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Posts Tagged ‘Volume’

The trouble with prisms

April 18, 2015 14 comments

Wherever I see incorrect maths, it annoys me, whether it be in election material, newspapers or anywhere else. But the place where it annoys me most is the maths classroom. I don’t mean students getting the answers wrong, that’s an invaluable part of the learning experience. What I mean is when teachers get it wrong. This happens more than people would expect. I’ve written before about people teaching things wrong (ie rounding or the order of operations) but today is want to discuss a different annoyance.

Take a look at this:

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It’s from a resource I downloaded from the TES website. The resource itself was pretty good, but this was one of a number of questions that infuriated me. Have you noticed why? Take another look.

Yes, indeed. The right angled triangle that forms the cross section of this triangular prism is that well known Pythagorean Triple the “4,9,10” triangle. Never heard of it? Neither have I! That’s because  4^2=16, 9^2=81 and 10^2=100. And 16+81 is very definitely 97, which in turn is very definitely NOT 100. It’s not even as though it’s hard to generate triples!

This sort of thing is lazy, if it had been put in front of me, as a student I’d have called a teacher out on it. The first time I saw something like this was during a micro teaching assignment while on my PGCE. The person in that case was rusty! I’ve seen it a couple of times with trainees or NQTs during observations, again these can be excused.

I even realise that experienced teachers can make innocent mistakes, but please, please, please check these things. Especially for triangular prisms, as this is THE area that I see this happening again, and again and again.

Have you encountered something like this? Do you get as angry as me about it? Do you think it doesn’t matter and I’m being overly pedantic on this? Please let me know.

Similarity, and other stories

November 15, 2013 1 comment

Recently I have been looking into a variety of things. One thing is “Inquiry Maths” and another is something I found on the #matheme site through the explore the MTBoS project called “Notice and wonder”.

These got me thinking about how I could introduce some of their elements into some of my lessons. I had just introduced similarity to my year elevens and I was going to move to similar area and volume problems. So I came up with this starter:

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I put it on the board and gave them ten minutes (I think) and let them get their teeth into it. A few were a little confused at first, but the discussions on each table enabled all pupils to make their own way to the correct answer. I didn’t know what they would notice or wonder, but I was pleasantly surprised to hear some of their comments:

“I notice that the area has gone up by four, not two. Does that mean you double the scale factor for area?”

-I loved this one, and refused to answer it, instead I asked him to enlarge the shape sf3 and see if the area was enlarged by six. I then got:

“It’s nine, not six. Why’s it nine? Stupid thing. Oh hang in, it’s squared. Oh, of course it’s squared! you times each side by it [the scale factor] and you times them together! Duh!”

Others I particularly liked were:

“I wonder if there’s a way of doing Pythagoras on triangles without right angles” (I told her that we would be meeting the cosine rule soon enough).

“the angles are the same! Wait, that’s how this SOHCAHTOA thing works isn’t it, cos it’s ratios an that.” (I said “very good, but can we use the proper name please!” then another pupil interjected with “Trigonometry”)

The lesson goes on to pose question prompts similar to those I’ve seen on inquiry maths in which we discussed similar volume and then I included a set of questions for then to attempt. I have uploaded the resource to TES:
http://www.tes.co.uk/teaching-resource/Similarity-and-other-stories-6374388/

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