helping granddaughter with math homework

[Thenryb]

My 6th grade granddaughter has always and continues to struggle with math. It has always been a hole in my education as well. However, I did learn arithmatic and figured I ought to be able to help her from time to time. The other day she brought home a problem which was "express the mixed number 8 1/3 as a percent". My wife and I both immediately answered 8.33 percent which is what my granddaughter had answered. Apparently the correct answer was 833 percent. I remain confused as to what I am missing here. I must be assuming something not in the question. Anyway, I guess I cannot be counted on to be of much assistance to her. Also, her district uses the connected math curriculum which apparently eschews teaching kids to learn how to calculate things manually etc. Bah!

[--Pete]

Hi,

My 6th grade granddaughter has always and continues to struggle with math. It has always been a hole in my education as well. However, I did learn arithmatic and figured I ought to be able to help her from time to time. The other day she brought home a problem which was "express the mixed number 8 1/3 as a percent". My wife and I both immediately answered 8.33 percent which is what my granddaughter had answered. Apparently the correct answer was 833 percent. I remain confused as to what I am missing here. I must be assuming something not in the question. Anyway, I guess I cannot be counted on to be of much assistance to her. Also, her district uses the connected math curriculum which apparently eschews teaching kids to learn how to calculate things manually etc. Bah!

As to the teaching of math, in general, it is done very poorly. Many who teach it don't really understand it themselves. And what is taught is often the basics to become a mathematician rather than the general knowledge (and ability) needed by the average person.

The specific problem you lay out hinges on the definition of 'percent'. It comes from the Latin, and can be translated as 'parts per hundred'. So, 1 percent (1%) is one part in a hundred or 1/100 or 0.01. A 100 percent is 100 parts per hundred, or 100/100 or 1.

Now, since 100% is the same as 1, then 8 is the same as 800% by simple ratio. Then 1/3 is (approximately) 33/100 and so 8 1/3 is 833% (more correctly, since 1/3 is a repeating decimal, it is 833.33...%)

Hope that helped.

--Pete

[Thenryb]

Hi,
As to the teaching of math, in general, it is done very poorly. Many who teach it don't really understand it themselves. And what is taught is often the basics to become a mathematician rather than the general knowledge (and ability) needed by the average person.

The specific problem you lay out hinges on the definition of 'percent'. It comes from the Latin, and can be translated as 'parts per hundred'. So, 1 percent (1%) is one part in a hundred or 1/100 or 0.01. A 100 percent is 100 parts per hundred, or 100/100 or 1.

Now, since 100% is the same as 1, then 8 is the same as 800% by simple ratio. Then 1/3 is (approximately) 33/100 and so 8 1/3 is 833% (more correctly, since 1/3 is a repeating decimal, it is 833.33...%)

Hope that helped.

--Pete

It did. Thanks:)

[Concillian]

It did. Thanks:)

Easiest way for someone who isn't very math oriented to think about it is to equate percent to cent.

Then put a $ in front of the number. This essentially turns a math problem that is potentially scary into something the person is usually pretty familiar with.

8.33 in percent?
8.33 --> $8.33
$8.33 = 833 cents
cents = percent
833 percent, or 833%

therefore 8.33 = 833%

[Delc]

You are still left with the question of does .02 cents = $.02?

[Nystul]

I think someone posted a story on the Lounge about a guy who got a quote for internet service at something like 0.33 cents for a certain amount of bandwidth. Then he was charged 0.33 dollars per unit when the bill came. The service provider in that case has made the opposite mistake that you made. They see the value less than one, and assume it is a fraction of the whole, when it is a fraction of the percentage. You saw a number greater than one, and assumed it was already meant to be the pennies. It was in fact the dollars and the problem is to convert to cents.

Also, her district uses the connected math curriculum which apparently eschews teaching kids to learn how to calculate things manually etc. Bah!

A funny thing happened when I was a senior in high school. I forgot to bring my calculator on the day of a physics test. Besides long division and multiplication, part of solving the problems was to take trig functions and punch them into your calculator. I didn't have my calculator. :ph34r: I worked the problems to the end with the trig functions still in the answer. Then, being way to smart for my own good when I was 18, I *estimated* the decimal equivalent of the trig functions in my head and put it behind one of those squiggly equals signs. :lol:I came close enough that when the science teacher handed back my graded test, he looked at me as if I had just beamed down from the Enterprise. Lot of good this stuff does me now that I work in shipping. :lol:

But yeah, I think it's nice for kids to be able to do simple arithmetic in their heads, and long arithmetic with a pencil and paper, by the end of grade 6. Otherwise, what are we teaching them in all those math classes for six years? Learning how to press x100 on a calculator to get a percentage? Sometime you may not have your calculator, or cell phone, or whatever it is they use these days to figure 2 + 2.

