I like the temp conversions. We'll try that one too.

__________________
Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

Yeah, now I see what you mean. Unfortunately, you seem to be right

__________________
If everyone had even a basic grasp of scientific principles, this planet would be a better place (Phil Plait)

Die Lücke, die wir hinterlassen, ersetzt uns vollkommen [The gap we will leave behind will take our place entirely] (Carl Heinz Schroth)

1 + e^i*pi = 0

With the ambiguous typography and no way to distinguish hyphen from minus without already understanding the problem, this looks like something deliberately written to confuse the innocents.

For me it would be much more logical that 0=m*x-intercept+b <=> -x=m*x-intercept+b-x <=> intercept-x=m*x-b <=> x-intercept=b-m*x ㋡

__________________
‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.

In principle, I agree (see also my earlier post to mike alexander). But I would be interested to know how you would type it in a way which distinguishes hyphen from minus. I´m asking this seriously, because I was stumbling over the same problem in some earlier posts.

__________________
If everyone had even a basic grasp of scientific principles, this planet would be a better place (Phil Plait)

Die Lücke, die wir hinterlassen, ersetzt uns vollkommen [The gap we will leave behind will take our place entirely] (Carl Heinz Schroth)

1 + e^i*pi = 0

I was confused at first by the notation used here, too. In my post, I wrote the variable y in italics, but perhaps a more legible solution in a message board would be to use quotation marks: "y"-intercept, "x"-intercept, etc.

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

Or ditch the hyphens: "y intercept"

__________________
Nothing beautiful was ever made from gravel.

Nooooo.

You're using quotation marks to break apart the thing that was difficult to see as a unit in the first place.

If you're trying to use quotation marks to disambiguate, at least use them to bind things together instead of using them to break linguistic units apart: "x intercept" and "y intercept".

__________________
‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.

I suggested using quotation marks to write down the name of a thing. This is common in everyday language.

Better suggestions are of course welcome. I rather liked Paul's proposal, myself.

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

Try thinking of writing it more as poetry than prose. Break up those long lines to give the reader a pause to absorb each nugget before plowing into the next line. Math is kind of poetic, anyway.

__________________
If they can get you asking the wrong questions, they don't have to worry about the answers.

We can make the lines much shorter by writing it all in mathematical notation.

Seriously, when you're teaching y=mx+b for the first time you just call "m" the slope, "b" the intercept, and you're done with it.

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

Back to the OP.

Perhaps the way to introduce the topic is to first leave out b entirely. I suspect that some little thing has been missed, and this may be the way to uncover it.

Ask your friend to plot on a piece of graph paper the points where "y is the same value as x", that is, y=x. Be sure to include negative values of x. Connect them with a line.

Then plot "y is twice the value of x", y=2x. As above, draw lines through the points. Do this for a number of values of m, without referring to it as "m", and ask her to describe what is different about each line.

Then do it all again, but ask her to just add some constant number, such as one or two, to each result and again ask her to explain what has happened to the lines. Be sure to build the lines from a number of points as before to emphasize that the relationship is true for every point on the line. The notion of slope and intercept should eventually become apparent, and with the right prompting (eg "see how the steepness of the line changes"), she might even come up with the actual words "slope" and "intercept" by herself.

Finally, use some of the good examples already provided earlier in the thread to show that the concept is useful in the real world.

That is pretty much what I did Torsten. I started with a real world problem to show her she can use it in real life. She had to see that it could be relevant to her life.

We simply graphed lines without the b. Then we graphed lines with a b. Then I had her put a problem in y intercept form and graph the line. Each time I had her select a point on the line to check her answer.

She gets it now!

She can even graph lxl absolute values and x^2.

I may be back. This semester is not even half over!

__________________
Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

That's great, Tinaa! It's fun to help someone turn on that light bulb, ain't it?

__________________
Relight the Firefly!

"It is quite clear that Occam's razor does not sharpen in your pyramid." (Nicolas)

"Still, a man hears what he wants to hear and disregards the rest." (Paul Simon)

She called me after her class at Texas State. She was so excited! Yep, I was pretty excited too. Woo Hoo!

__________________
Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

That's excellent, Tinaa. It's very rewarding to see that light come on.

Consider the following subtraction problem, which I will put up here: 342 minus 173. Now, remember how we used to do that:

Three from two is nine, carry the one, and if you're under 35 or went to a private school, you say seven from three is six, but if you're over 35 and went to a public school, you say eight from four is six ...and carry the one, so we have 169.

