Why Study Algebra?

[agzg]

Originally Posted by Munchkin03

But, maybe I have the same issue that you have--what I consider basic arithmetic (add/subtract/multiply/divide) is actually closer to algebra?

Well, arithmetic is part of algebra. Algebra is basically the concept of using one or more variables to stand for numbers, then solving for that variable. For example, when halving a recipe that yields 24 cookies, and for 24 you need 2 cups of sugar, how many cups of sugar do you use? If you were writing it out, you'd use "X" in the place of number of cups, and solve for it.

Plus, algebra is the application of rules(which is what seems makes it boring for MC Jr.), PEMDAS, FOIL, and so on.

[KSig RC]

Originally Posted by MysticCat

He loves video games (though has made clear to us and to his teacher that he doesn't want to design them; I still wonder, though). He loves to read, he takes walks and runs (but we can't get him interested in track), and he takes karate, which he really enjoys. (It's the only sport-like physical activity we've been able to get him involved in.)

From the video game angle ... a lot of the problem-solving in video games is figuring out the pattern or the unknown from a series of known "variables". For example, you know that there are 5 pieces to the puzzle, and 5 caves to explore - if you don't find that puzzle piece in Cave C, you can be pretty sure you missed something, so you backtrack, find what you missed, fill in the gaps, etc.

Even in something like a first-person shooter, you're constantly examining where you know people are, and what you don't know, to see if you can figure out what's going on from the context clues.

What kinds of games does he like? He may be using related critical thinking without even realizing, and that might be your hook.

[KSUViolet06]

This is sort of my lane-ish (I'm taking Teaching Math in SPED right now.)

You use algebra anytime you try to calculate an unknown based on other info you have.

Ex: Modifying a recipe is an algebraic function.

Everyone ahead of me pretty much stated what I was going to say. Apply it to what he likes and see if that changes anything. Good luck. He seems like a very bright boy. Remember that he's no less bright because he is struggling with math (you know that, as a dad but not every parent does.)

[Psi U MC Vito]

Maybe talk to him about Descartes and Newton. Both used math for philosophy. Not algebra, but algebra was a basis to what they used.

[AZTheta]

Hey MysticCat! check this out and tell me what you think. I know nothing about it but can vouch for the person who referred me to it. I'll come back and post the isbn here as soon as she sends it to me.

Visual Mathematics: A Step by Step Guide (title is what she quoted, so best to wait for the isbn, right?)

[melindawarren]

Ok, I win at worst HS math situation (I remember a board of education member once saying to me, "you never did quite have luck with math classes, did you?"). But I still see the value to a basic understanding of algebra. I can't think of anything specific that algebra taught me that, say, basic math didn't (especially because I somehow managed to get myself into a math class in my junior year called "Finite Math." It was basic math all the way to introductory algebra. We only got to do it that way because the first semester was statistics. I don't know how this managed to come after Algebra II, but it was SOOO cool that it did!), but I can say that, imo, some of these annoying classes (things like Algebra or World History) just teach useful skills.

My math classes taught me that some problems only one answer. They taught me how to collaborate with classmates when a particular teacher was being unreasonable, they taught me how to verbalize my concerns over a grade (with a less tangible subject like, say, English, where an essay is incredibly subjective, math tends to be more objective, and if a teacher marked an answer wrong but it was clearly right, you can easily win that one!), and how to attack one challenge multiple ways (because algebra is that kind of subject: there is [usually] only one answer, but there are [usually] multiple paths to that one answer).

Personally? I still hate math, and I avoid using anything beyond basic math when I can. Nonetheless, I still love solving ratios, calculating my grades with fancy formulas, and the occasional multiplication/division question. But algebra? I hardly remember it-I just remember that I learned about things other than math in my high school math classes.

[sigmagirl2000]

linear equations can be used in simple applications like "I have to pay my cell phone bill. It costs $50 a month, then $.10 for every text I go over however many are allotted in the plan." The .10 would be your slope, and the $50 would be your y-intercept. You can use those to graph and determine how much you will pay per month based on the number of texts over your plan you use, etc. You can compare your own cell phone plan to other plans to determine if you have the best plan based on your usage and needs (by solving a system of equations.) etc. I don't know. As a math teacher, I constantly apply what we are doing in classes to teens.... if you want more ways, let me know and I'll pay attention to the things that fall out of my mouth during class when I get "why do we need this?" questions. (because the responses are spontaneous, and without any thought)

[southbymidwest]

Originally Posted by sigmagirl2000

linear equations can be used in simple applications like "I have to pay my cell phone bill. It costs $50 a month, then $.10 for every text I go over however many are allotted in the plan." The .10 would be your slope, and the $50 would be your y-intercept. You can use those to graph and determine how much you will pay per month based on the number of texts over your plan you use, etc. You can compare your own cell phone plan to other plans to determine if you have the best plan based on your usage and needs (by solving a system of equations.) etc. I don't know. As a math teacher, I constantly apply what we are doing in classes to teens.... if you want more ways, let me know and I'll pay attention to the things that fall out of my mouth during class when I get "why do we need this?" questions. (because the responses are spontaneous, and without any thought)

I wish my kids could have had you for algebra.

