And if you don't have it, you may want to skip along. At the end of this post, there is a problem.

First, sympathy for my students as I can’t get them out of my head and I obsess. I have a new student, an extraordinarily bright Algebra I student, who wants to pull an A this last 9 weeks so he can take Honors Geometry next year. He’s pulling a B to B+, so it’s not a stretch.

We were going over something pretty simple and it occurred to me when I left his house that I’d been remiss in explaining a part. I started to obsess, worrying he’d not get it, and decided I’d send him an email via his Mom. I was on my way to Publix, composing the email in my head… when I saw him in Publix! How fortuitous!!!

So the poor kid, I accosted him in Publix. He had a buddy with him and I hailed him down and explained this math to him telling him to call me later if it didn’t make sense. He just kept grinning and promising he would.

I know in his head he was thinking, “Holy crap, she’s totally whack.”

Meanwhile, I was going over something for my girl Alg II student when I realized that my boy Alg II student may have missed it as we didn’t have time to go over everything and he had a test on Friday. Obsessing over him… I am sensing a trend… I called his Mom and said, “Have him come by and bring his book, or I’ll ride my bike over or something, but I have to go over this with him!”

He’s 16 and driving. He drove. Remember those days when you were excited to go get a carton of milk?

We went over it and I realized he didn’t have a grasp on Vertical and Horizontal asymptotes and Holes of rational equations and so I ended up doing 2 hours of research on line last night, composing my own simplified explanation… far frickin’ better than his damn book… and emailing it to his Mom last night.

And in the throes of this, I got a call from my nephew. He’s a junior in high school, #1 in his class, amazing athlete and all around good kid. I love this boy. I have hopes he’ll go to Holy Cross, Fordham or Georgetown… no pressure, but I can dream for the kid.

He said, “Aunt Bou, I’m taking an SAT prep class and I want to make sure I get this problem right and I’m confused. Can you help?”

I said, “Sure! Throw it at me…” to which he did and while on the phone… it did not go smoothly.

I finally said, “Let me call you back. I can solve this….” My sister in law told me later that my nephew said to her, “I know Aunt Bou. She’s doing all sorts of weird stuff to get the answer and in an SAT prep class, it should be easy. It’s Algebra…”

Well, I DID start out doing basic math, but I knew we were in trouble when I got an imaginary number in my answer.

Here’s how it was given to me:

m^2+n^2=12

mn=9

What does (m+n)^2=?

For my Math Geek readers... STOP RIGHT HERE and try to figure it out. I'll tell you what I did next. And I tried to get the little superscript thingie to work and it didn't, so we're stuck with these stupid ^.

Doing basic substitution, no matter how I did it using the first OR second to define one of the variables in terms of the other, I consistently got: m^4-12m^2+81.

Hello? Eighty-one has two sets of factors, 9*9 and 3*27 and neither of them, no matter what you do, will get you 12.

So I decided to create a variable u and make u=m^2 so I could use the quadratic equation, u2-12u+81. I ended up with a frickin’ imaginary number in my answer.

And actually, at this point, I wanted to just solve the damn thing because I know for a fact, they aren’t going to do any funky substitution for u=m^2 so an SAT student can use the quadratic on a timed test.

But I had to know.

I called my sil back and said, “Lee, I’m getting an imaginary number after I started to take the square root of a negative number. That can’t be right. So… one of two things happened… the teacher messed up when creating this problem OR my nephew wrote it down wrong. Write all this down for what I think the problem SHOULD be and have him put it in his back pocket. He’ll get credit for it then…”

And what I thought it should be is… m^2+n^2=18.

How arrogant of me really. But this is what I thought…

n=9/m

m^2+81/m^2=18

m^4+81=18m^2

m^4-18m^2+81=0

(m^2-9)(m^2-9)=0

m^2=9, m=3

Therefore n=3

(3+3)^2= 6^2=36

However… that is wrong. The real problem is the real problem… and the solution is in the extended entry. And I told my sil, I could have worked on this every day and all day on Sunday… and it would NEVER have occurred to me to work it this way… Never.

We are solving for (m+n)^2...

Using the foil method this equals to m^2+2mn+n^2.

We know what mn is… it equals 9.

m^2+ 2x9+n^2

m^2+18+n^2

And we know that m^2 +n^2 equals 12.

Therefore, 12+18=30.

Holy crap.

Frickin' foil method... I'm telling you... substitution was my first choice. I'd never have thought of foiling it out.

BUT I WILL NEXT TIME!!!

Comments

Without looking at the extended entry this looks like a simple "complete the square" problem.

You are given

m^2 + n^2 = 12

and

mn = 9

and asked for

(m+n)^2 = what?

(m+n)^2 = m^2 + 2mn + n^2

substitute

m^2 + n^2 (12) + 2mn (2*9) =

12 + 18 = 30.

QED.

Posted by: The Thomas at April 24, 2008 08:43 PMYes, FOIL.

Something very basic for the SAT.

Now if we can just get the students to write legibly for the essay part of the SAT, we will be all set.

Posted by: The Thomas at April 24, 2008 08:46 PMLOL!!! Got it! emailed it to you ... I see someone beat me to it though!

Posted by: Peggy U at April 24, 2008 08:53 PMSo I'm the only one who didn't think to expand it? Good Grief. I thought for sure substitution... it just seemed the simplest.

Posted by: Bou at April 24, 2008 08:55 PMWorst...post...ever.

Posted by: Toluca Nole at April 24, 2008 09:05 PMTN- Phht.

Posted by: Bou at April 24, 2008 09:11 PMIn my case, its because I have taught "complete the square" recently (last four years).

