Algebra Text?

[Jim Thompson]

I'm fighting the school system with, now, the 5th granddaughter, 6th
Grade.

Last week they were peddling how to cut corners out of a piece of
cardboard to form a box with the maximum volume, with no established
skill set.... "guess" your way to the solution :-(

This week they suddenly jumped to Algebra, simultaneous equations,
without even any single variable background.

And she says her teacher is already using the word "Calculus". I
guess that's the leftist way anymore, speaking the words makes you
expert :-(

No wonder US students rank so low, worldwide, in math (and science).

Fortunately the school year is almost over, and she'll be with us for
a month in July.

So my question...

Can anyone recommend an available Algebra book that instructs in the
old fashioned sequential way... lots of one variable word problems
first, then go on to more advanced topics?

I'll become teacher of the month ;-)

(I taught math back in 1964-65 to disadvantaged youth (aka "thugs")
from South Phoenix with a very high success rate :-)

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

[rickman]

On 5/17/2013 2:40 PM, Jim Thompson wrote:
> I'm fighting the school system with, now, the 5th granddaughter, 6th
> Grade.
>
> Last week they were peddling how to cut corners out of a piece of
> cardboard to form a box with the maximum volume, with no established
> skill set.... "guess" your way to the solution :-(

In another context I and likely *you* would talk about this as getting a
"feel" for the math. I know that some of the best stuff I ever learned
was from "playing" with things, be they blocks or oscilloscopes. No
matter how much math I have learned, I don't consider I know a topic
until I get an intuitive feel for it.

> This week they suddenly jumped to Algebra, simultaneous equations,
> without even any single variable background.

There may be more to this than you are getting second hand from a 12
year old.

> And she says her teacher is already using the word "Calculus". I
> guess that's the leftist way anymore, speaking the words makes you
> expert :-(

Why is this a political issue? Teachers are highly educated in...
teaching. It is not a subject that is trivial for the lay person. Try
sometime reading some of the material teachers have to master.

> No wonder US students rank so low, worldwide, in math (and science).

Or maybe its because we just don't value engineers, etc. as highly as
other occupations, so students aren't interested as much in those subjects?

--

Rick

[amdx]

On 5/17/2013 1:40 PM, Jim Thompson wrote:

> Can anyone recommend an available Algebra book that instructs in the
> old fashioned sequential way... lots of one variable word problems
> first, then go on to more advanced topics?
>
> I'll become teacher of the month ;-)
>
> (I taught math back in 1964-65 to disadvantaged youth (aka "thugs")
> from South Phoenix with a very high success rate :-)
>
> ...Jim Thompson
>

Don't have a book, but would the Khan Academy help you.
https://www.khanacademy.org/

Mikek

[Tim Wescott]

On Fri, 17 May 2013 11:40:50 -0700, Jim Thompson wrote:

> I'm fighting the school system with, now, the 5th granddaughter, 6th
> Grade.
>
> Last week they were peddling how to cut corners out of a piece of
> cardboard to form a box with the maximum volume, with no established
> skill set.... "guess" your way to the solution :-(
>
> This week they suddenly jumped to Algebra, simultaneous equations,
> without even any single variable background.
>
> And she says her teacher is already using the word "Calculus". I guess
> that's the leftist way anymore, speaking the words makes you expert :-(
>
> No wonder US students rank so low, worldwide, in math (and science).
>
> Fortunately the school year is almost over, and she'll be with us for a
> month in July.
>
> So my question...
>
> Can anyone recommend an available Algebra book that instructs in the old
> fashioned sequential way... lots of one variable word problems first,
> then go on to more advanced topics?
>
> I'll become teacher of the month ;-)
>
> (I taught math back in 1964-65 to disadvantaged youth (aka "thugs") from
> South Phoenix with a very high success rate :-)

Check out the Life of Fred books. They're written for homeschoolers
(home scholars?). IIRC you're mostly agnostic, so be aware that there's
a little bit of Christianity thrown in gratis -- it's not preachy, it's
just kind of in there. It's not enough to offend unless you're a Koran/
Torah/"The God Delusion"/"Book of Mormon"/whatever-thumping
fundamentalist.

They're written as biographies of Fred, who's a pre-pubescent professor
of math at KITTENS University (Kansas Institute for Teaching Technology
Engineering and Natural Science). Mixed in amongst his adventures with
coping in the real world are quite a few math lessons. This sounds
really dorky as I write it -- but the author is quite brilliant about
mixing in just enough "story" to keep the math engaging (the story line
is where the Christianity comes in), and keeping the math rigorous.

"Life of Fred, Beginning Algebra", Stanley F. Schmidt, 2009, Polka Dot
Publishing, ISBN: 978-9-9709995-1-1

"Life of Fred, Beginning Algebra", Stanley F. Schmidt, 2002, Polka Dot
Publishing, ISBN: 0-9709995-2-6

Do a search, you'll find plenty of reviews.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

[Jim Thompson]

Thanks, Tim!

I'm not the offendable type. My family consists of Christians, Jews
and Catholics, and Atheists/Agnostics like me; and well as Hispanics,
and we get on famously.

[Martin Brown]

On 17/05/2013 19:40, Jim Thompson wrote:
> I'm fighting the school system with, now, the 5th granddaughter, 6th
> Grade.
>
> Last week they were peddling how to cut corners out of a piece of
> cardboard to form a box with the maximum volume, with no established
> skill set.... "guess" your way to the solution :-(

To be fair to the teacher - giving them two pins, a length of string and
the challenge to construct an ellipse is actually a *very* good test of
innate mathematical intuition.

I think the reasoning for the biggest cardboard box one is similar.

You can pick out the geniuses more easily with tests that are beyond the
reach of linear progression from what has been actually taught.

Another really good test is:

given a^2 + b^2 = c^2 where a,b,c are integers

can you construct A^2 + B^2 = 2c^2 and state A, B

You can either see the answer to this instantly or not at all.
(this latter is more applicable to university entrance for maths)

> This week they suddenly jumped to Algebra, simultaneous equations,
> without even any single variable background.

Clearly madness if it is as you reported it.

I got into trouble at school once by framing quadratic equations as
untaught non-linear two variable problems. I got the right answer but
ignored the teachers hint how to do it. He was not amused.

> And she says her teacher is already using the word "Calculus". I
> guess that's the leftist way anymore, speaking the words makes you
> expert :-(

No idea what 6th grade US is so cannot comment.
In my day basic calculus was taught about age 14 ish. We did a lot of
spherical trig first for navigating around the empire on great circles.

It would be a sad day indeed if a teacher of mathematics did not fully
understand both integral and differential calculus. I'd expect most of
them to understand the finesse of calculus of variations as well.

My first year undergraduate maths for physicists course was something of
a notorious baptism of fire starting as it did with differential vector
calculus and assuming everything that went before it. The pure
mathematicians meanwhile spent most of that term proving that 0 != 1.

I truanted my last year of maths classes at high school as complete
waste of my time.

> No wonder US students rank so low, worldwide, in math (and science).
>
> Fortunately the school year is almost over, and she'll be with us for
> a month in July.
>
> So my question...
>
> Can anyone recommend an available Algebra book that instructs in the
> old fashioned sequential way... lots of one variable word problems
> first, then go on to more advanced topics?
>
> I'll become teacher of the month ;-)

The compendium of Lewis Carroll's works and Martin Gardener books are
much more fun to learn from and far more educational. Maybe just a bit
beyond the reach of your ward. Another really tricky one is construct a
triangle given only two sides and the radius of the inscribed circle
using ruler and compasses only. Algebra needed to work out what to do
unless you really are true genius level at physical geometry intuition.

>
> (I taught math back in 1964-65 to disadvantaged youth (aka "thugs")
> from South Phoenix with a very high success rate :-)
>
> ...Jim Thompson

Make it fun and you don't have to teach it.

Why is this cross posted to alt.binaries.*.* ?

--
Regards,
Martin Brown

[Jim Thompson]

On Fri, 17 May 2013 14:59:47 -0400, rickman <gnu...@gmail.com> wrote:

>On 5/17/2013 2:40 PM, Jim Thompson wrote:
>> I'm fighting the school system with, now, the 5th granddaughter, 6th
>> Grade.
>>
>> Last week they were peddling how to cut corners out of a piece of
>> cardboard to form a box with the maximum volume, with no established
>> skill set.... "guess" your way to the solution :-(
>
>In another context I and likely *you* would talk about this as getting a
>"feel" for the math. I know that some of the best stuff I ever learned
>was from "playing" with things, be they blocks or oscilloscopes. No
>matter how much math I have learned, I don't consider I know a topic
>until I get an intuitive feel for it.

That sort of problem, without the proper skill background, has no
"playing around" factor... it's just guessing... which I frown on
seriously.

When my granddaughter inquired, I suggested, that, with her skill
level, the only solution was to plot volume versus the size of the
cut-out and observe the maximum. She did so, and was rewarded with a
gift card as her prize... such is the level of education today.

>
>> This week they suddenly jumped to Algebra, simultaneous equations,
>> without even any single variable background.
>
>There may be more to this than you are getting second hand from a 12
>year old.

No second hand about it. This is the modern era. Though she's in
Palm Springs, Californica, she PDF'd her homework sheet. I have it
right here in front of me.

