Like everyone else, I've tried various ways to dispel this rumor: we've drawn models, we've used models, we've discussed. Seemingly to no avail. This year, I tried yet again with a different tactic.
We started out with a rectangular prism 3' x 2' x 4'. They found the volume in feet cubed. Then I asked them to find the volume in inches cubed, and to a person, they all wrote the wrong answer (24 x 12 = 288). Then without saying they were wrong I had them go back and redraw the prism into the inches equivalent and recalculate the volume, and OH NO, they were wrong with their first "288". Hmmmmm. So, this is stuff I've tried before. Now for the "new" attempt that MAYBE will work.
I had them write: 5 ft^3
Then change to: 5 * ft * ft * ft
Then EACH foot had to be converted to inches, so
= 5 *
= 5 * 12in * 12in * 12in
= 8640 in*in*in
= 8640 in^3
Let's see if this one sticks.
Good idea--let us know how it works!
ReplyDeleteThe linguist in me (yeah, I double majored in math and linguistics) discourages me from saying "feet cubed" in favor of "cubic feet" since in English the adjective comes before the noun...
ReplyDelete...but I will say that what you are doing is maybe the most easily understood way (that I've seen) of converting square or cubic feet.
I bet it'll work well.
Here's an idea I just had while reading your post.
ReplyDeleteGet a bunch of 1 inch connect blocks (forget what they are called) and have them start working in groups to create cubic feet from the cubic inch blocks. It will take some time, and a significant number of blocks, but hopefully after a few minutes of trying to get their 288 blocks to make a gigantic 2' by 3' by 4' block they may see the error in their logic (and remember the experience).
Thanks for all your comments. I'm not going to hold my breath that this will be the elixir, but maybe it's just another way that will catch some kids up.
ReplyDeleteDavid, I think you have a great idea. I also think that when kids start working with things algebraically, they go to "half brain" and don't reason things out.
We'll see what happens....
oh i love that idea! i'm always looking for ways to employ units to make math make more sense and that's a really nice one.
ReplyDeleteI am a new math teacher this year, and I too tried this method. I would have thought the visual model would have worked. We started, of course, with two dimensions which is always much easier to draw. I can only hope it will stick. I'm glad I have found your blog!!!
ReplyDelete