Ninth Grade Algebra

[mammal_mama]

Last Thursday, the fifteen year old next door came because she'd heard that we homeschool and she wondered if I could tutor her in 9th grade math. I said it had been a long time since I'd taken 9th grade math but I'd be glad to see if I could help. I invited her to come back the following afternoon as we were going out right then.

So...she finally made it back today, and we sat down together...well, first I had to send her back home to get something for us to work with, LOL, I guess she just thought I'd have 9th grade math problems in my head. Well, she brought back some quizzes her teacher had sent home with her and absolutely none of it made any sense.

Even the one where the teacher gave her the answer that x=2 made no sense when I tried to work it with that knowledge! The equation was "x to the second power minus 2x minus one equals zero" ... well if x=2, then 2 x 2 (the other way of saying 2 to the second power, right?) minus 2 x 2 minus one would equal negative one, not zero, right? I mean two to the second power minus two times two equals zero, of course, but adding -1 to it makes the answer -1.

Or is there someone here who is taking this equation and coming up with zero? If anyone knows of any free online help I can get learning algebra, please let me know! I'd like to be able to help the girl...so far today I just had to apologize and explain that since I'd graduated high school, I'd assumed that if I looked at her homework I could help her, I apologized for wasting her time and said I knew she'd want to find someone who could actually help her.

She and her sister stayed and played with our girls for a couple hours anyway, and she's planning to come back tomorrow for more help. My husband has just now rustled up a math dvd that he was watching back when he thought he might be trying to go back to school. So he's going to copy it so we can work on it and she can, too.

I know I'll need to learn this for when I help my girls get ready for college, and obviously I can learn it since I learned it before, right? -- I mean, I was never that good at math but I got through high school and college. The poor girl said she can go back to her teacher for more help but his explanations aren't making any sense at all to her, so I guess she'd rather come to me. 

[Climbing Rose]

I don't know if this will help, but I was looking at Teaching Textbooks online last night, and was really impressed.

I think if she could get a hold of the level she needs (used even), she should just about be able to take off on her own.

It has a cool little 'lecture,' and then practice problems, and then you are off doing it.

Maybe she could do them at your place, maybe just going through the ones she personally needed.

And you can brush-up then too, if you want to. 

As for as HSing your own, a lot of kids are self-taught by the older grades, so you might not need to know very much.  =D

http://www.teachingtextbooks.com/

I know they're not free, but they have to be cheaper than a tutor!  =)

Edited by Climbing Rose - 1/3/11 at 9:36pm

[love4bob]

Well, that's a quadratic equation I believe, so it would have 2 answers.

ax^2+bx+c=0

x^2-2x-1=0

So, using the quadratic formula to solve it you just plug in the numbers.(this is my favorite way, but her teacher might make her do it by factors which I hate and can't remember how to do right now...)

Quadratic formula= x= -b ± √b^2 - 4(a)(c)

                                 ---------------------------

                                            2(a) 

[moominmamma]

 Sounds like she's supposed to be practicing solving quadratic equations (equations which can be arranged in the form of ax^2 + bx + c = 0). The simplest way to solve an equation like you gave is to factor them into the form of (x + n)( x + m) = 0. There are a few strategies for doing this, and generally you try the simplest first. I would suggest going to http://www.khanacademy.org and searching for video tutorials on "factoring quadratics."

In the example you gave, x=2 is an erroneous solution. I had to use the quadratic equation to solve that one, and it gives solutions of 2.41 and -0.41.

Jumping into algebra in the middle with a 15-year-old is tough if you are rusty on it. Gradualy refreshing your knowledge of algebra as your pre-teen begins to move into that level of study is much easier!

Miranda

[mom2ponygirl]

http://www.myalgebra.com/algebra_solver.aspx

This site looked helpful.

[mammal_mama]

Originally Posted by mom2ponygirl 

http://www.myalgebra.com/algebra_solver.aspx

This site looked helpful.