>
>> And she says her teacher is already using the word "Calculus". I
>> guess that's the leftist way anymore, speaking the words makes you
>> expert :-(
>
>Why is this a political issue?

We have an educational system dominated by nutcases on the left...
with twisted views that the only way to do things is their way. And
"their way", no matter how wrong, is still to be considered the
correct way.

>Teachers are highly educated in...
>teaching.

Bwahahahahaha! Almost lost my lunch over that >:-}

>It is not a subject that is trivial for the lay person. Try
>sometime reading some of the material teachers have to master.

I'm hardly a lay person...

(1) I got 800 in Math on the SAT's. What did you get?
(2) I attended M.I.T. on a FULL Alumni Fund National Scholarship back
when scholarships were awarded on the basis of competency, not on
need... my parents were wealthy by the standards of the '50's.
(3) I graduated in Course 6-B, the HONORS Electrical Engineering
Program.
(4) And, though not worth all that much, an MSEE from ASU (*)

Teachers may be competent, but they're bound to parrot the line
established by the school boards and the administrators. Thus we have
children expelled for wearing NRA T-shirts, pointing with their
fingers, etc.

>
>> No wonder US students rank so low, worldwide, in math (and science).
>
>Or maybe its because we just don't value engineers, etc. as highly as
>other occupations, so students aren't interested as much in those subjects?

Our society has created a life-style based on texting, tweeting, and
sucking off the tit of the government.

The sooner the revolution the better.

(*) My first week at ASU, I was thrown out of a Physics class for
asking the Prof, "When do you plan to start teaching this course on a
college level".

After some "conversation" with the Dean, I got full credit for that
course and several others offered at ASU. Finally found some
non-linear control system courses that were useful ;-)

[Nico Coesel]

Jim Thompson <To-Email-Use-Th...@On-My-Web-Site.com>
wrote:

>I'm fighting the school system with, now, the 5th granddaughter, 6th
>Grade.
>
>Last week they were peddling how to cut corners out of a piece of
>cardboard to form a box with the maximum volume, with no established
>skill set.... "guess" your way to the solution :-(
>
>This week they suddenly jumped to Algebra, simultaneous equations,
>without even any single variable background.
>
>And she says her teacher is already using the word "Calculus". I
>guess that's the leftist way anymore, speaking the words makes you
>expert :-(
>
>No wonder US students rank so low, worldwide, in math (and science).
>
>Fortunately the school year is almost over, and she'll be with us for
>a month in July.
>
>So my question...
>
>Can anyone recommend an available Algebra book that instructs in the
>old fashioned sequential way... lots of one variable word problems
>first, then go on to more advanced topics?
>
>I'll become teacher of the month ;-)

I like the book called 'Modern Engineering Mathematics'. It starts
with 3+4=7 and ends with probability theory so it covers a lot of
ground. I also have the follow up called 'Advanced modern engineering
mathematics'.

--
Failure does not prove something is impossible, failure simply
indicates you are not using the right tools...
nico@nctdevpuntnl (punt=.)
--------------------------------------------------------------

[David Eather]

On Sat, 18 May 2013 04:40:50 +1000, Jim Thompson
<To-Email-Use-Th...@on-my-web-site.com> wrote:

> I'm fighting the school system with, now, the 5th granddaughter, 6th
> Grade.
>
> Last week they were peddling how to cut corners out of a piece of
> cardboard to form a box with the maximum volume, with no established
> skill set.... "guess" your way to the solution :-(
>
> This week they suddenly jumped to Algebra, simultaneous equations,
> without even any single variable background.
>
> And she says her teacher is already using the word "Calculus". I
> guess that's the leftist way anymore, speaking the words makes you
> expert :-(
>
> No wonder US students rank so low, worldwide, in math (and science).
>
> Fortunately the school year is almost over, and she'll be with us for
> a month in July.
>
> So my question...
>
> Can anyone recommend an available Algebra book that instructs in the
> old fashioned sequential way... lots of one variable word problems
> first, then go on to more advanced topics?
>
> I'll become teacher of the month ;-)
>
> (I taught math back in 1964-65 to disadvantaged youth (aka "thugs")
> from South Phoenix with a very high success rate :-)
>
> ...Jim Thompson

http://www.coolmath.com/index.html

(might be a bit leftest for you - she thinks maths can be fun!)

[Jim Thompson]

On Fri, 17 May 2013 14:59:47 -0400, rickman <gnu...@gmail.com> wrote:

[snip]

>
>Why is this a political issue? Teachers are highly educated in...
>teaching. It is not a subject that is trivial for the lay person. Try
>sometime reading some of the material teachers have to master.
>

[snip]

Forgot an important issue...

In Germany it is ILLEGAL to home-school your children.

A German couple with two children requested asylum in the USA based on
that German restriction of freedom.

The Obama regime just refused their request for asylum.

Wonder how long it will be before it is illegal to home-school in the
USA?

[Jim Thompson]

On Sat, 18 May 2013 10:01:13 +1000, "David Eather" <eat...@tpg.com.au>
wrote:

Math _is_ fun! That's why I'm so good at it... I only do things that
are fun. Designing chips is LOTS of fun! I don't think I've really
_worked_ a day in my life >:-}

[Jim Thompson]

On Fri, 17 May 2013 17:20:54 -0700, Jim Thompson
<To-Email-Use-Th...@On-My-Web-Site.com> wrote:

>On Fri, 17 May 2013 14:59:47 -0400, rickman <gnu...@gmail.com> wrote:
>
>[snip]
>>
>>Why is this a political issue? Teachers are highly educated in...
>>teaching. It is not a subject that is trivial for the lay person. Try
>>sometime reading some of the material teachers have to master.
>>
>[snip]
>
>Forgot an important issue...
>
>In Germany it is ILLEGAL to home-school your children.
>
>A German couple with two children requested asylum in the USA based on
>that German restriction of freedom.
>
>The Obama regime just refused their request for asylum.

http://tinyurl.com/cpuxoue

http://tinyurl.com/cbhtges

[Michael A. Terrell]

Jim Thompson wrote:
>
> I'm fighting the school system with, now, the 5th granddaughter, 6th
> Grade.
>
> Last week they were peddling how to cut corners out of a piece of
> cardboard to form a box with the maximum volume, with no established
> skill set.... "guess" your way to the solution :-(
>
> This week they suddenly jumped to Algebra, simultaneous equations,
> without even any single variable background.
>
> And she says her teacher is already using the word "Calculus". I
> guess that's the leftist way anymore, speaking the words makes you
> expert :-(
>
> No wonder US students rank so low, worldwide, in math (and science).
>
> Fortunately the school year is almost over, and she'll be with us for
> a month in July.
>
> So my question...
>
> Can anyone recommend an available Algebra book that instructs in the
> old fashioned sequential way... lots of one variable word problems
> first, then go on to more advanced topics?
>
> I'll become teacher of the month ;-)
>
> (I taught math back in 1964-65 to disadvantaged youth (aka "thugs")
> from South Phoenix with a very high success rate :-)

Check out:

http://www.algebra.com/

[Edward Lee]

On May 17, 6:55 pm, Jim Thompson <To-Email-Use-The-Envelope-I...@On-My-

780, i think. You beat me there. But i did get all As in college
math and physics.

BTW, my son's high school physics is too simple, not enough math.
What would be a good online site to find some challenging college
level physics problems for him.

[ABLE1]

> BTW, my son's high school physics is too simple, not enough math.
> What would be a good online site to find some challenging college
> level physics problems for him.

http://www.khanacademy.org/

[Tom Del Rosso]

Jim Thompson wrote:
>
> Can anyone recommend an available Algebra book that instructs in the
> old fashioned sequential way... lots of one variable word problems
> first, then go on to more advanced topics?

see https://www.youtube.com/watch?v=25NG6O4l724


--

Reply in group, but if emailing remove the last word.

[d...@kbrx.com]

Best starting point for algebra is a see-saw in the school yard and a
balence in the school room. Good luck finding a text.

Hul

[Tom Del Rosso]

Martin Brown wrote:
>
> given a^2 + b^2 = c^2 where a,b,c are integers
>
> can you construct A^2 + B^2 = 2c^2 and state A, B

A=B=0

But I get the impression that's not what you had in mind?

> Why is this cross posted to alt.binaries.*.* ?

Since it isn't archived, OT matters less there IMO.

[Greegor]

> Wonder how long it will be before it
> is illegal to home-school in the USA?

In my county Judge Sosalla is famous for
thinking homeschooling is illegal now.

[Jim Thompson]

If you can get your hands on this book....

http://tinyurl.com/acmurce

My freshman Physics book at M.I.T.

Absolutely superb! At M.I.T. it neatly tracked right along with
freshman Calculus... the Calculus you needed was right there to match
the need in the Physics course ;-)

[Edward Lee]

On May 18, 6:29 pm, Jim Thompson <To-Email-Use-The-Envelope-I...@On-My-

I found some good college level e-books from previous poster's link.
Some are published a century ago (1910), but laws of physics has not
changed. It's not so important with the content, but the manner of
presentations. Too many college fresh(wo)men (including my daughter)
found out the hard way that college text books are not written the
same way as high school books. Perhaps my son can be better prepared
with these readings.

