Geometry Perimeter and Volume

What is going on in these volume calculations?

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I’m stumped. Ideas?

6 replies on “What is going on in these volume calculations?”

Well, for the first one I added the three side lengths, doubled the result, and subtracted the unit volume, as I knew it involved volume.
The second one I couldn’t get anywhere with!
Seriously, though, the marking scheme should go like this:
Max 3
less 2 for not showing any working
less 2 for getting the wrong numerical answer
less 1 for not getting the units right
Total score -2

I suspect that the author never played with blocks in K-2

My guess is perimeter of base, plus height. Where they may have made different choices of which side should be the height… sometimes reusing one of the sides of the base, oops. Hm. 2*(7+4) + 4 seems right for the second one, and the units are even correct for that. 2*(6+5) + 3 would make sense but that’s only 25 feet, not 27. Still, seems like a reasonable idea of what the student was trying to do? Maybe?

This is sort of similar to the “length plus girth” measurement that shipping companies use to figure out whether your box is “large” and has to pay more, right? Except there the length is always the longest side and the girth is the perimeter perpendicular to that. I think.

Best guess… student attempted to find the perimeter of the shaded areas and made computational errors each time.

Hmm, how long before this was area and perimeter taught? Were other 3D volumes taught at the same time? Was the ‘prism’ concept only introduced through paper or through 3D models, as well? Were students taught via equations or taught by building up ‘unit block’ concept?

Having said that, my first thought about the second shape (7x4x4) was that the equation ‘half of base times height’. Then, either the shape looks ‘flat’ enough that the base is just the width (7+4) or the simply forgot that ‘base’ in this case means width ‘times’ length rather than ‘plus’.

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