Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Common Core snippet a little distressing
Replies: 73   Last Post: Jul 26, 2013 6:27 PM

 Messages: [ Previous | Next ]
 kirby urner Posts: 3,690 Registered: 11/29/05
Re: Common Core snippet a little distressing
Posted: Jul 15, 2013 9:55 AM
 att1.html (2.8 K)

On Sun, Jul 14, 2013 at 7:29 PM, Wayne Bishop <wbishop@calstatela.edu>wrote:

> My apologies, I thought you said something about equality because pouring
> liquids matched as opposed to mathematical verification of equality of the
> volumes.
>

Nothing opposed.

>
> Knee-jerk redneck bigoted academician that I am, would you at least agree
> that, at least historically, "cubing" has something to do with geometric
> cubes as in, say, the ancient problem of "duplicating a cube"? (I readily
> acknowledge that the word is used in its algebraic form in many other
> mathematical situations but we are talking about physical models.) Would
> you, for example, explain the idea of duplicating a cube using (as your
> primary model) a regular tetrahedron (where the impossibility is exactly
> the same) to your new generation of exceptionally creative and unblinded
> students?
>
> Wayne
>
>

I think you still misunderstand. I am not saying there's no connection
between 3rd powering and cubes or that this connection should be downplayed.

I'm saying that the tetrahedron may also be used as a model of 3rd powering
i.e. you have a dial you rotate clockwise / counter-clockwise to
boost-diminish the edge sizes of a tetrahedron from between 1 and 3. The
thing grows and shrinks from volume 1 to 27 and every value in between, and
its volume is precisely a 3rd power of the edge length. Why? Because we
*define* a unit edge tetrahedron to have volume 1. Can we do that? Yes.

Is there a reason to *never* show this in the classroom? I'm saying the
Common Core gives us an opportunity to brand curricula as not just
"aligned" but extending "well beyond".

Those parents and students who want something more than mere mediocrity
will find out about the unit volume tetrahedron whereas those sticking to
the standards will grow up with a mediocre math education more like that of
their parents.

As to how to duplicate a tetrahedron with a ruler and compass in 3D if
that's what's asked, it sounds doable, but not in a way I'd want to try
typing out in words here. Sounds like a CAD challenge of some kind.

Kirby

Date Subject Author
7/13/13 Peter Duveen
7/13/13 Robert Hansen
7/13/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/15/13 kirby urner
7/14/13 Wayne Bishop
7/14/13 kirby urner
7/14/13 Wayne Bishop
7/15/13 kirby urner
7/15/13 Robert Hansen
7/15/13 Christian Baune
7/15/13 kirby urner
7/16/13 Wayne Bishop
7/16/13 kirby urner
7/14/13 Wayne Bishop
7/14/13 Joe Niederberger
7/15/13 Joe Niederberger
7/15/13 Joe Niederberger
7/15/13 Robert Hansen
7/15/13 kirby urner
7/15/13 Robert Hansen
7/16/13 kirby urner
7/16/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/15/13 CCSSIMath
7/16/13 Joe Niederberger
7/16/13 Robert Hansen
7/16/13 kirby urner
7/17/13 Joe Niederberger
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 kirby urner
7/17/13 Robert Hansen
7/18/13 Wayne Bishop
7/17/13 Joe Niederberger
7/17/13 Joe Niederberger
7/17/13 Robert Hansen
7/18/13 Wayne Bishop
7/18/13 Joe Niederberger
7/18/13 kirby urner
7/18/13 Joe Niederberger
7/20/13 kirby urner
7/19/13 Joe Niederberger
7/19/13 kirby urner
7/19/13 Joe Niederberger
7/19/13 Joe Niederberger
7/20/13 kirby urner
7/21/13 Joe Niederberger
7/23/13 kirby urner
7/24/13 frank zubek
7/24/13 frank zubek
7/24/13 kirby urner
7/25/13 frank zubek
7/25/13 kirby urner
7/25/13 frank zubek
7/25/13 frank zubek
7/25/13 frank zubek
7/26/13 frank zubek
7/26/13 frank zubek