[Jester]

Sometime you may not have your calculator, or cell phone, or whatever it is they use these days to figure 2 + 2.

A text message that reads "5 lol".

-Jester

[--Pete]

Hi,

Sometime you may not have your calculator, or cell phone, or whatever it is they use these days to figure 2 + 2.

Never happen. As I sit here, I have a 6" slide rule (don't ask), an HP48GX calculator, a PDA with MathU Pro on it, and a cell phone with a simple four function calculator all within reach. Not to mention the laptop itself, with two calculator apps, MathCad, and -- of course -- XL.:)

--Pete

[Chesspiece_face]

I think someone posted a story on the Lounge about a guy who got a quote for internet service at something like 0.33 cents for a certain amount of bandwidth. Then he was charged 0.33 dollars per unit when the bill came. The service provider in that case has made the opposite mistake that you made. They see the value less than one, and assume it is a fraction of the whole, when it is a fraction of the percentage. You saw a number greater than one, and assumed it was already meant to be the pennies. It was in fact the dollars and the problem is to convert to cents.

Yeah I'm pretty sure I posted this a couple years ago when it happened. Here's a link:

Verizon Math.

[Lissa]

A funny thing happened when I was a senior in high school. I forgot to bring my calculator on the day of a physics test. Besides long division and multiplication, part of solving the problems was to take trig functions and punch them into your calculator. I didn't have my calculator. :ph34r: I worked the problems to the end with the trig functions still in the answer. Then, being way to smart for my own good when I was 18, I *estimated* the decimal equivalent of the trig functions in my head and put it behind one of those squiggly equals signs. :lol:I came close enough that when the science teacher handed back my graded test, he looked at me as if I had just beamed down from the Enterprise. Lot of good this stuff does me now that I work in shipping. :lol:

I just went about memorizing certain values. Like sin(pi/4) = cos(pi/4) = 0.7170, sin(pi/3) = cos(pi/6) = 0.8660, and sin(pi/6) = cos(pi/3) = .5 (then used the various mulitples of those around the circle by remembeingr what the sign of those trig functions were for each quadrant, so quad 1 = positive, quad 2 sin pos, cos neg, quad 3 both neg, quad 4 sin neg, cos pos). Then it just becomes a quick memorization of tan, cot, sec, and csc (sin/cos, cos/sin, 1/sin, and 1/cos) and doing that math quick in the head.

[--Pete]

Hi,

. . . sin(pi/4) = cos(pi/4) = 0.7170 . . .

Typo? 'Cause that should be 0.7071. There's a legend around Boeing that the 707 got its name from how often that number cropped up in the design because of the sweep of the wings.;)

--Pete

[Klaus]

I just went about memorizing certain values. Like sin(pi/4) = cos(pi/4) = 0.7170, sin(pi/3) = cos(pi/6) = 0.8660, and sin(pi/6) = cos(pi/3) = .5 (then used the various mulitples of those around the circle by remembeingr what the sign of those trig functions were for each quadrant, so quad 1 = positive, quad 2 sin pos, cos neg, quad 3 both neg, quad 4 sin neg, cos pos). Then it just becomes a quick memorization of tan, cot, sec, and csc (sin/cos, cos/sin, 1/sin, and 1/cos) and doing that math quick in the head.

I always did my trig conversions by knowing the proportions of the 45/45/90 and 30/60/90 triangles. Then, if you memorize sqrt(2) = 1.414 and sqrt(3) = 1.73205, the rest falls out from the unit-circle definitions of the trig functions (sin = op/hyp, cos = adj/hyp, etc.). sin(pi/4) = sqrt(2) / 2, etc. If needed, certain other angles can be generated from the trig identities (sin (x+y) and such).

Most exams when I was in school were happy to have you leave it in the form of sqrt(3)/2, or for weird angles just as sin(87.2), but we generally weren't allowed calculators.

