Home > Maths, Teaching > The trouble with prisms

## The trouble with prisms

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:

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.

Categories: Maths, Teaching
1. April 18, 2015 at 1:15 pm

Is it possible that that is NOT a RIGHT-angle prism… all the proportions are clearly way off, so unless it’s stated somewhere that it’s right angle perhaps it can’t be assumed? (tryin’ to give ’em some wiggle room 😉

• April 18, 2015 at 1:21 pm

A few folk have mentioned this possibility and i should have explained further in the post that unfortunately the rest of the slide had the solution worked through as an example and the area was found by (4×9)/2, implying that the intention of the author was for the triangle to be right angled. Its also aimed at pupils who wouldn’t have any other way to calculate tge area of a triangle!

• April 19, 2015 at 7:55 am

A few folk have mentioned this possibility and i should have explained further in the post that unfortunately the rest of the slide had the solution worked through as an example and the area was found by (4×9)/2, implying that the intention of the author was for the triangle to be right angled. Its also aimed at pupils who wouldn’t have any other way to calculate the area of a triangle!

2. April 19, 2015 at 12:33 am

Although I am with you on “keeping it real”, you could technically argue that it is correct when rounding all measurements to the nearest mm. The square root of 97 is 9.85 rounded to the nearest 100th. Clearly not 10 but pretty close. And I am not sure about you but if I was given this prism and asked to measure its dimensions with a standard ruler, I would probably measure that to be 10 mm. So unless the question explicitly said it was a Pythagorean Triple, then I think this is not the end of the world.

• April 19, 2015 at 8:02 am

Aye, i suppose that’s true. Although this is a maths classroom and we like to be precise!

3. April 21, 2015 at 11:51 am

Election results don’t include legitimate math…

4. May 2, 2015 at 12:52 pm

I agree in general. Yes, in this particular example I would probably justify it by saying these were rounded measurements, but time and again I find questions that have not been well thought out. A scale factors question that gives a plane with a 300m wingspan is a recent one, or a ring with a density of 2000g/cm^3. When I emphasize the value of checking answers are sensible, it really helps when they are. Do your homework, teachers! With Google at your fingertips there’s no excuse for not using the correct thickness of a £20 note (0.133mm) or the distance from Cardiff to Edinburgh (not 200 miles).

5. May 19, 2015 at 11:45 am

Awful.

6. December 19, 2015 at 12:42 pm

I understand your point but is all in all honesty it does not state it is a right angle triangle cross section in the picture (can’t see the words). I’m sure that this is not supposed to be solved using the cosine rule to find the obtuse angle and then 1/2absinC for ks3 students but it could used as a nice extension for a top set y11. How do you know this was not the intent. I feel your criticism is a little arrogant.

• December 19, 2015 at 1:44 pm

The solution on the resource used 4mm as the base and 9mm for the height. This can only be the case if it is a right angled triangle and I feel that makes the criticism perfectly valid.

7. April 18, 2016 at 10:07 pm

You’d love a resource I wrote to use when I teach Pythagoras’ Theorem – basically “real or fake?”.

20 triangles – each with a right angle marked and 3 side lengths noted but “not drawn to scale”.

And that’s all the info they are given.

• April 18, 2016 at 10:16 pm

Sounds great, you’ll have to share! I have a similar resource but it’s less inventively titled “are these triangles right angled”..

8. April 19, 2016 at 3:24 am

If one insists that this is a right prism but not that the triangle is necessarily right, then the volume of the prism is determined — it is 180 x area of 4-9-10 triangle (use cosine law or Heron’s formula). But the obvious intent of the stated problem is a … er … problem as you explain

1. May 17, 2015 at 5:00 pm