[Jasen Betts]

On 2013-05-18, Tom Del Rosso <tom...@verizon.net.invalid> wrote:
>
> Martin Brown wrote:
>>
>> given a^2 + b^2 = c^2 where a,b,c are integers
>>
>> can you construct A^2 + B^2 = 2c^2 and state A, B
>
> A=B=0
>
> But I get the impression that's not what you had in mind?

if A=a and B=b that is the only integer solution
(other solutions exist on the comples plane eg: A=iB, also B=iA)

theres a few more solutions if you allow

a =/= A and b =/= B

you get A=B=c (and possibly other solutions?)

but this is usenet and the mixed case may be a typographic error.

--
⚂⚃ 100% natural

--- news://freenews.netfront.net/ - complaints: ne...@netfront.net ---

[Martin Brown]

On 18/05/2013 17:11, Edward Lee wrote:

> BTW, my son's high school physics is too simple, not enough math.
> What would be a good online site to find some challenging college
> level physics problems for him.

How good are *you* at working out the correct answers?

This set of physics problems that will challenge even the brightest
students and for that matter most high school physics teachers.

http://www.amazon.com/Cavendish-Problems-Classical-Physics-Pippard/dp/0521083095/ref=sr_1_1?s=books&ie=UTF8&qid=1368949138&sr=1-1&keywords=pippards+physics+problems


When I was at school "Physics is Fun" series were newly published and
reasonably priced - especially if you had prize money to spend. They are
a bit dated now and have become collectors items with insane prices.

http://www.amazon.com/Physics-Fun-Bk-Jim-Jardine/dp/0435674706/ref=sr_1_20?s=books&ie=UTF8&qid=1368949013&sr=1-20&keywords=Physics+is+fun

ISTR Series of four books covering most of high school physics.

Working through the Martin Gardener series of books taken from his
Mathematical Games column in SciAm is likely to be more rewarding.

Or a decent undergraduate text in whichever branch of physics he is most
interested in. If you make it too much like hard work then his interest
in the subject can easily be killed off at this stage.

He is probably best off borrowing books from your local library until he
finds one that really catches his interest.

--
Regards,
Martin Brown

[Martin Brown]

On 18/05/2013 23:10, Tom Del Rosso wrote:
> Martin Brown wrote:
>>
>> given a^2 + b^2 = c^2 where a,b,c are integers
>>
>> can you construct A^2 + B^2 = 2c^2 and state A, B
>
> A=B=0
>
> But I get the impression that's not what you had in mind?

I forgot to exclude a=b=0 in the problem statement
although we normally allowed that option as a first try

But there is another solution with a, b, A, B != 0

>
>
>> Why is this cross posted to alt.binaries.*.* ?

Because the OP is a cross posting clueless *MORON*.

>
> Since it isn't archived, OT matters less there IMO.
>
>


--

Regards,
Martin Brown

[Jasen Betts]

On 2013-05-19, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
> On 18/05/2013 23:10, Tom Del Rosso wrote:
>> Martin Brown wrote:
>>>
>>> given a^2 + b^2 = c^2 where a,b,c are integers
>>>
>>> can you construct A^2 + B^2 = 2c^2 and state A, B
>>
>> A=B=0
>>
>> But I get the impression that's not what you had in mind?
>
> I forgot to exclude a=b=0 in the problem statement
> although we normally allowed that option as a first try
>
> But there is another solution with a, b, A, B != 0

probably you should have said positive integers at the start.

anyway:

a,b,A,B

5,5 (and more variations on Pythogaras triangle hypotenuse)

1,7 and probably more like that too, certainly multiples of it.

[rickman]

On 5/17/2013 6:55 PM, Jim Thompson wrote:
> On Fri, 17 May 2013 14:59:47 -0400, rickman<gnu...@gmail.com> wrote:
>
>> On 5/17/2013 2:40 PM, Jim Thompson wrote:
>>> I'm fighting the school system with, now, the 5th granddaughter, 6th
>>> Grade.
>>>
>>> Last week they were peddling how to cut corners out of a piece of
>>> cardboard to form a box with the maximum volume, with no established
>>> skill set.... "guess" your way to the solution :-(
>>
>> In another context I and likely *you* would talk about this as getting a
>> "feel" for the math. I know that some of the best stuff I ever learned
>> was from "playing" with things, be they blocks or oscilloscopes. No
>> matter how much math I have learned, I don't consider I know a topic
>> until I get an intuitive feel for it.
>
> That sort of problem, without the proper skill background, has no
> "playing around" factor... it's just guessing... which I frown on
> seriously.

I don't agree. I often delve into areas I have no specific knowledge in
and then once I run into my limitations, seek information from other
sources. At that point I have questions I want answered. When I find
the answers I remember them. You can call it guessing, but the point is
they learned the problem first, then learned the solution, rather than
just being spoon fed lessons to be regurgitated at a later date. Do you
really not see the utility of this?

> When my granddaughter inquired, I suggested, that, with her skill
> level, the only solution was to plot volume versus the size of the
> cut-out and observe the maximum. She did so, and was rewarded with a
> gift card as her prize... such is the level of education today.

I don't follow what you are saying here. Did you give her the gift card
or was that in class? Are you saying that is good or bad?

>>> This week they suddenly jumped to Algebra, simultaneous equations,
>>> without even any single variable background.
>>
>> There may be more to this than you are getting second hand from a 12
>> year old.
>
> No second hand about it. This is the modern era. Though she's in
> Palm Springs, Californica, she PDF'd her homework sheet. I have it
> right here in front of me.

Oh, you are in the classroom watching it all first hand?

>>> And she says her teacher is already using the word "Calculus". I
>>> guess that's the leftist way anymore, speaking the words makes you
>>> expert :-(
>>
>> Why is this a political issue?
>
> We have an educational system dominated by nutcases on the left...
> with twisted views that the only way to do things is their way. And
> "their way", no matter how wrong, is still to be considered the
> correct way.

Educators are left nut cases, or just the ones who promote anything you
don't like?

>> Teachers are highly educated in...
>> teaching.
>
> Bwahahahahaha! Almost lost my lunch over that>:-}

Exactly. That's the problem, you have no respect for teachers even
though you don't understand their methods.

>> It is not a subject that is trivial for the lay person. Try
>> sometime reading some of the material teachers have to master.
>
> I'm hardly a lay person...
>
> (1) I got 800 in Math on the SAT's. What did you get?

You sound like Larkin now. But this has *nothing* to do with teaching.

> (2) I attended M.I.T. on a FULL Alumni Fund National Scholarship back
> when scholarships were awarded on the basis of competency, not on
> need... my parents were wealthy by the standards of the '50's.

Again, *nothing* to do with teaching.

> (3) I graduated in Course 6-B, the HONORS Electrical Engineering
> Program.

*Nothing* to do with teaching.

> (4) And, though not worth all that much, an MSEE from ASU (*)

So you acknowledge that you have learned *nothing* about teaching?!

> Teachers may be competent, but they're bound to parrot the line
> established by the school boards and the administrators. Thus we have
> children expelled for wearing NRA T-shirts, pointing with their
> fingers, etc.

Unlike you, teachers are all educated in *teaching* and are accredited
in teaching. What are your qualifications again? Oh yeah, your
qualifications are all in being *taught* by *teacher*.

>>> No wonder US students rank so low, worldwide, in math (and science).
>>
>> Or maybe its because we just don't value engineers, etc. as highly as
>> other occupations, so students aren't interested as much in those subjects?
>
> Our society has created a life-style based on texting, tweeting, and
> sucking off the tit of the government.

I think you must be many decades older than myself. You sound like a
grandparent... no you sound like *all* grandparents through history.

> The sooner the revolution the better.
>
> (*) My first week at ASU, I was thrown out of a Physics class for
> asking the Prof, "When do you plan to start teaching this course on a
> college level".

Yes, and your level of disrespect for others continues. You don't get
that your critera for others is of no interest to the rest of the world.

> After some "conversation" with the Dean, I got full credit for that
> course and several others offered at ASU. Finally found some
> non-linear control system courses that were useful ;-)

So you have a huge ego. That doesn't mean you ar equalified to judge
teachers.

--

Rick

[Edward Lee]

> >> Teachers are highly educated in teaching.

Not always in the US.

>
> > Bwahahahahaha!  Almost lost my lunch over that>:-}

Have to agree with him on this, despite his political views.

>
> Exactly.  That's the problem, you have no respect for teachers even
> though you don't understand their methods.

But i know the results.

My daughter graduated #2 (should have been #1 including course
difficulties) in high school. 750+ SAT, 4s and 5s ACT. She is the
top student by US standard, but failing some beginning courses at
UCLA, where she is competing with international students who are much
better prepared. She might be OK after repeating some classes, but
that show you the current US educational system. Their (my son and
daughter) high school is supposed to be a good school relative to
others, but absolutely failing to prepare students for college. SAT
and ACT are not too useful indicators either.

When i ask them to study college level materials like most
international students. The answer is: My school is not teaching
this stuff, why should we learn that.

