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/
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