I would expect the Juniors taking the SAT to have also seen it recently, at least in Freshman Advanced Algebra and have covered it as a Junior in PreCalc.

Most of the schools cover it multiple times through High School because the students haven't mastered the concept of prerequisites and tend to forget everything from the school year as soon as Spring finals are over.

Colleges don't baby students that way and expect to teach something only once. They let you flunk the next semester if you choose to forget the things you were taught in the last class.

Posted by: The Thomas at April 24, 2008 09:11 PMObviously this went right over TN's head.

He is the artist of the family, isn't he?

Posted by: The Thomas at April 24, 2008 09:13 PMI tried the rhythm method.

Posted by: Toluca Nole at April 24, 2008 09:14 PMI think I just had a small stroke reading this...

I am with TN on this....

sorry....

but I think that just gave me a migraine.

SR would like to hang out with you

Posted by: AWTM at April 24, 2008 09:21 PMTom- Yeah, but I'm doing foil constantly... and I just didn't see it. But... this is something I'm going to start stressing to my students.

Yeah, TN is our artist. Heh. Worst...Post...Ever. heh.

TN- You know what they call people who use the rhythm method?

Posted by: Bou at April 24, 2008 09:23 PMYou also tried the rhythm method?

Posted by: Toluca Nole at April 24, 2008 09:24 PMCurses FOILED again!!!

Posted by: Peggy U at April 24, 2008 09:40 PMAWTM- I would have a FIELD DAY with SR!

TN- yes... he's called... Mr. T.

Peggy- Frickin' FOIL!

Posted by: Bou at April 24, 2008 09:42 PMOk, but you know what Bou? It's much more interesting finding m and n. So, I think I'm going to do that too. You think too much!! :) Sometimes it pays to be lazy!

Wow, I must have stayed awake that day in Algebra II because I actually got that. I like math problems but am not always great at them.

Posted by: Sissy at April 24, 2008 09:54 PMPeggy- I think I got m to equal (12+/-13.4i)/2... but that was on some weird iteration and it could be way wrong. That was with substitution, a=1, b=-12 and c= 81, assuming u=m^2. Good Grief. I probably botched that up too. come to think of that... that may be m^2...

Sissy- I'm really enjoying this tutoring gig. I'm the frickin' Algebra QUEEN when it comes to finding asymptotes.

Posted by: Bou at April 24, 2008 10:01 PMI only found some M n M's...

Posted by: That 1 Guy at April 24, 2008 10:12 PMI think I got it boiled down to something UGLY, like m = +/-(6 +/- 3(5^.5)(i))^.5, and then I didn't go back to find out what the corresponding n's would have been and which pair would be the actual values. However, I didn't really spend much time on that yet. Should I get a moment to myself - I will!

Posted by: Peggy U at April 24, 2008 11:12 PMYeah, that works:

m (or n) = +(6 + 3i(5^.5))^.5

n (or m) = +(6 - 3i(5^.5))^.5

Arrghh. I couldn't get it. And I was a math major. I blame the fact that it is 2:30 in the morning. I'm going to bed thinking about m's and n's.

Stupid math!

Posted by: Jerry at April 25, 2008 01:22 AMOnce I realized I couldn't do in on a calculator, I just went directly to the answer. Yeah, you should have seen my head spinning the father down I read.

Never saw the M&M's correlation, but now I'm craving some.........

I'm thinkin' "Math Wiz" is NOT one of my new job options.....

;-)

Posted by: Tammi at April 25, 2008 05:24 AMOk, I feel bad now. What you said made sense on the phone, so I never wrote it down when I got home. As soon as I saw it on your blog I knew what to do... I had helped R with a problem just like this. My visualization of math while driving a car just ain't what it use to be. GRIN.... And T1G and TN are cracking me up. Very funny.

Posted by: vw bug at April 25, 2008 05:26 AM.... whoa... I tried the problem and could not figure it out.....

.... I think I have a headache now!...

yeah, sorry, bou; i didn't even have to read anything behind what they gave to get it via foil. what you did does interest me, however...

Posted by: amelie at April 25, 2008 07:52 AMBou - step away from the calculator, please. For god's sake...I'm scared!

Posted by: Kris, in New England at April 25, 2008 09:00 AMI'm going to go sit by T1G and see if he'll share his MnM's - my brain just doesn't work that way...

Posted by: Richmond at April 25, 2008 12:49 PMHmm...I may have gotten it.

You are given

m^2 + n^2 = 12

and

mn = 9

and asked for

(m+n)^2 = what?

(m+n)^2 = m^2 + 2mn + n^2

substitute

m^2 + n^2 (12) + 2mn (2*9) =

12 + 18 = 30.

QED.

Posted by: Toluca Nole at April 25, 2008 02:54 PMQED is so stuffy. I think proofs should end with something more contemporary like Woot!

Posted by: Peggy U at April 25, 2008 03:46 PMPeggy: Don't you think yelling "In your face, Flanders!" would be even better?

That's what my family do...

Posted by: That 1 Guy at April 25, 2008 04:25 PMI've been on the computer too long... even after reading the problem I kept thinking I had to solve the values of m and n.

OMG - I have a certification test coming up at the end of May... if I can't even solve a simple math problem I think I'm sunk.

Posted by: Teresa at April 25, 2008 05:05 PMMath is an aphrodesiac. Oh baby, give us more -- harder. HARDER!

Posted by: Bob at April 26, 2008 12:23 AMBefore this post the only foil method I knew refered to Thanksgiving turkey...

PT

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