[Jim Thompson]

On Sun, 19 May 2013 13:03:05 -0400, rickman <gnu...@gmail.com> wrote:

>On 5/17/2013 6:55 PM, Jim Thompson wrote:
>> On Fri, 17 May 2013 14:59:47 -0400, rickman<gnu...@gmail.com> wrote:
>>
>>> On 5/17/2013 2:40 PM, Jim Thompson wrote:
>>>> I'm fighting the school system with, now, the 5th granddaughter, 6th
>>>> Grade.
>>>>
>>>> Last week they were peddling how to cut corners out of a piece of
>>>> cardboard to form a box with the maximum volume, with no established
>>>> skill set.... "guess" your way to the solution :-(
>>>
>>> In another context I and likely *you* would talk about this as getting a
>>> "feel" for the math. I know that some of the best stuff I ever learned
>>> was from "playing" with things, be they blocks or oscilloscopes. No
>>> matter how much math I have learned, I don't consider I know a topic
>>> until I get an intuitive feel for it.
>>
>> That sort of problem, without the proper skill background, has no
>> "playing around" factor... it's just guessing... which I frown on
>> seriously.
>
>I don't agree. I often delve into areas I have no specific knowledge in
>and then once I run into my limitations, seek information from other
>sources. At that point I have questions I want answered. When I find
>the answers I remember them. You can call it guessing, but the point is
>they learned the problem first, then learned the solution, rather than
>just being spoon fed lessons to be regurgitated at a later date. Do you
>really not see the utility of this?

You can not "learn" such a problem by guessing. You "learn" a problem
by understanding how a solution is developed. That kind of problem
_does_not_belong_ in a 6th grade class.

>
>
>> When my granddaughter inquired, I suggested, that, with her skill
>> level, the only solution was to plot volume versus the size of the
>> cut-out and observe the maximum. She did so, and was rewarded with a
>> gift card as her prize... such is the level of education today.
>
>I don't follow what you are saying here. Did you give her the gift card
>or was that in class?

The teacher gave her the gift card.

>Are you saying that is good or bad?

I'm unsure. I am somewhat Pavlovian >:-}

But the problem has no business in 6th grade.

>
>
>>>> This week they suddenly jumped to Algebra, simultaneous equations,
>>>> without even any single variable background.
>>>
>>> There may be more to this than you are getting second hand from a 12
>>> year old.
>>
>> No second hand about it. This is the modern era. Though she's in
>> Palm Springs, Californica, she PDF'd her homework sheet. I have it
>> right here in front of me.
>
>Oh, you are in the classroom watching it all first hand?

Of course not. But you have no clue how tight-knit our family is.

>
>
>>>> And she says her teacher is already using the word "Calculus". I
>>>> guess that's the leftist way anymore, speaking the words makes you
>>>> expert :-(
>>>
>>> Why is this a political issue?
>>
>> We have an educational system dominated by nutcases on the left...
>> with twisted views that the only way to do things is their way. And
>> "their way", no matter how wrong, is still to be considered the
>> correct way.
>
>Educators are left nut cases, or just the ones who promote anything you
>don't like?

Teachers shouldn't be "promoting" ANY philosophy, pro or con, religion
or "lifestyle" or politics... that's strictly a parent's job. Teachers
should stick strictly to teaching Reading/Writing/'rithmetic, as the
old saw goes. If they promote ANY philosophy they should be fired.

You are apparently of that elitist class who think teachers know
better than parents what is good for their child.

They don't, and the day of retribution is coming.

>
>
>>> Teachers are highly educated in...
>>> teaching.
>>
>> Bwahahahahaha! Almost lost my lunch over that>:-}

DOUBLE Bwahahahahaha!

>
>Exactly. That's the problem, you have no respect for teachers even
>though you don't understand their methods.

I have no respect for teachers who do other than teach. I blame
administrators and school boards for curriculum, and that speeding
thru courses beats rote.

>
>
>>> It is not a subject that is trivial for the lay person. Try
>>> sometime reading some of the material teachers have to master.
>>
>> I'm hardly a lay person...
>>
>> (1) I got 800 in Math on the SAT's. What did you get?
>
>You sound like Larkin now. But this has *nothing* to do with teaching.

It simply means I can run circles around you in math :-)

>
>
>> (2) I attended M.I.T. on a FULL Alumni Fund National Scholarship back
>> when scholarships were awarded on the basis of competency, not on
>> need... my parents were wealthy by the standards of the '50's.
>
>Again, *nothing* to do with teaching.

You said I was a "lay person". Clearly I'm not.

>
>
>> (3) I graduated in Course 6-B, the HONORS Electrical Engineering
>> Program.
>
>*Nothing* to do with teaching.

You said I was a "lay person". Clearly I'm not.

>
>
>> (4) And, though not worth all that much, an MSEE from ASU (*)
>
>So you acknowledge that you have learned *nothing* about teaching?!

I have (very successfully) taught seminars in Integrated Circuit
Design for more years than you probably are old.

>
>
>> Teachers may be competent, but they're bound to parrot the line
>> established by the school boards and the administrators. Thus we have
>> children expelled for wearing NRA T-shirts, pointing with their
>> fingers, etc.
>
>Unlike you, teachers are all educated in *teaching* and are accredited
>in teaching. What are your qualifications again? Oh yeah, your
>qualifications are all in being *taught* by *teacher*.

Teaching is a union. I offered to teach a technician-level course at
Scottsdale Community College for FREE (the course had been dropped
because they had no instructor). I was denied because I didn't have a
"teacher's certificate". Teaching is a union that must be busted.

>
>
>>>> No wonder US students rank so low, worldwide, in math (and science).
>>>
>>> Or maybe its because we just don't value engineers, etc. as highly as
>>> other occupations, so students aren't interested as much in those subjects?
>>
>> Our society has created a life-style based on texting, tweeting, and
>> sucking off the tit of the government.
>
>I think you must be many decades older than myself. You sound like a
>grandparent... no you sound like *all* grandparents through history.

I can kick your ass in math or circuit design any day of the year,
grandparent or not.

>
>
>> The sooner the revolution the better.
>>
>> (*) My first week at ASU, I was thrown out of a Physics class for
>> asking the Prof, "When do you plan to start teaching this course on a
>> college level".
>
>Yes, and your level of disrespect for others continues. You don't get
>that your critera for others is of no interest to the rest of the world.
>
>
>> After some "conversation" with the Dean, I got full credit for that
>> course and several others offered at ASU. Finally found some
>> non-linear control system courses that were useful ;-)
>
>So you have a huge ego. That doesn't mean you ar equalified to judge
>teachers.

Wrong! I am qualified because I have a huge math, science and
engineering background... because M.I.T. teaches undergrad to a level
exceeding what most universities offer as graduate level courses. (And
the ASU Physics level was just plain JUVENILE.)

Rickman, I have authorized your graduation to the rank of butt-buddy.
Bye >:-}

[Martin Brown]

On 19/05/2013 13:15, Jasen Betts wrote:
> On 2013-05-19, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
>> On 18/05/2013 23:10, Tom Del Rosso wrote:
>>> Martin Brown wrote:
>>>>
>>>> given a^2 + b^2 = c^2 where a,b,c are integers
>>>>
>>>> can you construct A^2 + B^2 = 2c^2 and state A, B
>>>
>>> A=B=0
>>>
>>> But I get the impression that's not what you had in mind?
>>
>> I forgot to exclude a=b=0 in the problem statement
>> although we normally allowed that option as a first try
>>
>> But there is another solution with a, b, A, B != 0
>
> probably you should have said positive integers at the start.

I should perhaps have said non-zero but it was normal not to bother.

The even powers mean that positive or negative makes no difference.

Anyone that didn't spot a=b=A=B=0 as a solution would fail immediately.

> anyway:
>
> a,b,A,B
>
> 5,5 (and more variations on Pythogaras triangle hypotenuse)
>
> 1,7 and probably more like that too, certainly multiples of it.

Valid concrete examples I grant you.

The final problem statement is for given a,b,c with

a^2 + b^2 = c^2

find algebraic expressions for A,B

s.t A^2 + B^2 = 2c^2

--
Regards,
Martin Brown

[Tom Del Rosso]

I wasn't sure how you wanted to define the relationship between a,b and A,B,
but if that is the only thing that relates them, and you just want A,B in
terms of a,b, then...

A^2 + B^2 = 2(a^2 + b^2)

...and simplify, solving for A and B.

Am I misunderstanding the question again, or are you really just asking for
a restatement of that equation with A and B isolated?

Maybe I forgot how to read math books, but I used to understand the
questions at least, a long time ago.

[Jim Thompson]

It's that "new math" >:-}

[Tom Del Rosso]

Jim Thompson wrote:
>
> It's that "new math" >:-}

I learned with new math. It seems like anybody with a deep understanding
would prefer it since it uses place value logically. Don't you think so?

[Jim Thompson]

On Sun, 19 May 2013 20:44:21 -0400, "Tom Del Rosso"
<tom...@verizon.net.invalid> wrote:

>
>Jim Thompson wrote:
>>
>> It's that "new math" >:-}
>
>I learned with new math. It seems like anybody with a deep understanding
>would prefer it since it uses place value logically. Don't you think so?

Of course. I agree wholeheartedly!

[Martin Brown]

You have one equation and two unknowns. How do you propose to do that?

