Comments: Summer Math Part I

They are starting him halfway through the class. Find somewhere else. Pass the EOC next year. Whatever. Algebra should go like this:

1) variables, what are they and how do they work
2) linear equations and solving problems that have constant growth
3) non-linear equations (parabolas) starting with patterns that result in parabolic growth
4) analyzing quadratic equations to find out more about them (roots, intercepts, vertex, etc)

Contact your local home school association for recommendations. There have to be hands-on programs that use algebra tiles for basic concepts, and have mind catching situations.

PS It is a good thing that he remembers the rockets, but a less good thing that he doesn't remember anything about them. That means that rockets would be a great way to approach quadratics. Calculating the vertex of a model rocket to find out how high it gets it a great motivator for working with quadratic equations.

Posted by Heresolong at June 12, 2014 11:40 PM

That's what I thought. I was trying to think back to 1979 when I took Algebra I. I remember learning absolute values and lines and solving two step equations before I did parabolas. I actually don't remember doing parabolas in Alg I and I know for a fact I have NEVER seen how they taught him to find a vertex. I need to rethink what they had on-line because I had never seen that formula and I've passed Alg I about 20 times at this point.

The problem is... the school signed him up for this. This is THE program the school uses. They are monitoring his progress.

That said, I was happy when he had a polynomial and he could solve for X. He broke it down and was actually able to solve for both roots.

And he understands that something squared, the square root is + and -.

Posted by Bou at June 13, 2014 12:09 AM

Heresolong... have you seen this?

I always thought the x of the vertex was -b/2a. They have him solving it down to it's zeros, so you have (x+s)(x+t) and the x coordinate point of the vertex is (s+t)/2.

It works, but I had never seen it done that way.

Posted by Bou at June 13, 2014 12:14 AM

I suppose they are using that to drive home the understanding that the x-coordinate of the vertex is halfway between the zeros and to make them think about the symmetry of the graph (?).

That being said, x = -b/2a is surely the quickest and easiest way to find it (unless it is already factored), so why use a more cumbersome approach?

Posted by PeggyU at June 13, 2014 02:50 AM

Oh ... you could get a copy of October Sky. :) Bones would probably like that!

Posted by PeggyU at June 13, 2014 02:51 AM

A couple of options. FLVS has tutors for free - they don't come to the house but you can call them... the teacher that is assigned to the class is suppose to be available 8am to 8pm, M-F. Also... I am more than happy to come over and work with him in the evenings for free. My hubby can make sure the kids brush their teeth and get pjs on before going to bed. They aren't babies any more. Just let me know.

Posted by vwbug at June 13, 2014 05:19 AM

On a side note... use music with the parabolas if rockets don't work... voice going up and down.

Posted by vwbug at June 13, 2014 05:20 AM

Peggy- That's it. That's what they're driving at... it's halfway between the zeros and symmetry. I couldn't figure out why they'd want to do it that way. I'd never ever done it that way or seen it done that way in any book I've used.

VW- We're OK. He's working well with me. It's just aggravating. The evenings are the times I can work with him and I think I'm going to have T work with him during the day.

This isn't through FLVS, I don't think. It's called edgenuity.

Posted by Bou at June 13, 2014 07:38 AM

Halfway between the zeros is more intuitive. Kids get symmetry because it is very visual. It is also a little more time consuming but the idea is that they aren't memorizing a formula but rather thinking about what they know about the shape of the graph.

The -b/2a comes from completing the square and we don't teach that til Algebra 2 in our curriculum.

We generally try to avoid formulas as much as possible as the problem I see is that kids promptly misapply the formulas (especially kids who aren't great at math, ie most of them). I run into this all the time that we develop the ideas, the kids are doing decently, we write it down in a "Toolkit" as a formula and they either don't write it down properly or they promptly stop working through the process and start incorrectly shoving numbers into the formula because "it is easier" than thinking.

We still come up with and write down the formulas just because I want those kids moving on to have experience with them but I spend a fair amount of my time guiding the kids back to the basic concept when they are working on problems.

Me: Where did this number come from and does it make sense?

Them: Well the formula says this.

Me: "Why is that the vertex? Where on the graph of a parabola do you find the vertex? What is the relationship to the intercepts? How can you have a highest point that is below some other point"

We always end up back at the basics until the next time, when they try to apply the formula wrong again.

Posted by Heresolong at June 13, 2014 08:03 AM

Ok... that makes sense, the visual. I'll sit down with him this afternoon and take it from a visual standpoint. He gets symmetry.

The formula thing does not work well for him. I guess I never had a problem with them because I always understood the application.

And October Sky... I think that was the movie with the rockets.

Posted by Bou at June 13, 2014 08:48 AM

October Sky is the movie with the rockets, the one about Homer Hickam. As I recall, they go through a lesson on parabolas (albeit very briefly) in their class.

Posted by PeggyU at June 13, 2014 12:05 PM

Yes, he remedial math teacher had them watch it one class. Anything he learned was from his remedial math teacher. And that class was supposed to be a supplement to his actual math class.


Posted by Bou at June 13, 2014 12:25 PM

Jesus and his disciples were walking around one day, when Jesus said, "The Kingdom of Heaven is like 3x squared plus 8x minus 9." The disciples looked very puzzled, and finally asked Peter, "What on earth does Jesus mean -- the Kingdom of Heaven is like 3x squared plus 8x minus 9? Peter said, "Don't worry. It's just another one of his parabolas."

Posted by Toluca Nole at June 13, 2014 06:27 PM

TN- That is funnier as that would be Bones. My post tonight will relate to that..

Posted by Bou at June 13, 2014 10:32 PM