that.

Great post! Sometimes the order that helps students understand concepts isn't what is viewed as “normal”. If it worked for your students, then that is what mattered. I would be interested in seeing if it works for the students next year. There is so much from your post that I hope to apply to my Alg 1 Quadratic unit…I will hit you up when I get there!

Plus…I can totally use your deck of card workout information for my swim team workouts. I am sure my 13-18 year olds will just LOVE it. 🙂

Thanks!

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Thanks for the post! We're starting our quadratics unit in a couple weeks and I did the exact same order you used to do had similar poor results. This year I know I need to change it up since I have the lower alg2 students (all juniors and seniors). I like the sequencing and ideas and will probably give most (or all) a try this year. Thanks!

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I've done quadratics somewhat similarly before (although I had the solve by square root before factoring – I like what you did better by the way) and had some success. I still have to fit completing the square in there before quad form though (doing the CCSSM this year). I really like what you did. Thanks for sharing!

And, for the record, you have lots of good stuff to contribute – don't sell yourself short. 🙂

–Lisa

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I love this post! Your blog is always entertaining to read. I feel like my quadratics unit didn't go too well my first year and I am looking to change it this year. One thing that I struggled with is finding good real world problems to use. If you have time to send any suggestions, ideas or resources that you have on real world quadratics my way, it would be greatly appreciated!

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