>
> Am I misunderstanding the question again, or are you really just asking for
> a restatement of that equation with A and B isolated?

The algebraic solution is in the form

A = F(a,b)
B = G(a,b)

Where A,B,a,b are all integers with some of them non-zero.
In the general case they are all non-zero.
Your task is to find the functions F(), G().

> Maybe I forgot how to read math books, but I used to understand the
> questions at least, a long time ago.

There isn't a lot of math involved. This is more of a puzzle.
Only basic high school algebra is required.

--
Regards,
Martin Brown

[Martin Brown]

On 19/05/2013 23:01, Jim Thompson wrote:
> On Sun, 19 May 2013 17:09:37 -0400, "Tom Del Rosso"
> <tom...@verizon.net.invalid> wrote:
>
>>
>> Martin Brown wrote:

>>> The final problem statement is for given a,b,c with
>>>
>>> a^2 + b^2 = c^2
>>>
>>> find algebraic expressions for A,B
>>>
>>> s.t A^2 + B^2 = 2c^2
>>
>> I wasn't sure how you wanted to define the relationship between a,b and A,B,
>> but if that is the only thing that relates them, and you just want A,B in
>> terms of a,b, then...
>>
>> A^2 + B^2 = 2(a^2 + b^2)
>>
>> ...and simplify, solving for A and B.
>>
>> Am I misunderstanding the question again, or are you really just asking for
>> a restatement of that equation with A and B isolated?
>>
>> Maybe I forgot how to read math books, but I used to understand the
>> questions at least, a long time ago.
>
> It's that "new math" >:-}
>
> ...Jim Thompson

No. It is actually very old math, but it does require some innate
mathematical ability to see the correct solution.

How someone approaches this problem is very informative at interview
even if they cannot immediately see the right answer.

A much nastier Victorian one is construct with rule and compasses the
triangle specified by two sides and the radius of the inscribed circle.

--
Regards,
Martin Brown

[Jasen Betts]

On 2013-05-20, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
> On 19/05/2013 22:09, Tom Del Rosso wrote:

> The algebraic solution is in the form
>
> A = F(a,b)
> B = G(a,b)
>
> Where A,B,a,b are all integers with some of them non-zero.
> In the general case they are all non-zero.
> Your task is to find the functions F(), G().

functions?

F(a,b) = sqrt(a^2+b^2)
G=F

that seems way too easy

[Martin Brown]

On 20/05/2013 10:49, Jasen Betts wrote:
> On 2013-05-20, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
>> On 19/05/2013 22:09, Tom Del Rosso wrote:
>
>> The algebraic solution is in the form
>>
>> A = F(a,b)
>> B = G(a,b)
>>
>> Where A,B,a,b are all integers with some of them non-zero.
>> In the general case they are all non-zero.
>> Your task is to find the functions F(), G().
>
> functions?
>
> F(a,b) = sqrt(a^2+b^2)
> G=F
>
> that seems way too easy

sqrt(a^2+b^2) isn't an integer except in a handful of special cases.

There is a closed form exact algebraic solution for all a,b.

--
Regards,
Martin Brown

[George Herold]

On May 19, 3:49 am, Martin Brown <|||newspam...@nezumi.demon.co.uk>
wrote:

> On 18/05/2013 17:11, Edward Lee wrote:
>
> > BTW, my son's high school physics is too simple, not enough math.
> > What would be a good online site to find some challenging college
> > level physics problems for him.
>
> How good are *you* at working out the correct answers?
>
> This set of physics problems that will challenge even the brightest
> students and for that matter most high school physics teachers.
>

> http://www.amazon.com/Cavendish-Problems-Classical-Physics-Pippard/dp...

>
> When I was at school "Physics is Fun" series were newly published and
> reasonably priced - especially if you had prize money to spend. They are
> a bit dated now and have become collectors items with insane prices.
>

> http://www.amazon.com/Physics-Fun-Bk-Jim-Jardine/dp/0435674706/ref=sr...

>
> ISTR Series of four books covering most of high school physics.
>
> Working through the Martin Gardener series of books taken from his
> Mathematical Games column in SciAm is likely to be more rewarding.
>
> Or a decent undergraduate text in whichever branch of physics he is most
> interested in. If you make it too much like hard work then his interest
> in the subject can easily be killed off at this stage.
>
> He is probably best off borrowing books from your local library until he
> finds one that really catches his interest.
>
> --
> Regards,
> Martin Brown

Hi Martin, I assume you have heard of the "back of the envelope"
column written by Ed Purcell for AJP back in the 80's. Here's a web
link, if not.
http://ajp.dickinson.edu/Readers/backEnv.html

Good fun!

George H.

[Jim Thompson]

On Fri, 17 May 2013 21:41:06 +0100, Martin Brown
<|||newspam|||@nezumi.demon.co.uk> wrote:

>On 17/05/2013 19:40, Jim Thompson wrote:
>> I'm fighting the school system with, now, the 5th granddaughter, 6th
>> Grade.
>>
>> Last week they were peddling how to cut corners out of a piece of
>> cardboard to form a box with the maximum volume, with no established
>> skill set.... "guess" your way to the solution :-(
>

>To be fair to the teacher - giving them two pins, a length of string and
>the challenge to construct an ellipse is actually a *very* good test of
>innate mathematical intuition.

That I'm OK with.

>
>I think the reasoning for the biggest cardboard box one is similar.

But you can't "reason" your way to a numerical answer. You can reason
that the flat piece of cardboard has no volume, and that cutting away
all the cardboard yields no volume. But you have to plot it to find
the maximum.

>
>You can pick out the geniuses more easily with tests that are beyond the
>reach of linear progression from what has been actually taught.
>
>Another really good test is:

>
> given a^2 + b^2 = c^2 where a,b,c are integers
>

>can you construct A^2 + B^2 = 2c^2 and state A, B
>
>You can either see the answer to this instantly or not at all.
>(this latter is more applicable to university entrance for maths)

As soon as you state "integers" it becomes a guessing game. I "guess"
the engineer in me frowns on guessing.

I took the exam and was admitted to Mensa (at age 30), but most of the
exam questions were guessing.

>
>> This week they suddenly jumped to Algebra, simultaneous equations,
>> without even any single variable background.
>

>Clearly madness if it is as you reported it.

Yep. I've already ordered several of the recommended books to make
sure she has a solid background in Algebra.

>
>I got into trouble at school once by framing quadratic equations as
>untaught non-linear two variable problems. I got the right answer but
>ignored the teachers hint how to do it. He was not amused.

I've "unamused" a number of teachers along the way.

>
>> And she says her teacher is already using the word "Calculus". I
>> guess that's the leftist way anymore, speaking the words makes you
>> expert :-(
>

>No idea what 6th grade US is so cannot comment.
>In my day basic calculus was taught about age 14 ish. We did a lot of
>spherical trig first for navigating around the empire on great circles.

"In my day" we had Algebra, Plane Geometry, Trigonometry and Solid
Geometry in High School. My first exposure to Calculus was my
Freshman year at M.I.T. By then it was easy for me to understand. I
ended up taking 6 semesters of Calculus... all the way up to Tensors.

Modern "education" seems to think quantity is better than quality...
just because you've taken a course labeled "Calculus" makes everything
all marvelous.

>
>It would be a sad day indeed if a teacher of mathematics did not fully
>understand both integral and differential calculus. I'd expect most of
>them to understand the finesse of calculus of variations as well.
>
>My first year undergraduate maths for physicists course was something of
>a notorious baptism of fire starting as it did with differential vector
>calculus and assuming everything that went before it. The pure
>mathematicians meanwhile spent most of that term proving that 0 != 1.
>
>I truanted my last year of maths classes at high school as complete
>waste of my time.

>
>> No wonder US students rank so low, worldwide, in math (and science).
>>

>> Fortunately the school year is almost over, and she'll be with us for
>> a month in July.
>>
>> So my question...
>>
>> Can anyone recommend an available Algebra book that instructs in the
>> old fashioned sequential way... lots of one variable word problems
>> first, then go on to more advanced topics?
>>
>> I'll become teacher of the month ;-)
>

>The compendium of Lewis Carroll's works and Martin Gardener books are
>much more fun to learn from and far more educational. Maybe just a bit
>beyond the reach of your ward.

She's up to it. The reason she's visiting us this summer is that we
pay her way every year to Phoenix Valley Youth Theater Summer Camp.
She's been three years now... and has managed to be the star in their
final performance every time. She's quite the thespian and she's an
honor student... in spite of my fuming over the teaching methods.

>Another really tricky one is construct a
>triangle given only two sides and the radius of the inscribed circle
>using ruler and compasses only. Algebra needed to work out what to do
>unless you really are true genius level at physical geometry intuition.

I'm a master of those games... I still remember how to construct a
pentagon with compass and straight-edge ;-)

>>
>> (I taught math back in 1964-65 to disadvantaged youth (aka "thugs")
>> from South Phoenix with a very high success rate :-)
>>
>> ...Jim Thompson
>

>Make it fun and you don't have to teach it.

Certainly! Make it fun, and you don't ever have to "work". I've
never worked a day in my life ;-)

>
>Why is this cross posted to alt.binaries.*.* ?

It's not. Just to circuit groups.

