Hey guys - I have a question about a problem I gave on a recent Algebra test and wondering if anyone can fill me in on the (probably obvious) reason why this won't work. Question: Evaluate V=1/3lwh for l=12in., w=6in., and h=10ft. When making the key, I solved it this way: I changed the height to 120 inches, so I'm multiplying by the same term in inches. So I had 1/3(12)(6)(120). I took 1/3 of 12, which is 4, so my new problem was (4)(6)(120) which equals 2880 inches cubed. I then divided that by 12 to get feet and ended up with 240 ft. cubed. Is this correct? It's cubed, so I shouldn't have divided by 12, right? I had a student answer 5/3 on the test and she claimed she was correct because this is what she did: She changed all the terms to feet. So 1/3(1)(.5)(10) = 5/3ft. cubed. Logically, when I look at it, her answer seems more correct, but I can't figure out why both ways didn't yield the same answer. I know I should know this, but there's so many other things going on in my head right now and I can't seem to figure it out. Help!!
Okay, you calculated 2880 cubic inches. That is correct. To convert from cubic inches to cubic feet, you have to divide by 12 cubed, or 1728 (you just divided by 12; that was your error). (There are 1728 cubic inches in a cubic foot). When you divide 2880 cubic inches by 1728, you get 5/3 cubic feet, which is what your student got as well.
Thank you so much robinsky! I had a feeling it had something to do with dividing by 12 that threw me off. I try to keep these brain farts to a minimum in front of the kids, but every once in a while...
No one is perfect not even teachers. I always tell the kids it has been a while since I had so so grade and so and so subject. I may have to look back to jog my brain a sec. Good thing I sub Elementary. It would kinda hard to tell Highschoolers that is has been a while(its only been 2 yrs lol). I am in college now so I am still learning haha. Glad someone was able to help you out there.
I make plenty of mistakes as I'm working at the board. Kids never want to own up to their mistakes, so I try to model it. We all have our oops moments!
I always give out extra points towards whatever goal they're working on if they can catch my mistakes. Don't worry about it...we're all human. I had a major brain fart moment tonight at the college. I made a REALLY stupid simple mistake in computing standard deviation and couldn't find my mistake....My master's degree is in Mathematical statistics and probability theory
