Explaining basic mathematics to a math illiterate

[yyttr2]

The other day, someone came to me with the deep desire to learn the basics of algebra and he believed it would be best, not to get his information for say...a book, but rather a student.

So, I thought it would be evil not to help him. I started off with basic arithmetic put into algebraic logic.
I.E. x+5=6 or x+7=6
and then, I got to exponents.
I gave him the problem: $$x^{2}=9$$
He asked me what the super script '2' truly meant.
Now, I have always thought of $$x^{2}$$ as a two dimensional representation of a one dimensional quantity (I.E. a one dimensional line with the length of x, and to square x is to extent it equally into the second dimension or...to make it a square). I tried to explain this to him, and that to find the value of x, you just had to think of the nine as a two dimensional quantity, and represent it as a one dimensional line.

He looked to perplexed no matter how much I tried to explain it... I tried to tell him just to think of it in terms of blocks...still nothing.

Can anyone give me a better way to explain this?

 

[pbandjay]

Perhaps just explain what the notation means rather than an interpretation. The power of 2 in x² is the same as 2 x's being multiplied together: x² = x*x = 9. A power of 3 in x³ then is the same as 3 x's being multiplied together.

Or, maybe try to show him an 'inductive' structure for an n^th power. That is,
$$x^2 = x \times x$$
$$x^3 = x \times x \times x$$
$$x^n = \underbrace{x\times x\times ... \times x}_{n}$$

Maybe even compare it to:
$$nx = \underbrace{x+x+...+x}_{n}$$

In explaining x² as an area, maybe showing some numerical examples would help him more. If 3² is drawn as a 3x3 square, it is pretty easy to count a total of 9 unit squares. If multiplication between two numbers is interpreted as length times width, you can always just count the unit squares as opposed to multiplying length times width, and in the special case where length = width, the total number of unit squares is length² = width².

 

[Noxide]

2x = x + x
multiplication is repeated addition

x^2 = (x)(x)
exponents indicate repeated multiplication



ps.
I think of it the same way you do. I am weird.

 

[Landau]

He asked me what the super script '2' truly meant.
Now, I have always thought of $$x^{2}$$ as a two dimensional representation of a one dimensional quantity (I.E. a one dimensional line with the length of x, and to square x is to extent it equally into the second dimension or...to make it a square). I tried to explain this to him, and that to find the value of x, you just had to think of the nine as a two dimensional quantity, and represent it as a one dimensional line.

He looked to perplexed no matter how much I tried to explain it... I tried to tell him just to think of it in terms of blocks...still nothing.

I'm not very surprised that this math illiterate didn't understand it; I don't either. If someone asks what a power truly means, I wouldn't start talking about 'dimensions'. I am curious to hear your explanation of what $$3^{\sqrt{2}}$$ means

I would follow the approach of pbandjay and Noxide (of course this doesn't explain what a non-natural exponent means, but that will come later).