[George Herold]

On May 20, 7:52 am, Martin Brown <|||newspam...@nezumi.demon.co.uk>
wrote:

> Martin Brown- Hide quoted text -
>
> - Show quoted text -

Hmm, Well in a few days will you post it. I can only get there by
guessing.


So just picking Pythagorean triples (a,b,c) 3,4,5; A=1 and B=7 works
(as Jasen said.)
Then for 5,12,13; A=7 and B=17 works.
But that’s the end of the line for simple triples that I know.

[Jim Thompson]

Maybe I'm missing the obvious, but I see no closed-form solution as
soon as you say "integer"... you have to guess.

[George Herold]

> But that’s the end of the line for simple triples that I know.- Hide quoted text -

>
> - Show quoted text -

Dang... never mind I see it!

George H.

[George Herold]

On May 20, 3:48 pm, Jim Thompson <To-Email-Use-The-Envelope-I...@On-My-

> | E-mail Icon athttp://www.analog-innovations.com|    1962     |
>
> I love to cook with wine.     Sometimes I even put it in the food.- Hide quoted text -

>
> - Show quoted text -

Well look at my two solutions, and your math brain should be able to
see the connection... and then the general solution is 'obvious'. (Of
course it's obvious only in hind sight.)

George H.

[rickman]

This is getting pointless. If you want teachers to teach, let them
teach. Before you criticize their methods, why not learn them. Or you
can come here and whine.

>>>> It is not a subject that is trivial for the lay person. Try
>>>> sometime reading some of the material teachers have to master.
>>>
>>> I'm hardly a lay person...
>>>
>>> (1) I got 800 in Math on the SAT's. What did you get?
>>
>> You sound like Larkin now. But this has *nothing* to do with teaching.
>
> It simply means I can run circles around you in math :-)

HA. That just shows you poor you are at logic which is part of math.
So you are wrong.

>>> (2) I attended M.I.T. on a FULL Alumni Fund National Scholarship back
>>> when scholarships were awarded on the basis of competency, not on
>>> need... my parents were wealthy by the standards of the '50's.
>>
>> Again, *nothing* to do with teaching.
>
> You said I was a "lay person". Clearly I'm not.
>
>>
>>
>>> (3) I graduated in Course 6-B, the HONORS Electrical Engineering
>>> Program.
>>
>> *Nothing* to do with teaching.
>
> You said I was a "lay person". Clearly I'm not.

Look, you are being silly. You know nothing about teaching. You are
not willing to learn about teaching. So why are you actively
criticizing teachers who do know? Oh right, you are a *math* wiz, so
you must know more than everyone else including the subjects you never
studied.

>>> (4) And, though not worth all that much, an MSEE from ASU (*)
>>
>> So you acknowledge that you have learned *nothing* about teaching?!
>
> I have (very successfully) taught seminars in Integrated Circuit
> Design for more years than you probably are old.

But you still know nothing about teaching grade school. Do you really
thing they are the same?

>>> Teachers may be competent, but they're bound to parrot the line
>>> established by the school boards and the administrators. Thus we have
>>> children expelled for wearing NRA T-shirts, pointing with their
>>> fingers, etc.
>>
>> Unlike you, teachers are all educated in *teaching* and are accredited
>> in teaching. What are your qualifications again? Oh yeah, your
>> qualifications are all in being *taught* by *teacher*.
>
> Teaching is a union. I offered to teach a technician-level course at
> Scottsdale Community College for FREE (the course had been dropped
> because they had no instructor). I was denied because I didn't have a
> "teacher's certificate". Teaching is a union that must be busted.

There's your problem. You know nothing about teaching school and you
think those who do know are just union drones. Get out and learn
something about the subject at hand.

>>>>> No wonder US students rank so low, worldwide, in math (and science).
>>>>
>>>> Or maybe its because we just don't value engineers, etc. as highly as
>>>> other occupations, so students aren't interested as much in those subjects?
>>>
>>> Our society has created a life-style based on texting, tweeting, and
>>> sucking off the tit of the government.
>>
>> I think you must be many decades older than myself. You sound like a
>> grandparent... no you sound like *all* grandparents through history.
>
> I can kick your ass in math or circuit design any day of the year,
> grandparent or not.

Yes, very Larkinesque.

>>> The sooner the revolution the better.
>>>
>>> (*) My first week at ASU, I was thrown out of a Physics class for
>>> asking the Prof, "When do you plan to start teaching this course on a
>>> college level".
>>
>> Yes, and your level of disrespect for others continues. You don't get
>> that your critera for others is of no interest to the rest of the world.
>>
>>
>>> After some "conversation" with the Dean, I got full credit for that
>>> course and several others offered at ASU. Finally found some
>>> non-linear control system courses that were useful ;-)
>>
>> So you have a huge ego. That doesn't mean you ar equalified to judge
>> teachers.
>
> Wrong! I am qualified because I have a huge math, science and
> engineering background... because M.I.T. teaches undergrad to a level
> exceeding what most universities offer as graduate level courses. (And
> the ASU Physics level was just plain JUVENILE.)
>
> Rickman, I have authorized your graduation to the rank of butt-buddy.
> Bye>:-}

Yes, you are quite the logician and debating expert too. How about you
stick to the subjects you know something about or at least have an open
mind about learning something new?

--

Rick

[Ivan Shmakov]

>>>>> George Herold <ghe...@teachspin.com> writes:

>>>>> On May 20, 3:48 pm, Jim Thompson wrote:
>>>>> On Mon, 20 May 2013 12:45:06 -0700 (PDT), George Herold

[...]

>>> So just picking Pythagorean triples (a,b,c) 3,4,5; A=1 and B=7
>>> works (as Jasen said.) Then for 5,12,13; A=7 and B=17 works. But
>>> that's the end of the line for simple triples that I know.

>> Maybe I'm missing the obvious, but I see no closed-form solution as
>> soon as you say "integer"... you have to guess.

> Well look at my two solutions, and your math brain should be able to
> see the connection... and then the general solution is 'obvious'.

A wonderful one, indeed!

> (Of course it's obvious only in hind sight.)

Agreed.

Not by any means an unusual "construct," yet well hidden.

--
FSF associate member #7257

[Jim Thompson]

Me too. Gaaaack!

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |

| E-mail Icon at http://www.analog-innovations.com | 1962 |

[Ivan Shmakov]

>>>>> rickman <gnu...@gmail.com> writes:
>>>>> On 5/19/2013 1:39 PM, Jim Thompson wrote:
>>>>> On Sun, 19 May 2013 13:03:05 -0400, rickman<gnu...@gmail.com> wrote:

[Dropping news:alt.binaries.schematics.electronic from
Newsgroups:.]

[...]

>>> Unlike you, teachers are all educated in *teaching* and are
>>> accredited in teaching. What are your qualifications again? Oh
>>> yeah, your qualifications are all in being *taught* by *teacher*.

>> Teaching is a union. I offered to teach a technician-level course
>> at Scottsdale Community College for FREE (the course had been
>> dropped because they had no instructor). I was denied because I
>> didn't have a "teacher's certificate". Teaching is a union that
>> must be busted.

> There's your problem. You know nothing about teaching school and you
> think those who do know are just union drones. Get out and learn
> something about the subject at hand.

Frankly, my opinion is that one who aspires to teach math,
should learn /math/, not teaching; be it university, high
school, primary school, or something else. Similarly, for one
aiming to program a spacecraft, there's much more to know about
spaceflight, than about programming per se.

And yes, I've taken courses on (university's) teaching, even
though I've never managed to get my certificate. And, I can ask
a family member on the matter; he's got his, in school teaching.

[...]

[Cydrome Leader]

In sci.electronics.basics Jim Thompson <To-Email-Use-Th...@on-my-web-site.com> wrote:
> On Fri, 17 May 2013 14:59:47 -0400, rickman <gnu...@gmail.com> wrote:
>

> [snip]
>>
>>Why is this a political issue? Teachers are highly educated in...
>>teaching. It is not a subject that is trivial for the lay person. Try

>>sometime reading some of the material teachers have to master.
>>

> [snip]
>
> Forgot an important issue...
>
> In Germany it is ILLEGAL to home-school your children.
>
> A German couple with two children requested asylum in the USA based on
> that German restriction of freedom.
>
> The Obama regime just refused their request for asylum.
>
> Wonder how long it will be before it is illegal to home-school in the
> USA?

well, homeschooled kids in the US tend to give off really broken vibes.
There's something weird about it most of the time.

[Bob Penoyer]

On Mon, 20 May 2013 17:24:40 -0400, rickman <gnu...@gmail.com> wrote:

>>>>> On 5/17/2013 2:40 PM, Jim Thompson wrote:
>>>>>> I'm fighting the school system with, now, the 5th granddaughter, 6th
>>>>>> Grade.
>>>>>>
>>>>>> Last week they were peddling how to cut corners out of a piece of
>>>>>> cardboard to form a box with the maximum volume, with no established
>>>>>> skill set.... "guess" your way to the solution :-(

<snip>

>>>>>> This week they suddenly jumped to Algebra, simultaneous equations,
>>>>>> without even any single variable background.
>>>>>
>>>>> There may be more to this than you are getting second hand from a 12
>>>>> year old.
>>>>
>>>> No second hand about it. This is the modern era. Though she's in
>>>> Palm Springs, Californica, she PDF'd her homework sheet. I have it
>>>> right here in front of me.
>>>
>>> Oh, you are in the classroom watching it all first hand?