[MysticCat]

Originally Posted by sigmagirl2000

linear equations can be used in simple applications like "I have to pay my cell phone bill. It costs $50 a month, then $.10 for every text I go over however many are allotted in the plan." The .10 would be your slope, and the $50 would be your y-intercept. You can use those to graph and determine how much you will pay per month based on the number of texts over your plan you use, etc. You can compare your own cell phone plan to other plans to determine if you have the best plan based on your usage and needs (by solving a system of equations.) etc.

How sad is it that I read this three times and still thought "I would have no clue how to do that"?

If it hasn't already been obvious, clearly part of the problem is that our son has two parents for whom math was always something of a foreign language. So, for example, when he was struggling with linear equations, I had to look them up and try to remember/learn again what they are before I could even think of helping him -- I was basically trying to learn them along with him.

Seriously. thanks for the suggestion. Once I wrap my head around it -- and I'll do my best to do that -- I'll try it on him. And yes, I wish he had you for a teacher, too.

[sigmagirl2000]

I've also taught older HS students how different gambling games have different odds.... and how to calculate them so should they ever visit a casino at some point in their lives, they can maximize winning potential

[ElieM]

Can you do it backwards? Graphs some points on a graph and then work out the equation that would put them there?

[sigmagirl2000]

Well that was a few sentence explanation of a larger idea. Let's say your monthly plan is $50. You only get 150 texts a month with your plan.

your equation would be y=.10x+50

(x would be number of texts a month over the 150 you get included in plan. y would be the total amount you have to spend)

If you use less than 150 texts in the month, you only pay the $50. So your first point on the graph would be (0,50).

Now let's say you have a super social teenager, and he decides that "texts are pretty cheap!" and uses 1,000 texts in that one month. That's 850 more texts that you get in your plan. Each additional text over your plan costs .10 (I think that's what I used as a random example in previous post). so 850 texts at .10 each comes out to be $85 in texts. (craziness!)

So if you wanted to graph that point, it would be (850, 135) (the 850 is the number of texts beyond what you get. the 135 is the total cost for the month, the $50 monthly charge + the $85 in texts.

If you plot those two points, connect them with a ruler, and you have your line graphed.

Did that make any more sense or just cause more confusion? (it's hard to explain without writing down or speaking)

[sigmagirl2000]

sure. If you have two points (x1, y1) and (x2, y2) just plug them in to m= (y2-y1)/((x2-x1).

That gives you the slope.

Then plug the slope (m) and one of the points you already have into point-slope form of a linear equation:

(y-y1) =m(x-x1)

where m is your slope, y1 is the y-coordinate of one of your points given, and x1 is the x-coordinate of that same point you took y from)

If you feel the need you can simplify to get it in slope-intercept form (y=mx+b), but I personally leave equations in point-slope form and try to get students to do the same.

(yes, I am a nerd. I have a preference for forms of linear equations)

[AlwaysSAI]

Originally Posted by sigmagirl2000

sure. If you have two points (x1, y1) and (x2, y2) just plug them in to m= (y2-y1)/((x2-x1).

That gives you the slope.

Then plug the slope (m) and one of the points you already have into point-slope form of a linear equation:

(y-y1) =m(x-x1)

where m is your slope, y1 is the y-coordinate of one of your points given, and x1 is the x-coordinate of that same point you took y from)

If you feel the need you can simplify to get it in slope-intercept form (y=mx+b), but I personally leave equations in point-slope form and try to get students to do the same.

(yes, I am a nerd. I have a preference for forms of linear equations)

Two things:

-One of my students stayed after school for tutoring yesterday. He shared with me that I made him think he wanted to be a math teacher.

-It makes me so happy, as a math teacher, to see someone who remembers all the gobblety-gook and how to utilize it.

@MC: I never knew your son was on the spectrum (not that you advertise it), but those are some of my favorite students.They have....such a way with words.

[ElieM]

Sorry, I know you CAN do it backwards, but I was wondering if that would be more interesting for MCs son as it might seem more creative.