Edge of a Cube Given Volume

Date: 10/06/97 at 22:49:59
From: Priscilla Neo
Subject: Volume

Hi Dr. Maths,

I am a teacher currently teaching volume to a class of Grade 5 pupils. 
I found that most of them do not know how to find the edge of a cube 
given the volume of the cube.

I understand that under the teacher's guide I am not supposed to 
teach them by the cube root method, but by recalling using the 
times table up to 1000 cubic unit.

Please advise me how I can conduct my lesson so that they will 
understand the basic concept well.

Thanks.

Date: 10/08/97 at 20:05:40
From: Doctor Tom
Subject: Re: Volume

Hi Priscilla,

I should first warn you that I'm not a fifth grade teacher - most
of my students have been at the high school or college level - so
take my suggestion with a grain of salt.

I've found that when I'm completely mystified about how to "undo" an 
operation, I first look at how to work it in the "other direction."

Presumably your kids could work the problem of finding the volume
of the cube if they knew the measure of an edge, right?  The trouble
here is that they're trying to work the opposite problem - given
the volume, find the edge.

I would point this out, and then say that since we're mystified, let's 
work the other problem for a few examples and see what's going on.

If the cube has side 2, the volume is 2x2x2 = 8. If the side is 3, the 
volume is 3x3x3 = 27. If the side is 4, the volume is 4x4x4, or 64. 
If the side is 1.5, the volume is 1.5x1.5x1.5.

After three or four examples, ask what the pattern is, and it's pretty 
obvious that you take the side and multiply three copies of it 
together to get the volume, WHATEVER the side may be.

So you're trying to find some number which, if three copies of it
are multiplied together, would give 1000.

This way you don't tell them "use the cube root"; rather, you let them 
see what kind of a number they're looking for. With 1000, it's 
probably pretty obvious that three 10s multiplied together give the
answer, but you might have a couple of trickier examples worked out
already that are not as easy to guess.

For example, what if the volume of the cube were 4913? They can then 
try answers, see which ones are too small or too large, and gradually 
zero in on the cube root of 4913 without even knowing what they're 
doing.

If you've got any really bright students, you can ask them to do the 
same sort of approximation thing for some cubes that don't come out 
even.

For example, if the volume is 12, what's the side?

Try 2:  2*2*2 = 8              too small
Try 3:  3*3*3 = 27             too big
Try 2.5:  2.5^3 = 15.625       too big
Try 2.3:  2.3^3 = 12.167       too big
Try 2.2:  2.2^3 = 10.648       too small
Try 2.27:  2.27^3 = 11.697     too small
Try 2.29:  2.29^3 = 12.0089    too big
Try 2.289:  2.289^3 = 11.9932  too small

and so on.  With a calculator, it isn't too hard to get 3 or 4
decimal places of accuracy.

Have a contest to see how close they can get to the answer using this 
method: roughly 2.2894284851.

Good luck.  I hope this helps.

-Doctor Tom,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/