Mathematical adventures

[Intelligently_Designed]

When I was a kid, I was told that you either get math or you don’t. Some nuances are probably in order, but I’ve grown to believe that there is some (possibly hard to calculate) to it that’s true.

I have a colleague. Brilliant in every way. Except for math. She can explain with great detail all means of strategy in many of human’s behaviors, but she comes to me every time she has to figure a damn percentage. She just cannot. Imagine when I tell her that going from 3 to 4 is a 33% raise but going from 4 to 3 is a 25% decrease. It’s over, though she believes in me.

A friend of mine is a university math teacher. He loves what he calls “mathematical adventures”, situations where he is confronted to people who don’t get math. His example: “I went to a grocery store to buy some grapes. There were green grapes and red grapes. They were both the same price, 99¢ a pound. So I put of some of both in the same bag.”

“When I got to the cash, the cashier began to separate the green from the red grapes. I said to the cashier, “oh, you’re doing that because of the bar code, because if not it ends all the same”. The cashier said “no, it’s not the bar code”. Then she weighs both types of grapes, and she says: “red grapes, $2.19, green grapes $1.95. You see it doesn’t end all the same.””

Do any Dopers care to share their mathematical adventures? We could have some fun.

[AHoosierMama]

[QUOTE=Intelligently Designed]
When I was a kid, I was told that you either get math or you don’t. Some nuances are probably in order, but I’ve grown to believe that there is some (possibly hard to calculate) to it that’s true.

I have a colleague. Brilliant in every way. Except for math. She can explain with great detail all means of strategy in many of human’s behaviors, but she comes to me every time she has to figure a damn percentage. She just cannot. Imagine when I tell her that going from 3 to 4 is a 33% raise but going from 4 to 3 is a 25% decrease. It’s over, though she believes in me.

A friend of mine is a university math teacher. He loves what he calls “mathematical adventures”, situations where he is confronted to people who don’t get math. His example: “I went to a grocery store to buy some grapes. There were green grapes and red grapes. They were both the same price, 99¢ a pound. So I put of some of both in the same bag.”

“When I got to the cash, the cashier began to separate the green from the red grapes. I said to the cashier, “oh, you’re doing that because of the bar code, because if not it ends all the same”. The cashier said “no, it’s not the bar code”. Then she weighs both types of grapes, and she says: “red grapes, $2.19, green grapes $1.95. You see it doesn’t end all the same.””

Do any Dopers care to share their mathematical adventures? We could have some fun.
[/QUOTE]

I’m in the “either you get it or not” camp. I’d classify myself as reasonably intelligent. I hold a BA and professional position. I doubt anybody would say I’m any smarter than the next guy, or that I’m a dunce. I will say that my SAT score was almost all verbal points and nearly no math. I can perform general arithmetic, but once Greek symbols and the like are involved, I’m lost. Had to take a calculus class to earn my degree. Showed up for every class, had a tutor, visited prof.'s office hours at every opportunity, and still only passed by the skin of my teeth. I found that my tutor just couldn’t back step far enough to my level and assumed I knew things that I didn’t - like everybody was born knowing that stuff or something.

I can figure out percentages though, and have met at least one person that could not (even with a calculator) but she wasn’t exactly the sharpest tool in the shed otherwise either.

Small aside here: the only BA you could get without a math requirement at my alma mater was EDUCATION! :smack:

[Thudlow_Boink]

[QUOTE=Intelligently Designed]
When I was a kid, I was told that you either get math or you don’t. Some nuances are probably in order, but I’ve grown to believe that there is some (possibly hard to calculate) to it that’s true.
[/QUOTE]
I wonder to what degree that’s true, and to what degree it’s a cop-out or self-fulfilling prophecy. I’m pretty sure it’s some of each.

I have a colleague. Brilliant in every way. Except for math. She can explain with great detail all means of strategy in many of human’s behaviors, but she comes to me every time she has to figure a damn percentage. She just cannot. Imagine when I tell her that going from 3 to 4 is a 33% raise but going from 4 to 3 is a 25% decrease. It’s over, though she believes in me.

I’m guessing her head would explode if you tried to explain the missing dollar riddle to her!