Thanks! I just went there and entered today's equation which I realized should actually read as follows (since ^ is the way to indicate exponents while typing):

x^2- 2x-1=0

And the site just showed me my equation as the answer. So I'm not sure what's goin' on. The other two sites send by moominmamma and Love look intresting, too. Dh started listening to his dvd that he found which seems to start with fractions and lead all the way into algebra. So this may be a good foundation for us and her, too, if she's not bored ... she could always skip ahead of what she already knows.

They don't currently have internet access but I suppose if they bought the textbooks recommended by Love they could use them in a computer without any internet...if they still have a computer.

love4bob, you make me see how truly clueless I am, as I have no idea how my equation of x^2- 2x-1=0 could be rewritten as --

"ax^2+bx+c=0

x^2-2x-1=0"

or as --

"Quadratic formula= x= -b ± √b^2 - 4(a)(c)

                                 ---------------------------

                                            2(a) "

I mainly just remember that it was kinda fun figuring out what x was, but it sounds like with quadratic equations you never really figure anything out. Maybe I never took this level of algebra? I mean, I graduated high school, and I got a degree in social work in college which required me to pass a course in inermediate algebra -- so maybe 9th grade math these days is a whole lot more than what I took in college? Poor kid!

Of course, I guess it's useful for managing your money. Or something.

[domesticidyll]

I wanted to second the recommendation for the Khan Academy videos. Sal has such a clear, calm way of explaining each small chunk of information--and DS finds him to be hilarious. He really wants learners to understand the concepts behind each algorithm, and embeds just enough information at a time to process. Each video is short (5-15 minutes), talks about one small aspect of math, and builds forward. DS really enjoys watching the videos. For some of the harder concepts, he's enjoyed watching with a pen and pencil so he can do the math alongside, or pause, do the problem, see if he gets it right, and then move forward.

I would recommend maybe letting the student take an online test to see what she understands/what she wants a little review on, and start there, moving forward as fast as needed. If she doesn't feel at home in math, there may be earlier gaps that need filling in, or maybe she will find it helpful to watch some earlier stuff to get not just how to solve the problem, but why, what the problem means. I know Singapore has tests through 5B (6th grade or so?) and Art of Problem Solving has a pre-algebra test that might be useful.

Good luck! It's hard to see someone struggling with learning, especially when math can be so joyful and elegant.

Heather

ETA, sorry, I just saw that the family doesn't have internet access. It sounds like the video is a good possibility.

[ollyoxenfree]

Originally Posted by mammal_mama 

Originally Posted by mom2ponygirl 

http://www.myalgebra.com/algebra_solver.aspx

This site looked helpful.

Thanks! I just went there and entered today's equation which I realized should actually read as follows (since ^ is the way to indicate exponents while typing):

x^2- 2x-1=0

And the site just showed me my equation as the answer. So I'm not sure what's goin' on. The other two sites send by moominmamma and Love look intresting, too. Dh started listening to his dvd that he found which seems to start with fractions and lead all the way into algebra. So this may be a good foundation for us and her, too, if she's not bored ... she could always skip ahead of what she already knows.

They don't currently have internet access but I suppose if they bought the textbooks recommended by Love they could use them in a computer without any internet...if they still have a computer.

love4bob, you make me see how truly clueless I am, as I have no idea how my equation of x^2- 2x-1=0 could be rewritten as --

"ax^2+bx+c=0

x^2-2x-1=0"

or as --

"Quadratic formula= x= -b ± √b^2 - 4(a)(c)

                                 ---------------------------

                                            2(a) "

I mainly just remember that it was kinda fun figuring out what x was, but it sounds like with quadratic equations you never really figure anything out. Maybe I never took this level of algebra? I mean, I graduated high school, and I got a degree in social work in college which required me to pass a course in inermediate algebra -- so maybe 9th grade math these days is a whole lot more than what I took in college? Poor kid!

Of course, I guess it's useful for managing your money. Or something.