But in the new approach, as you know, the important thing is to understand what you're doing, rather than to get the right answer. Here's how they do it now:


You can't take three from two,
Two is less than three,
So you look at the four in the tens place.
Now that's really four tens
So you make it three tens,
Regroup, and you change a ten to ten ones,
And you add 'em to the two and get twelve,
And you take away three, that's nine.
Is that clear?

Now instead of four in the tens place
You've got three,
'Cause you added one,
That is to say, ten, to the two,
But you can't take seven from three,
So you look in the hundreds place.

From the three you then use one
To make ten ones...
(And you know why four plus minus one
Plus ten is fourteen minus one?
'Cause addition is commutative, right!)...
And so you've got thirteen tens
And you take away seven,
And that leaves five...

Well, six actually...
But the idea is the important thing!

Now go back to the hundreds place,
You're left with two,
And you take away one from two,
And that leaves...?

Everybody get one?
Not bad for the first day!

Hooray for New Math,
New-hoo-hoo Math,
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!

Now, that actually is not the answer that I had in mind, because the book that I got this problem out of wants you to do it in base eight. But don't panic! Base eight is just like base ten really - if you're missing two fingers! Shall we have a go at it? Hang on...

You can't take three from two,
Two is less than three,
So you look at the four in the eights place.
Now that's really four eights,
So you make it three eights,
Regroup, and you change an eight to eight ones
And you add 'em to the two,
And you get one-two base eight,
Which is ten base ten,
And you take away three, that's seven.
Ok?

Now instead of four in the eights place
You've got three,
'Cause you added one,
That is to say, eight, to the two,
But you can't take seven from three,
So you look at the sixty-fours...

"Sixty-four? How did sixty-four get into it?" I hear you cry! Well, sixty-four is eight squared, don't you see? "Well, ya ask a silly question, ya get a silly answer!"

From the three, you then use one
To make eight ones,
You add those ones to the three,
And you get one-three base eight,
Or, in other words,
In base ten you have eleven,
And you take away seven,
And seven from eleven is four!
Now go back to the sixty-fours,
You're left with two,
And you take away one from two,
And that leaves...?

Now, let's not always see the same hands!
One, that's right.
Whoever got one can stay after the show and clean the erasers.

Hooray for New Math,
New-hoo-hoo Math!
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!


Come back tomorrow night...we're gonna do fractions!

-Tom Lehrer

__________________
If they can get you asking the wrong questions, they don't have to worry about the answers.

__________________
Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

Holy crud, did I just break my nose in the generation gap?

Will some other geezer vouch for Tom Lehrer's classic (i.e., old) satirical song about teaching basic mathematics? Circa 1964, I think it was on his (vinyl) album "That Was the Year That Was".

__________________
If they can get you asking the wrong questions, they don't have to worry about the answers.

Sorry... I thought I was old being born in 1963.

__________________
Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

Two things, Mike:

1) That worked for me when I was in grade school.

2) Crap, that's how I sound when I teach.

It was clear when my 3rd grade teacher demonstrated it on the blackboard in similar terms one step at a time. Her opinion was that understanding and getting the right answer were equally important.

This was in the school year 1956-57, a few years before the dreaded "new math" reared its partially ugly head. It is as if she anticipated some of its good points without going to some of the outrageous extremes of abstraction. Since I was spared much of that stuff I don't know all of the details. Perhaps others can fill me in.

Not sure if I count as an old geezer, as the song is two years older than me, but it's definitely on the list of associations to pop up whenever people talk about teaching mathematics.

Here's a couple of linkies to his actual performance of that song.
This one is just That Was The Year That Was, tracks 9 and 10. New Math(track 10) starts around 2:15.
This one is from the same record, but someone animated the calculations.

__________________
‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.

I think my age is showing again. Pardon me while I cover up.

I think quite a few of us survived the new math. For me it was just math.

The problem I recall with new math was that it caused for many people the centipede's dillemma. The centipede walks just fine until it has to think about which foot to put down next, then trips and can't get up. Like driving a car, if you have to think about shifting gears you will ruin the gearbox.

Understanding both the numerical base of calculation and the underpinnings of positional notation are laudable goals that just about everyone has no need of.

For that matter, the old English system of volume measures is a binary system (all those powers of 2), from jigger to tun.

__________________
If they can get you asking the wrong questions, they don't have to worry about the answers.