<snip>

I've followed this thread for a while and I'm struck by your strident
support for teachers and teaching.

You seem to suggest that we mere mortals can't understand teaching
despite being educated in grade school, high school, college, and
graduate school. And, despite having children and grandchildren go
through the same process.

Consider these facts about teaching and teachers:

* As a group, teaching majors have the lowest SAT scores

* Schools of education are regarded as the dregs of universities'
schools

* If it required special training to teach, why is it that a
5-year-old can teach a 3-year-old how to do something?

* University professors--people who teach--aren't required to have
teacher training or teaching credentials

* Teaching majors learn such things as teaching methods, teaching
tools, etc. The one thing they don't learn--specifically, elementary
school teachers--is something to teach; they are no better educated in
basic subjects than they were when they left high school.

When I was in elementary school, several teachers told our classes,
for example, that "I was never very good at math," or "I was never
very good at spelling." But they taught those subjects nevertheless.

Public schools are worse now than they were 50 years ago, and they
continue to get worse.

When I was in grade school, we had smart kids and we had dumb kids,
but ALL could read. That's not true today, even for high school kids.

Your vaunted teachers have failed us. Jim Thompson's examples of how
his granddaughter was given a problem for which she was not equipped,
and the teacher jumping into simultaneous equations with no prior
preparation in single-variable algebra are only two examples. The
examples of misguided teachers and teaching methods are endless.

[T]

In article <tdvkp8tforcepg4o4...@4ax.com>, To-Email-Use-
The-Enve...@On-My-Web-Site.com says...

> >But that?s the end of the line for simple triples that I know.

>
> Maybe I'm missing the obvious, but I see no closed-form solution as
> soon as you say "integer"... you have to guess.
>
> ...Jim Thompson

The best advice I can give - study basics of algebra (solving for x) and
then maybe polynomial functions.

Then learn a computer programming language. You'll use some of the
algebra you used.

And in addition learn number systems to base x. Binary and Hexadecimal
for starters.

[T]

In article <80tlp8do3m6s968bk...@4ax.com>,
b...@NOSPAMbobpenoyer.com says...

> >Yes, you are quite the logician and debating expert too. How about you
> >stick to the subjects you know something about or at least have an open
> >mind about learning something new?
>
> I've followed this thread for a while and I'm struck by your strident
> support for teachers and teaching.
>
> You seem to suggest that we mere mortals can't understand teaching
> despite being educated in grade school, high school, college, and
> graduate school. And, despite having children and grandchildren go
> through the same process.
>
> Consider these facts about teaching and teachers:
>
> * As a group, teaching majors have the lowest SAT scores
>
> * Schools of education are regarded as the dregs of universities'
> schools

I've met a number of teachers - some of whom shouldn't even be in the
classroom. One of the more eye opening things I ever did was do program
reviews in area public high schools.

One of the classes was teaching the kids how do use the MS Office suite.
The day we were reviewing they were doing a payroll spreadsheet and I
noted they all had a cheat sheet for the tax on earnings.

I asked the teacher if they intended to teach the kids how to use VBA.
With VBA you could just write code to get it to calculate the tax.

The teachers response was that you needed advanced math to be able to
program a computer.

So on my review notes I said that the most math you might need is the
first few weeks of Algebra I. Apparently this caused great consternation
in the school. Good - anything that rocks them out of their little
comfort zone is a good thing.

Of course it also serves as a lesson, never invite an I.T. type to do
program reviews.

[Jasen Betts]

On 2013-05-20, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
> On 20/05/2013 10:49, Jasen Betts wrote:
>> On 2013-05-20, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
>>> On 19/05/2013 22:09, Tom Del Rosso wrote:
>>
>>> The algebraic solution is in the form
>>>
>>> A = F(a,b)
>>> B = G(a,b)
>>>
>>> Where A,B,a,b are all integers with some of them non-zero.
>>> In the general case they are all non-zero.
>>> Your task is to find the functions F(), G().
>>
>> functions?
>>
>> F(a,b) = sqrt(a^2+b^2)
>> G=F
>>
>> that seems way too easy
>
> sqrt(a^2+b^2) isn't an integer except in a handful of special cases.

hey! stop changing the rules!

>>>>>> Martin Brown wrote:
>>>>>>>
>>>>>>> given a^2 + b^2 = c^2 where a,b,c are integers
>>>>>>>

[Martin Brown]

On 21/05/2013 09:11, Jasen Betts wrote:
> On 2013-05-20, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
>> On 20/05/2013 10:49, Jasen Betts wrote:
>>> On 2013-05-20, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
>>>> On 19/05/2013 22:09, Tom Del Rosso wrote:
>>>
>>>> The algebraic solution is in the form
>>>>
>>>> A = F(a,b)
>>>> B = G(a,b)
>>>>
>>>> Where A,B,a,b are all integers with some of them non-zero.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

>>>> In the general case they are all non-zero.
>>>> Your task is to find the functions F(), G().
>>>
>>> functions?
>>>
>>> F(a,b) = sqrt(a^2+b^2)
>>> G=F
>>>
>>> that seems way too easy
>>
>> sqrt(a^2+b^2) isn't an integer except in a handful of special cases.
>
> hey! stop changing the rules!

I didn't change the rules. Though I left the question open at first.

>
>>>>>>> Martin Brown wrote:
>>>>>>>>
>>>>>>>> given a^2 + b^2 = c^2 where a,b,c are integers
>>>>>>>>

I am actually not going to post the answer here and would ask that
anyone who does work it out do likewise. It is obvious once you see it.

I thought by now this one would be too well known but apparently not.
Google doesn't find a suitable crib for this one.

--
Regards,
Martin Brown

[Jasen Betts]

a-b , a+b satisfies those two sets of results

but c,c satisfies them too, and can trivially be proven correct,
and if a function is all that's required why make more effort?

> Maybe I'm missing the obvious, but I see no closed-form solution as
> soon as you say "integer"... you have to guess.

my (and possibly your) conjecture is

(a+b)² + (a-b)² = 2c²

multipying out the parenteses

a²+2ab+b² + a²-2ab+b² = 2c²

combining like terms

2a² + 2b² = 2c²

dividing by constant 2

a² + b² = c²

which was given at the start.
looks it's a correct conjecture.

[Jasen Betts]

On 2013-05-21, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
> On 21/05/2013 09:11, Jasen Betts wrote:
>> On 2013-05-20, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
>>> On 20/05/2013 10:49, Jasen Betts wrote:
>>>> On 2013-05-20, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
>>>>> On 19/05/2013 22:09, Tom Del Rosso wrote:
>>>>
>>>>> The algebraic solution is in the form
>>>>>
>>>>> A = F(a,b)
>>>>> B = G(a,b)
>>>>>
>>>>> Where A,B,a,b are all integers with some of them non-zero.
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>>>>> In the general case they are all non-zero.
>>>>> Your task is to find the functions F(), G().
>>>>
>>>> functions?
>>>>
>>>> F(a,b) = sqrt(a^2+b^2)
>>>> G=F
>>>>
>>>> that seems way too easy
>>>
>>> sqrt(a^2+b^2) isn't an integer except in a handful of special cases.
>>
>> hey! stop changing the rules!
>
> I didn't change the rules. Though I left the question open at first.

you said sqrt(a^2+b^2) AKA "c" was an integer in your first
post:

>>>>>>>> Martin Brown wrote:
>>>>>>>>>
>>>>>>>>> given a^2 + b^2 = c^2 where a,b,c are integers
>>>>>>>>>

What was c^2 for? is it an attempt at misdirection?
the problem with that is it makes finding a valid answer easier.

> I am actually not going to post the answer here and would ask that
> anyone who does work it out do likewise. It is obvious once you see it.

the pattern is obviuos, I had to derive 2a^2 + 2b^2 before I believed it.
I posted it before I read this.

[Martin Brown]

On 21/05/2013 11:37, Jasen Betts wrote:
> On 2013-05-21, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
>>
> What was c^2 for? is it an attempt at misdirection?
> the problem with that is it makes finding a valid answer easier.

No. Me misremembering an old maths interview algebra puzzle.

On reflection. It almost certainly was = c and = 2c.

>> I am actually not going to post the answer here and would ask that
>> anyone who does work it out do likewise. It is obvious once you see it.
>
> the pattern is obviuos, I had to derive 2a^2 + 2b^2 before I believed it.
> I posted it before I read this.

I guessed that. Please don't put it onto Wiki though.

--
Regards,
Martin Brown

[ABLE1]

"Bob Penoyer" <b...@NOSPAMbobpenoyer.com> wrote in message
news:80tlp8do3m6s968bk...@4ax.com...