It might be helpful to step back a little and explore what a quadratic equation represents. It determines the roots of the formula to graph a curve. It's a particular kind of curve - a parabola. The formula is called a "quadratic function". A lot of natural phenomena follow parabolic curves - projectiles (throwing a baseball or launching a rocket), reflective surfaces (satellite dishes), the lens of the eye....

You are being asked to find the roots of the quadratic equation, i.e. the value of X where the curve crosses the X-axis (in other words, where the formula = 0) 

The graph for your formula looks like this: 

Root plot:

 

The answers for the roots are: 

The Wolfram Alpha site is a fantastic resource. I'd make sure that students know how to use it properly for useful learning, otherwise they can just plug in their homework questions and generate the results. 

Studying functions is the first step in learning higher math like calculus, which is useful for true understanding of physics, statistics, epidemiology, economics, and finance. It isn't chequebook math, but I know quite a few math majors, MScs and PhDs, who stepped out of university and straight into fascinating careers at banks and investment houses (yes, managing money - theirs and lots of other people's). 

Edited by ollyoxenfree - 1/4/11 at 6:34am

[kathymuggle]

A few thoughts...not related to the original math question as I think that has been covered quite well.

1.  I think most school system did cover quadratic equations.  Mine certainly did around grade 10 or so...maybe you have just blanked it out? 

2.  My Ds is taking grade 9 math as we speak.  Stress the following to eliminate numerous errors:

-What you do to one side of the equation you do to the other!  If you minus 2x from one side, you need to minus to 2x from the other side.

-write neatly and check your signs

-use highlighter, underlining , circling etc, to collect like items, and collect them with their sign in front of them.  Ex - circle all the x squared, underline all the x, and highlight all the numbers without x's.  When things get complicated it help for simplification

I would also consider covering basic test taking skills - read everything over, do the easy questions first, do not waste too much time on a question worth 1 point, when the test is timed and you have 49 other questions to do.  

Lastly, if she does not have the internet, how about the library?

this is widely available, and lot of fun (and math!)

http://www.danicamckellar.com/hotx/reviews/#top

I would literally have her order in a bunch of pre-algebra and algebra books - you never know which one will click!

[ollyoxenfree]

Hmm, I just checked in on this thread, and discovered that in my earlier post, I now can't "see" the graph and answers that I cut and pasted from the Wolfram Alpha site. It looked fine this morning when I first posted, so maybe it's just the web browser I'm using right now. If you can't see them either, use the link I posted, and you'll see them there. 

I think it's great that you are taking the time and making the effort to help this girl.  

[moominmamma]

My school did quadratics in 10th & 11th grades. Our local school introduces them in a cursory way in 9th grade, then in considerable depth in 10th. They really are the basis of what I think of as intermediate algebra and I can't imagine that they wouldn't be covered extensively in standard high school math. They can be quite badly taught, though. 

OP: The workbook series Key to Algebra is an excellent unthreatening refresher in early algebra, including a bit of an introduction to quadratics. It might work for both you and your neighbour kid.

Miranda

[mammal_mama]

I am really appreciating all this great advice! I haven't had much time to look into it yet, and need to go do a lesson soon, but all of this information, and all of these resources, is truly great to have on hand, possibly for others besides me!

She didn't make it over today, so it's possible that she's found a better tutor which would be great for her, as it looks like it will take me some time to get to where she's at. kathymuggle, it's possible I blanked it all out...I know that as I looked at her equations the other day, all these horrid memories came back to me of "having" to focus on something that was so totally frustrating and unclear. I realize now that I'd honestly brainwashed myself into thinking that I would've loved math if I hadn't been forced into it. Well, now nobody's forcing me but I really don't like it.

Still, I'd like to help my own dd's prepare for college in their teen years, so maybe having time to pursue it at my own pace will make it more fun. Dd1 did take the girl the copy of the dvd that dh made for her, and for the time being I'm going to start watching that to ease my way into algebra...and we'll see from there. Thanks again and I'll be glad if this thread continues! I think you all have a lot of good things to say!