## Saturday, December 29, 2012

### Is This a Bad Volume Problem?

As I was shoveling all the snow that fell where I live recently, I wondered exactly how much snow I was shoveling. As my 7th graders are struggling with volumes right now it came to me that after a little practice with regular shapes I could ask them exactly how much snow I was shoveling.

To the left, my humble abode. I have no clue what the scale is here (does anyone know how to get that information from Google/Bing/MapQuest?), but I can measure it if I have to. What is hard to see from the picture is that my driveway is actually a trapezoid. The kids don't have a neat formula for volume of a trapezoid, so it might be interesting to see what they do with it.

But is this even a good question? I mean, *I* care how much snow I shoveled because I was sore afterward. But would my students even care? They might like seeing my house, I suppose. But that doesn't make it a good math problem.

I have several students who struggle with the basic shapes and formulas. But those shapes are so abstract. Who really cares about the volume of a triangular prism? I don't unless it's filled with Toblerone. Then I might care. But then I wonder if throwing in an actual object from reality might be too much for those kids. My more advanced kids might think this is totally obvious and lame.

What I like about my driveway is that I can give them the picture and make up a scale if I can't find it. Then, they have to use what they supposedly know about scales to get measurements. Then, since we've talked about you never really need to memorize a formula for a right prism because you can always come up with the answer, they CAN find the volume of my driveway snow. They'll think they can't, but they can.

Is the scale thing too much/too hard? Should I just give them the measurements?  Is this a really bad attempt at bringing in relevance? I really want them to THINK about volumes, not just learn how to use the formula from the state test reference sheet. What would be a better problem? I could add on to it by making the problem about the number of calories I burned while shoveling all that snow, since I'm sure there's an estimate rate for that sort of thing somewhere. I have to admit, given how sore I was, I'm curious about the number of calories I burned. But would the kids care?

Heck, I'm not even sure I can devote a whole period or more to this, though I'd like to. I'm off the departmental pace as it is and I'm the new kid so I don't want to make too many waves.

1. Hi Patti,

I'd be interested too in finding volume of a Toblerone if I can eat it afterward. You're right of course about asking kids to find volume when they can just look up the formula and plug in numbers.

That said, teaching volume was one of my favorite lessons last year with my 6th graders, and I shared them on my blog:

1. Volume of cylinder: http://fawnnguyen.com/2012/06/13/20120608.aspx

2. Surface area and volume of filing cabinet: http://fawnnguyen.com/2012/04/25/mr-stadels-file-cabinet-3act-lesson.aspx

3. These two really motivated them because they got to eat donuts here: http://fawnnguyen.com/2012/04/16/i-am-a-donut.aspx

... and they ate popcorn here: http://fawnnguyen.com/2012/05/19/20120518.aspx

2. Thank you so much for your comment! I left a comment on your first link, but these are super helpful. Luckily I have a week before the end of break to digest it all and come up with a plan such as yours. Amazing how food is such a good motivator, even if no one's getting those cupcakes you mentioned!