I too have been following this thread. Some of the comment have put a smile
on my face. I have been working in and around schools and teachers for many
years. I even had a few opportunities to actually teach the teaching staff
in some local elementary schools a few years back how to use their newly
installed alarm system. The results of those classes proved that my efforts
fell on deaf ears since most did not learn much of anything with all the
problems that happened after. Either I am not a good teacher or the
students were not good learners. :-)

On a different circumstance I was asked to repair a classroom phone that was
not ringing in Room 224 at a particular elementary school. Upon arrival I
checked in at the office and said I was going up to Rm 224 to take a look.
Entered the room and the teacher was at her desk on the other side of the
room. I identified myself and said why I was there. She started into a
rant about the phone not working for over 2 weeks bla bla bla.. I explained
that I just received the work order a couple of hours
before........................... I looked at the phone and flipped up the
lever that was marked "ringer on/\ - ringer off \/" I called the office and
asked them to call Rm 224. Of course the phone rang and the teacher jumped
out of her chair. "WHAT did you do??" She asked. I motioned for her to
come over to the phone and pointed to the lever and said; "This was in the
OFF position" She said; "Is THAT what THAT is for??" I sent the school
district a invoice for an hour of my time.

The point of these little stories................. from my point of view
teachers that are in the teaching field are only as good as their desires.
Most do not have common sense. Some are better than others. All will
defend what they do, some are right and some are not. And lastly, it is a
proven fact that 50% of all certified teachers graduated in the bottom half
of their class.

Have a nice day. I will now retreat to my lurking position.

Les

[Charlie E.]

On Mon, 20 May 2013 21:25:28 -0700, Bob Penoyer
<b...@NOSPAMbobpenoyer.com> wrote:
<snip>

>Your vaunted teachers have failed us. Jim Thompson's examples of how
>his granddaughter was given a problem for which she was not equipped,
>and the teacher jumping into simultaneous equations with no prior
>preparation in single-variable algebra are only two examples. The
>examples of misguided teachers and teaching methods are endless.

Exactly! It was on the 'approved' syllabus, so that is how it MUST be
taught! Since the teacher doesn' really know what it means, anyway,
it must be right!

Or, she could be the opposite problem, the teacher is a wiz at math,
who just 'does' it, and never really thought about the process
involved. I had one teacher in grad school like that. For him, it
was just obvious and he couldn't understand that his explanation made
absolutely non sense!

Charlie

[Jim Thompson]

On Tue, 21 May 2013 10:26:26 +0100, Martin Brown

<|||newspam|||@nezumi.demon.co.uk> wrote:

>On 21/05/2013 09:11, Jasen Betts wrote:
>> On 2013-05-20, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
>>> On 20/05/2013 10:49, Jasen Betts wrote:
>>>> On 2013-05-20, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:
>>>>> On 19/05/2013 22:09, Tom Del Rosso wrote:
>>>>
>>>>> The algebraic solution is in the form
>>>>>
>>>>> A = F(a,b)
>>>>> B = G(a,b)
>>>>>
>>>>> Where A,B,a,b are all integers with some of them non-zero.
>^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>>>>> In the general case they are all non-zero.
>>>>> Your task is to find the functions F(), G().
>>>>
>>>> functions?
>>>>
>>>> F(a,b) = sqrt(a^2+b^2)
>>>> G=F
>>>>
>>>> that seems way too easy
>>>
>>> sqrt(a^2+b^2) isn't an integer except in a handful of special cases.
>>
>> hey! stop changing the rules!
>
>I didn't change the rules. Though I left the question open at first.
>>
>>>>>>>> Martin Brown wrote:
>>>>>>>>>
>>>>>>>>> given a^2 + b^2 = c^2 where a,b,c are integers
>>>>>>>>>
>
>I am actually not going to post the answer here and would ask that
>anyone who does work it out do likewise. It is obvious once you see it.
>

[snip]

But it falls into my category of "trick" questions. I finally figured
it out, but I frown on using such gimmicky problems with students.

[Jim Thompson]

On Tue, 21 May 2013 08:20:45 -0400, "ABLE1" <nospa...@nowhere.net>
wrote:

$1 for pushing the lever, $49 for knowing which lever to push, BTDT
>:-}

[Jim Thompson]

On Mon, 20 May 2013 21:25:28 -0700, Bob Penoyer
<b...@NOSPAMbobpenoyer.com> wrote:

>On Mon, 20 May 2013 17:24:40 -0400, rickman <gnu...@gmail.com> wrote:
>

[snip snarky rickman BS]

>
>I've followed this thread for a while and I'm struck by your strident
>support for teachers and teaching.
>
>You seem to suggest that we mere mortals can't understand teaching
>despite being educated in grade school, high school, college, and
>graduate school. And, despite having children and grandchildren go
>through the same process.
>
>Consider these facts about teaching and teachers:
>
>* As a group, teaching majors have the lowest SAT scores

As per the old saw, "Those that can, DO; those that can't, TEACH"

>
>* Schools of education are regarded as the dregs of universities'
>schools

Absolutely!

>
>* If it required special training to teach, why is it that a
>5-year-old can teach a 3-year-old how to do something?
>
>* University professors--people who teach--aren't required to have
>teacher training or teaching credentials
>
>* Teaching majors learn such things as teaching methods, teaching
>tools, etc. The one thing they don't learn--specifically, elementary
>school teachers--is something to teach; they are no better educated in
>basic subjects than they were when they left high school.
>
>When I was in elementary school, several teachers told our classes,
>for example, that "I was never very good at math," or "I was never
>very good at spelling." But they taught those subjects nevertheless.
>
>Public schools are worse now than they were 50 years ago, and they
>continue to get worse.
>
>When I was in grade school, we had smart kids and we had dumb kids,
>but ALL could read. That's not true today, even for high school kids.
>
>Your vaunted teachers have failed us. Jim Thompson's examples of how
>his granddaughter was given a problem for which she was not equipped,
>and the teacher jumping into simultaneous equations with no prior
>preparation in single-variable algebra are only two examples. The
>examples of misguided teachers and teaching methods are endless.

Indeed! Even worse, the system seems designed to destroy the family
unit and place that authority in the hands of the government. Observe
how many holidays and traditions have been effectively killed by the
"education" system. If your kid says "Christmas" in school he's
likely to be suspended. And the kids can't even celebrate Halloween.

Rickman labels me "Larkinesque". What a laugh!

Rickman is the one that is "Larkinesque", because he meets the full
specification:

Head fully up butt. Head turned 90-degrees to lock it in place.

Unfortunately I'd also guess that Rickman _is_ a teacher :-(

[Jim Thompson]

On Tue, 21 May 2013 07:16:36 -0700, Charlie E. <edmo...@ieee.org>
wrote:

Even had one of those at M.I.T., Gordon Brown... couldn't teach for
shit. Fortunately this was by the time I had been admitted to Honors
EE, so there were only six of us in the class, so we all marched in
unison to the Dean's office and had Brown replaced by Paul Penfield...
only a grad student at the time, but a real winner!

[Martin Brown]

On 21/05/2013 15:20, Jim Thompson wrote:
> On Tue, 21 May 2013 10:26:26 +0100, Martin Brown
> <|||newspam|||@nezumi.demon.co.uk> wrote:
>
>>>>>>>>> Martin Brown wrote:
>>>>>>>>>>
>>>>>>>>>> given a^2 + b^2 = c^2 where a,b,c are integers
>>>>>>>>>>
>>
>> I am actually not going to post the answer here and would ask that
>> anyone who does work it out do likewise. It is obvious once you see it.
>>
> [snip]
>
> But it falls into my category of "trick" questions. I finally figured
> it out, but I frown on using such gimmicky problems with students.
>
> ...Jim Thompson

I disagree. That one isn't a trick question at all. It is difficult to
find the solution under pressure in an interview but how someone goes
about trying is very informative as to their capabilities. You really
either see it pretty much instantly or you don't without playing around.

Anyone who could be a top grade mathematician is reckoned to get it.

If you want a trick question what is the next number in the series:

10, 11, 12, 13, 14, 20, 22, 31, ?

Unhelpful hint - it isn't 42.

--
Regards,
Martin Brown

[Mike Kaddaver]

"Jim Thompson" wrote in message
news:3qtcp8pqupgsueqs7...@4ax.com...

I'm fighting the school system with, now, the 5th granddaughter, 6th
Grade.

Last week they were peddling how to cut corners out of a piece of
cardboard to form a box with the maximum volume, with no established
skill set.... "guess" your way to the solution :-(

This week they suddenly jumped to Algebra, simultaneous equations,
without even any single variable background.

And she says her teacher is already using the word "Calculus". I
guess that's the leftist way anymore, speaking the words makes you
expert :-(

No wonder US students rank so low, worldwide, in math (and science).

Fortunately the school year is almost over, and she'll be with us for
a month in July.

So my question...

Can anyone recommend an available Algebra book that instructs in the
old fashioned sequential way... lots of one variable word problems
first, then go on to more advanced topics?

I'll become teacher of the month ;-)

(I taught math back in 1964-65 to disadvantaged youth (aka "thugs")
from South Phoenix with a very high success rate :-)

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

To solve a problem with more than two variables, or even with two variable
equations is easier with simultaneous equations. Once you learn how to do
it, you can solve problems that you could not before. You can also use a
matrix which simplifies solving the problem. I learned them in 1990 and
into college too.

[Jim Thompson]

Of course. The debate is not about HOW to solve such a problem but
whether such a problem belongs in 6th grade. There are numerous ways
to solve it... none of which comes from the typical skill set of a 6th
grader.