Teaching Algebra

[sweet2kill210]

Okay, my sister plans on attending college whenever I apply but the problem is she doesn't remember anything from math. She wasn't exactly the best student and skipped a lot during high school, but then again, she didn't exactly go to the best school either.

Anyways, being the good brother that I am, I agreed to help tutor her in math so that she may be prepared to complete her basics which is all she'll need. I'm very good at math and have the grades to prove it, so it's not that I don't have knowledge extensive enough to teach it, I just don't know what I should teach first.

The method I'm using is I'm going to make short worksheets (because she works full time at the moment and has 2 kids...), and back them up with typed explanations and if she has any questions I can answer them. However, I'm worried that if I cover things in the wrong order that it will need an explanation that would be beyond her current comprehension of things and thus require further explanation and you get the point. It's going off in a tangent from what I meant to teach originally and then I'm going to end up having to backtrack to teach that instead. Definitely not how it should be done. Basically, it will lead to further confusion if I teach something in the wrong order.

For example, if I were to make a problem with cubic roots and multiple variables, but I haven't taught those things yet, I would have to explain those. Or maybe there's also fractions involved and I'd have to go over that.

Overall, I'm just wondering what other people think I should teach first. I'm basically starting off with Pre-Algebra. At the moment I was going to start off with basic equations such as x + 8 = 25 or (5/8x) + 2 = (3/4x) - 8 and solve for x. Then, back that up on the same day with teaching how to simplify equations that have only variables.

So again, my question is: What should I teach first? Thanks for any and all help that I receive in advance. Sorry if this is a confusing post. I'm not a very good writer. :/

EDIT: It did not allow me to attach the word document so I will just not bother with it.

[Evnoir]

I would assess her current skill before heading straight into a certain topic. In other words, let her do a placement test to check how much she already knows and how much she doesn't know. To do this, write up a test for her that starts off with general algebra and then slowly make the questions progress towards more complex problems - maybe up to differentiation?

For material, check over your high school math curriculum. That way, you'll know what to teach her and in what order. If you don't have such a thing, maybe try the order used in Kumon.
Once you assess her, check for the spot where she starts to show some signs that she does not understand how the problem is solved. Most likely, all of the question after that point will be incorrect. Now that you know where the mistakes start, you can start teaching from that point onwards.

I hope this was of some help

[sweet2kill210]

It was definitely a helpful post. I don't know why I didn't think of it. Lol. I've had to take diagnostic tests myself of course.

Also, I wanted to do that, but I'm not sure how to check over my high school math curriculum. :/ Although, I made sure my first lesson is guaranteed to be understood because it's one of the simplest concepts. It will be simple to explain, I made sure. Thanks for the good ideas. Also, I'll look into what "Kumon" is before I find out what order is used. :P

[rushyrulz]

Order in which I would teach things:

-Order of Operations
Please Excuse My Dear Aunt Sally (Pneumonic Device for remembering the order of operations)
Parenthesis
Exponents
Multiplication and Division
Addition and Subtraction

-basic solve for x equations
4x - 9 = 15
4x = 24
x = 6

-foiling
(x+3)(x-4) = x² - x - 12

-factoring
Great Danes Go Poop For Constipated Queens (Pneumonic Device for remembering the correct order in which to factor)

*Greatest Common Factor
(15x + 3) = 3(5x +1)

*Difference of two squares
(x - 25)² = (x + 5)(x - 5)
(x + 3)(x - 3) = (x - 9)²

*Grouping
6x³ + 2x² + 9x + 3
= 2x²(3x + 1) 3(3x + 1) common factor (3x + 1)
= (2x² + 3)(3x + 1)

*Perfect Square Trinomial
(x + 5)² = x² + 10x + 25
x² + 14x + 49 = (x + 7)²

*Factor (unfoiling)
(x² + 4x - 12)
= (x + 6)(x - 2)
x = -6, x = 2

*Complete the Square
x² + 12x + 11 = 0
x² + 12x + _ = -9 + _
x² + 12x + 36 = -11 + 36
(x + 6)² = 25
x + 6 = ±5
x = -11, x = -1

*Quadratic Formula
-b ± sqrt(b² - 4ac)
----------2a
with the formula ax² + bx + c

-Graphing
*Basic graphs of x, x², x³, sqrt(x), ln(x), e^x, |x|, 1/x and the modifications that can shift these graphs vertically and horizontally as well as widen or narrow them.

that's basically algebra 1 in a nutshell.

[reuben_tate]

Don't forget word problems. Especially the rate/time/distance problems (like the type that are like "Train A heads east...and train b heads west...when are they 100 m apart?" ,combined work problems such as "Bob can chop 10 logs in 4 minutes, Sally can chop 5 logs 6 minutes, how many minutes would it take to chop 70 logs if Bob and Sally work together?", and also some problems that involve solving a quadratic equation like "There is a pool complex (pool + the walkway around it) that is 30 ft by 40 ft. The area of the pool itself is 800 itself. If the walkway around the pool is of constant width, what is the width of the walkway of the pool?"

Also, you also want to make sure she thoroughly understands what a function is. Most of the time, teachers start off with the y=... notation, then later introduce the function notation f(x) = . You could have a worksheet where she circles which of the graphs are and which are not functions.

[dore]

I'm actually a TA for a people-who-didn't-place-into-math101 class. What rushy put is basically the start of how our class is organized, and I can help with the rest.

-For all the factoring stuff we do word problems that utilize these techniques.

-Rational expressions, stuff like simplifying (p^2-16)/(4-p) times (-4-p)/(-4+p) or similar problems with addition/subtraction. Then we solve equations involving those expressions, and then word problems (using simpler expressions).

-Linear equations (graphing, slope/solving algebraically and graphically)

-Systems of linear equations (graphically/algebraically/word problems)

-Simplifying radicals, radical equations, fractional exponents

This finishes our course designed to prepare students for Math 1000 (or 101 in most colleges), and should probably prepare your sister for the beginning math classes that her gen ed. will require.