[ITR_champion]

[QUOTE=Intelligently Designed]
Do any Dopers care to share their mathematical adventures? We could have some fun.
[/QUOTE]

My Mom once commented, while looking at a weather report, that since there was a 30% chance of rain on Monday and a 30% chance on Tuesday, there must be 60% chance of rain total. My brother responed by asking her, if there was a 60% chance of rain each day, would that make a 120% chance total. She figured out that it would not, but it took her a while.

A professor once was speaking about the birthday problem. (i.e. how many people must you have in a room for their to be a 50% chance that some pair of people share the same birthday.) He told us that he’d asked a number of people for answers over the years. One man had answered 1,500 people. The professor assumed that he’d misunderstood the problem, and said “No, we’re only asking for one pair of people who were born on the same day of the year.” The man says “Oh” and thinks for several minutes, then says “3,000 people.”

Once in a high school economics class I took the average of six one-digit numbers mentally. A fellow students at first refused to believe that anyone could “do that in their head”. Also my sixth grade teacher once insisted that I must be cheating because there’s no way that anybody could compute 5 to the 6th power mentally, and since I didn’t have any computations written on my paper, I must have illegally used a calculator or spied on the test before it was written.

Now that I teach math at one of America’s top universities, my math adventures are much more frequent and more depressing.

[ZipperJJ]

I’ll admit to being math-dumb. I’m pretty smart but I just can’t do numbers - abstract numbers or percentages.

Luckilly, my best friend is a math whiz. We even eachother out because he sucks at teh words and I’m pretty good with language.

Anyway, every month I have to fill out the withholding tax forms for my company. We pay 2% of the total payroll in city tax. In the form I have to fill out the total payroll amt, the total withholding amt and the percentage. I have the total withholding amt in front of me but it’s a bit of a pain to look up the total payroll so I have to figure it out.

So… TotalWithheld = .02*X

I can NEVER figure out X. I had to ask my best friend how to figure it out. He told me just multiply TotalWitheld by 50…I think. Or was it 20? Or 5? I can’t remember until I put the amounts into the form and click “submit”…when it tells me whether I was right or wrong.

And yes, I DO handle all of the money for the company

[GorillaMan]

[QUOTE=ITR champion]
My Mom once commented, while looking at a weather report, that since there was a 30% chance of rain on Monday and a 30% chance on Tuesday, there must be 60% chance of rain total.
[/QUOTE]

My A Level maths has clearly faded from my mind…what is the chance of precipitation on at least one day? (I’m 99% certain it isn’t 30%!)

[ultrafilter]

I don’t have any good stories (except for the time I spent an hour trying to prove something only to realize it was the intermediate value theorem…that was an adventure), but I thought I’d throw a couple comments out.

[QUOTE=GorillaMan]
My A Level maths has clearly faded from my mind…what is the chance of precipitation on at least one day? (I’m 99% certain it isn’t 30%!)
[/QUOTE]

60% minus the probability that it rains both days. There’s not enough information to narrow it down any further.

@Intelligently Designed

When I was a kid, I was told that you either get math or you don’t. Some nuances are probably in order, but I’ve grown to believe that there is some (possibly hard to calculate) to it that’s true.

I’m not sure that I buy this. I think that math teaching is so poorly done in the US that you can’t draw any conclusions from people’s passing or not passing classes. I suspect that it’s not a question of whether you get math or not, but how much effort you need to make. The people who do well in math classes these days are the people who don’t really need to put that much effort in, so it seems like they just get it.

[Captain_Carrot]

[QUOTE=GorillaMan]
My A Level maths has clearly faded from my mind…what is the chance of precipitation on at least one day? (I’m 99% certain it isn’t 30%!)
[/QUOTE]

Easier than that: the probability that it won’t rain at all on either day, which is equivalent and easier to calculate.

Each day has a 30% chance of rain, which means a 70% chance that it won’t; .7 for Monday*.7 for Tuesday=49% chance that it won’t rain=51% chance that it will rain on Monday, Tuesday, or both days.

Note: this result assumes that rain or lack thereof on Monday does not affect Tuesday’s precipitation. ultrafilter, are you sure that there isn’t enough information?

[El_Perro_Fumando]

[QUOTE=GorillaMan]

[QUOTE=ITR champion]
My Mom once commented, while looking at a weather report, that since there was a 30% chance of rain on Monday and a 30% chance on Tuesday, there must be 60% chance of rain total.
[/QUOTE]
My A Level maths has clearly faded from my mind…what is the chance of precipitation on at least one day? (I’m 99% certain it isn’t 30%!)
[/QUOTE]

There is a 51% chance of rain on at least one day of the two. I’ll let you stew on how I got it.