[Wyrm]

I just went about memorizing certain values. Like sin(pi/4) = cos(pi/4) = 0.7170, sin(pi/3) = cos(pi/6) = 0.8660, and sin(pi/6) = cos(pi/3) = .5 (then used the various mulitples of those around the circle by remembeingr what the sign of those trig functions were for each quadrant, so quad 1 = positive, quad 2 sin pos, cos neg, quad 3 both neg, quad 4 sin neg, cos pos). Then it just becomes a quick memorization of tan, cot, sec, and csc (sin/cos, cos/sin, 1/sin, and 1/cos) and doing that math quick in the head.

That hurts my brain.

[Vandiablo]

and -- of course -- XL.:)

Forty smilies??

If you attempt that many, you get this:

<span style="font-family:Franklin Gothic Medium">You have posted a message with more emoticons that this board allows. Please reduce the number of emoticons you've added to the message<!--fontc--><!--/fontc--></span>

Evidently no one is that happy.

[Crusader]

I remember my VWO-level high school biology exam. I forgot my calculator.:(

Then I had to calculate the chance in percentage a heritage question, with a non-diminant gene combined with a semi-dominant gene (only in the female line) affecting the same position of the RNA chain in a a line of 8 people (4 couples), whose children would then meet, followed by grand-children, or somethign close to that. It wasn't a pretty calculation. I had to use 1,5 A4 pages. On top I noted "forgot calculator, sorry". I had it right.:D

Oh, and the best way to learn math? Ditch the calculator. I had a hardliner math teacher in my first year at high school. Everything by head, no calculators. That served me well. I still can do some decent math when I close my eyes and start calculating, faster then my mates, when we play role playing games. Dividing, adding, multiplying, etc. I'm totally worthless at cos, sin, tan, root, etc stuff though. Start->run->calc ftw. But I never use those any more anyhow.

[Lissa]

I remember my VWO-level high school biology exam. I forgot my calculator.:(

Then I had to calculate the chance in percentage a heritage question, with a non-diminant gene combined with a semi-dominant gene (only in the female line) affecting the same position of the RNA chain in a a line of 8 people (4 couples), whose children would then meet, followed by grand-children, or somethign close to that. It wasn't a pretty calculation. I had to use 1,5 A4 pages. On top I noted "forgot calculator, sorry". I had it right.:D

Oh, and the best way to learn math? Ditch the calculator. I had a hardliner math teacher in my first year at high school. Everything by head, no calculators. That served me well. I still can do some decent math when I close my eyes and start calculating, faster then my mates, when we play role playing games. Dividing, adding, multiplying, etc. I'm totally worthless at cos, sin, tan, root, etc stuff though. Start->run->calc ftw. But I never use those any more anyhow.

Best way I've ever seen a teacher teach math was that the homework and tests/quizes *never* included a final numerical answers, everything was always left as x, y, z so a quadratic was left something like x^2-5x+6 (for simplicity sake of example). Much better to understand the logic behind how you get to the final answer than how to just plug in numbers and come up with the final answer.

[--Pete]

Hi,

Forty smilies??

That's 60! I'm a traditionalist, none of this neologistic 'small before big subtract'. If it was good enough for Julius, it's good enough for me. :lol:

--Pete

[Xukuth]

A funny thing happened when I was a senior in high school. I forgot to bring my calculator on the day of a physics test. Besides long division and multiplication, part of solving the problems was to take trig functions and punch them into your calculator. I didn't have my calculator. :ph34r: I worked the problems to the end with the trig functions still in the answer. Then, being way to smart for my own good when I was 18, I *estimated* the decimal equivalent of the trig functions in my head and put it behind one of those squiggly equals signs. :lol:I came close enough that when the science teacher handed back my graded test, he looked at me as if I had just beamed down from the Enterprise. Lot of good this stuff does me now that I work in shipping. :lol:

Next time just remember that sin(x) is about x for small values of x, and cos(x) is about 1 - x^2/2 for small values of x. Or memorize the Taylor expansions, they're not very complicated for sin and cos.

[Rhydderch Hael]

You are still left with the question of does .02 cents = $.02?

No. It means ¢.02

Out of sight, out of mind. Ever since they removed the "¢" from the shifted set on a keyboard, people never have a mind to use it anymore.

[--Pete]

Hi,

Or memorize the Taylor expansions, they're not very complicated for sin and cos.

No need to memorize them, they're easy enough to generate. But, do you know how many terms you have to calculate to get even 1% accuracy? That's why they're not used in practice.

Oh, and by the way, that 'sin(x) ~ x for small x' is true only if x is expressed in radians. I've never seen a protractor calibrated in radians, and 180/pi is a pita. I can't begin to tell you how many lab students screwed up the pendulum lab by missing that point.

--Pete