Re: Bah!
@aggood
The internal angles of regular 2d shapes are (180 * (number of sides - 2))/number of sides
Apart from the fact that you have answered the wrong question...
http://www.telegraph.co.uk/education/11971692/Can-you-solve-the-50-cent-maths-exam-question-that-is-dividing-the-internet.html
This one 'broke my head' until I waved wet fingers at it. I believe 'rote' has been mentioned elsewhere but to my mind this is a matter of visualisation leading you to a solution which of itself is not necessarily a 'proof' but looks robust, cough. Perhaps I should really have committed all of this stuff permanently to my brane.
Let's say we are dealing with internal angles, IA, and consider a regular hexagon because dealing with 7 makes head division a bit hard.
You quote @gerdesj
"it's a flat septahedron so 360/7 degrees is the internal angle." - ??????
Why not call it a Septagon.? I thought Hedron referred to three dimensional shapes, could be wrong but there is this thing called a Dodecadildron,.. an interesting twelve faced shape with a tool at each corner, so your Flat Septahedron is a Septoganol Prism.
Apparently a Heptagon is a Septagon. Let's listen to a 'Maths Person' explain it. Top hit via You Tube,
https://www.youtube.com/watch?v=9pXgiyLvDzA
Note how he has to glance at the 'right numeric answer' before scribbling it on the board.
So... 'I'm Charlie Kasov. I'm a Math Teacher. Now you know the difference between a Septagon and a Heptagon'.
OK. Now I might have missed his point there but if I replay that one a number of times I might only conclude I have not been smoking the right drugs coz... 'No I fucking Do Not'.
In my case as a first stab, and I would be inclined to do exactly the same for the internal angle, would make the answer 360/6 or 60°.. at which point I might be happy, tick the required 'multi-guess' box and carry on. In this case it turns out to be the right answer using the wrong number of sides.
However if I had a picture of a hexagon in front of me I would have a 'wait what!?' moment and notice that the internal angles are certainly greater that 60° so have to think again. If I picked a regular dodecagon then my answer would be 360/12 or 30° and the angle has become more acute.
It would seem that my thinking is in some way upside down. The more sides I have the more acute the angle becomes with an apparent limit of a regular infinigon, aka a circle, with 360/∞ or 0° internal angles which would mean that my infinigon would, in some way, have to tend towards being a straight line.... or something like that.
That makes me wave another wet finger and think I should be taking another guess and subtracting my original guess from something else. So I wave more wet fingers and reach the conclusion that in some limit, as I tend to an infinigon, I end up with something to do with tangents which are straight lines and 180° should enter into my thoughts.
180 - 360/6 = 120°
or more generally for a regular polygon with n sides,
IA = 180 - 360/n <- Yay. Charlie!! n = 7 IA = 128.57°.. pity you had to look.
In your suggestion,
IA = (180 * (n - 2))/n
..... notice how my hand waving ends up with what I consider to be a simpler but equivalent expression to your own....
(180*(n - 2))/n = (180*n - 360)/n
(180*n - 360)/n = 180 - 360/n
Of course it would appear, as per the link offered above, that 'we' are answering the 'wrong question' and it would appear that Mr Chirgwin may have been trolling a bit tongue in cheek by not offering the original version.
However having worked out what the internal angle is we can, once again, guess by inspection/visualisation that the final answer for two coins butted against each other as shown that the final answer for the angle requested is...
AR = 360 - 2*IA
AR = 360 - 2*(180 - 360/n)
AR = 360 - (360 + 720/n)
AR = 720/n
Of course one of the major problems with 'multi-guess' is that you cannot really tell who knew the answer they learned as of rote, who understood why the rote answer was the right one or who when presented with a 'new' problem either took an initial guess and realising it was wrong went back and worked out what the right answer should be.
Then again if 'the student' were asked to give their reasoning, rather than ticking a box you might get closer to someone who can actually reason through a problem to find a solution, assuming they are not just regurgitating the reasoning offered to them. Even so you might almost feel confident that they understood the reasoning rather than just regurgitating the result....
Hmmmm...
https://www.youtube.com/watch?v=gY7BKdNxjeQ
No doubt I would be marked down for producing non-standard 'wiffle' however I would still maintain that answers without reasoning are worthless.
http://www.telegraph.co.uk/news/newstopics/howaboutthat/11960777/Why-555-doesnt-always-make-15-Maths-exam-question-divides-the-internet.html
"I would totally argue with the teacher over that for my child," commented one user.
However another replied: "This is a mark of a good teacher. If your question doesn't achieve the desired result then the question was the problem, not the answer."
I almost get the impression that they are dealing with Matrices here. Unsurprisingly Maths is a Language. I had a Geography question once...
"There are several countries somewhere that do Nom. Name them?"
I had no concept of the meaning of 'several' and could only remember two of what looked like the requested seven. It turns out there were three, that they told us about, so I got that one wrong even though I tried to argue, having found out what several might mean, two names should have qualified.
Oh Crap..
http://imgur.com/KtKNmXG
I might get the concept that 'the order' of a Matrix is important, this 'looks like' something beyond 'BODMAS and The Pit' but that looks like shite to me.
I assume this drivel is meant to be leading on to the concept of Matrices but if so then why not go the full banana and explain why such matters are going to be important 'later on' if not introducing the 'later on' in the same lessons.
"I would totally argue with the teacher over that for my child," commented one user.
However another replied: "This is a mark of a good teacher. If your question doesn't achieve the desired result then the question was the problem, not the answer."
Really? I might be inclined to read the teacher course notes, attend class and try to figure out where things may have gone wrong.... after poking my brain back up my nose because it dribbled out as a result of not being able to properly decipher the above comments....
Like WTF!1!
http://imgur.com/KtKNmXG
Math Formative:
3.OA.1: I can use multiplication strategies to help me multiply.
3.OA.3: I can use the structure of a word problem to help me solve it.
Looks like 'teachers instructions', as delivered by 'department of' to me. Perhaps 3.OA.2 was a 'special effort' from 'teacher'.
... and someone is complaining about the kids?
Biting the hand that feeds IT