With love,
El Perro Fumando,
Math teacher

[Taber]

[QUOTE=GorillaMan]
My A Level maths has clearly faded from my mind…what is the chance of precipitation on at least one day? (I’m 99% certain it isn’t 30%!)
[/QUOTE]

Mathematically, if we assume the events are independent, it’s about 51%. each day has a 70% chance of not raining. For there to be no rain, both days have to hit that 70% chance, which is .7 * .7 = .49 = 49% of there being no rain.

but the events aren’t independent. If it rains on monday, it is less likely to rain on tuesday, as there is less water in the air, and if it doesn’t rain on monday, it is more likely to rain on tuesday. So we can’t calculate the chance unless we knew a lot more about meteorology and so forth.
I see I’ve been beaten to the punch

[GorillaMan]

Thanks, all for reminding me how boring Statistics was

[Shagnasty]

I am a little strange in math. I am not terrible but my verbal and analytical skills overshadow it by far making me feel like I am not good at it at all. Oddly, I am very good at science and I am excellent at the programming aspect of my job easily excelling over people that have math type degrees.

I just can’t grasp math that doesn’t relate to the real world in my head. That rules out much of Algebra and any math that is just a long string of formulas. I hear that lots of people fear statistics. I got the highest grade in the class in both undergraduate and graduate school in rigorous statistics classes because I could transform everything into a real-life problem. As soon as that is taken away, I am toast.

[ultrafilter]

[QUOTE=Captain Carrot]
Note: this result assumes that rain or lack thereof on Monday does not affect Tuesday’s precipitation. ultrafilter, are you sure that there isn’t enough information?
[/QUOTE]

Quite. Independence is a strong assumption, and you shouldn’t make it unless you have justification. It’s particularly bad in weather models. Consider an extreme example: Approximately 25% of the days in a year will have summer weather, and 25% will have winter weather. The probability that you’ll have summer weather on Monday and winter weather on Tuesday is not 6.25%.

[Santo_Rugger]

[QUOTE=Shagnasty]
<snip>
I just can’t grasp math that doesn’t relate to the real world in my head. >
[/QUOTE]

Cast my vote for those that think learning math falls into two categories. To me, advanced calculus, vector analysis, and differential equations all relate to the real world in my head.
Sorry Shagnasty, I’m not trying to be rude, just using your post to illustrate my point.

[MissMossie]

I have been blessed with the interesting experience of being a peer instructor for lower level calculus classes. At my school, a PI’s job is to spend an hour each week in the class reviewing material that the professor has already taught. More often than not, despite the fact that the material has been taught, the students have not learned it.

My favorite mathematical adventure took place during one of these review hours. The class had a word problem that involved drawing a graph showing how much money a driver spends on her/his car in a month vs how many miles a driver travels in a month. Money was on the y-axis and miles were on the x-axis. The kicker of the problem, at least for most of the class, was that they had to explain the graph. The question of why the y-intercept did not equal zero stumped them. With a little prodding on my part, they started thinking in real life terms of what costs went in to owning and driving a car. Gas was the obvious ones, but also expences like insurance and parking. It was neat because I could see the light bulbs going off over their heads. The graph actually made sense to them. Whether or not they gave a damn about it, I don’t know, but they understood it and that was pretty cool.

On days when I have students tell me that the square root of two is equal to one (so what does one times one equal?) or that (x + y)^2 = x^2 + y^2 (uhhh…sorry, not in our number system!), I reflect on the one day that my whole class understood a problem.

[QUOTE=Pygmy Rugger]

Cast my vote for those that think learning math falls into two categories. To me, advanced calculus, vector analysis, and differential equations all relate to the real world in my head.
[/QUOTE]

Amen!

[Captain_Carrot]

[QUOTE=ultrafilter]
Quite. Independence is a strong assumption, and you shouldn’t make it unless you have justification. It’s particularly bad in weather models.
[/quote]

Good point. I was thinking of this more as a word problem than an actual situation.

Consider an extreme example: Approximately 25% of the days in a year will have summer weather, and 25% will have winter weather. The probability that you’ll have summer weather on Monday and winter weather on Tuesday is not 6.25%.

No, it’s more like 50%, given the last two or three months around DC.