The Mathematics Thread

[anat0l]

THREE minutes! Jeez, what were you doing for the remaining 2:55? Trivial maths.

Well, my naive approach produced the answer in a few seconds, but I didn't know if it was correct.

Thinking up how to do it another way took a bit longer.

Clearly if it is so trivial, then it may be surprising why many year 12 students would find it hard, and moreover what the hell is this random question doing in a write up in the local rag? Must be slow news day at the newspaper office.


The question from the UK exam about the probability in a quadratic proof is more difficult than this. So is the logic based question about the girl's birthday in the Singaporean exam.

 

[whatmeworry]

I don't see why they are complaining. I've had more difficult questions than that in my senior exams. Perhaps this is a story that's a bit out of control or context. I mean, kids will find questions that they can't answer, then share them on Facebook. When I was their age, we usually shared them by word of mouth. Sometimes we'd have really tough questions that many people couldn't solve; the handful that could, well, naturally they scooped up the A or A+ grades.

But that is the purpose of exams - not only do they assess skill, but they should also be discriminating, clearly able to distinguish who should get an A and who should get a C. An exam might be marked way too tough if the percentage of those who get an A is very, very low, but I don't think it has happened too often yet. Sometimes the grade boundaries get relaxed anyway, sometimes on the insistence of a few problem parents (or those with backdoor connections and influence to members of the board of education).




Answer Spoiler!












At first, I assumed that if you joined the "base" of the triangle (the side opposite angle x) it would be an equilateral triangle, hence 60[SUP]o[/SUP]. However, I couldn't convince myself that that side would be the same length as the sides of the coin, even if the triangle is at least isosceles.

The longer method I did was similar to the second solution in the article. The internal angle of a dodecagon (12 sided regular polygon) is 150[SUP]o[/SUP]. (If you don't know how to find this, start with a corner of the polygon, draw a line joining that corner with another corner, then draw another line joining the first corner with another corner, and so on, until all corners are joined by a single line to a single corner. This forms a number of triangles - in the case of a 12-sided polygon, this makes 10 triangles. That means the sum of the angles in the polygon is 1800[SUP]o[/SUP], and divided by 12 gives 150[SUP]o[/SUP].)

Examining the point around x, we have two of the internal angles of the dodecagon, plus x, and all three of these must add up to 360[SUP]o[/SUP]. So the answer is 60[SUP]o[/SUP].

Yeah you over thought it.

 

[GarrettM]

Jeeze. I just looked at it and figured it was 60 degrees cause it looked about 60 degrees. But maths has never been my thing.

 

[moa999]

Jeeze. I just looked at it and figured it was 60 degrees cause it looked about 60 degrees. But maths has never been my thing.

Agree. Bit of common sense - looks like an equilateral triangle so if I'll guess that.
Prefer multi choice where the obvious guess isn't correct

 

[TheRealTMA]

Agree. Bit of common sense - looks like an equilateral triangle so if I'll guess that.
Prefer multi choice where the obvious guess isn't correct

Or you could treat it as the trivial mathematical problem it is and just solve it in a few seconds.

 

[JessicaTam]

Or you could treat it as the trivial mathematical problem it is and just solve it in a few seconds.

Yep. It took three sides to turn 90 degrees, so each change in angle was 30 degrees. So two of them at the top must be 60 degrees. Took longer to type.

 

[anat0l]

Jeeze. I just looked at it and figured it was 60 degrees cause it looked about 60 degrees. But maths has never been my thing.

Agree. Bit of common sense - looks like an equilateral triangle so if I'll guess that.
Prefer multi choice where the obvious guess isn't correct

Yep. It took three sides to turn 90 degrees, so each change in angle was 30 degrees. So two of them at the top must be 60 degrees. Took longer to type.

The irony is that the diagram is machine produced and accurate. If protractors were allowed in the VCE exam, you really could just measure the angle and get the answer correct, without any calculations.

I remember most of our problem diagrams in high school exams were hand drawn. I got "burned" one time when a diagram of a war memorial was drawn and we had to find the size of a particular angle. I found an answer based on the diagram being "correct" that it was an obtuse angle. Turns out I was wrong and the angle was acute. So I learned never to trust the diagram too much.

Didn't think of it like JessicaTam did, but that makes sense.

What would be interesting is if this exam question was not a multiple choice but rather full working had to be shown to prove the size of angle x. It'd certainly be a lot more work for those correcting the exams, but I personally think it is the only fair way to administer a maths or (analytical) science based exam.

 

[Deleted member]

I thought hard about this and decided the answer was $1.00.

 

[TheRealTMA]

Yep. It took three sides to turn 90 degrees, so each change in angle was 30 degrees. So two of them at the top must be 60 degrees. Took longer to type.

Once can consider it as a smoke and mirrors argument and ignore the dodecagon so it's a simple (tautology - can it be a complex?) isosceles triangle for 60 degree angles or the dodecagon is a 12 sided polygon so 360/12 with 150 degree inner angles hence the joining angle is 30 degrees x 2. YMMV!

 

[serfty]

Took me 45 seconds - 30 of that was wondering if a trick while rereading a couple of times.

Then I just divided 360 by 12 and multiplied by two.

Then used the answer table to convert to D)

 

[TheRealTMA]

Took me 45 seconds - 30 of that was wondering if a trick while rereading a couple of times.

Then I just divided 360 by 12 and multiplied by two.

Then used the answer table to convert to D)

A thought, maybe modern (English) high school students can't divide 360 by 12 in their heads so makes it much more difficult!

 

[JessicaTam]

This very question was discussed by Dr Karl on ABC Melbourne this evening. He felt it may be an attempt by the assessors to show that rote learning is not always the way to an answer. Sometimes we have to think.

 

[anat0l]

This very question was discussed by Dr Karl on ABC Melbourne this evening. He felt it may be an attempt by the assessors to show that rote learning is not always the way to an answer. Sometimes we have to think.

I don't see the rote learning element. Where is it?

If you mean kids trying to rote learn the types of questions out there, yeah, of course that's not going to work. It's inevitable that some questions will be repeated from year to year (even with numbers modified), but it's naive to think that all of them will, especially the more difficult ones. Unless the Victorian school board is that lazy.

So it took me longer to get the answer - but I did get it rather easily. Again, I don't see why it's made the rag - they could have chosen so many other tougher questions, or at least a selection of them.

 

[Deleted member]

Well , what I find more disturbing than this, is the day to day basic counting skills that are lacing . For example I had a dozen bottles of soda water in my shopping trolley. Advised checkout chick of said dozen and handed one for scanning. Was asked if a dozen =10? Unless I'm much mistaken , Eggs still (mostly) come in dozens.

 

[whatmeworry]

Well , what I find more disturbing than this, is the day to day basic counting skills that are lacing . For example I had a dozen bottles of soda water in my shopping trolley. Advised checkout chick of said dozen and handed one for scanning. Was asked if a dozen =10? Unless I'm much mistaken , Eggs still (mostly) come in dozens.

What about the decline of spelling?

 

[anat0l]

Well , what I find more disturbing than this, is the day to day basic counting skills that are lacing . For example I had a dozen bottles of soda water in my shopping trolley. Advised checkout chick of said dozen and handed one for scanning. Was asked if a dozen =10? Unless I'm much mistaken , Eggs still (mostly) come in dozens.

"Dozen" should still be commonplace these days, since eggs are still sold in dozens or half-dozens, mostly (where I am right now, you can buy eggs in sets of four, ten, fifteen, or loose one-by-one if you wish).

"Score" and "gross" I think can be safely retired from common knowledge.

 

[JessicaTam]

I don't see the rote learning element. Where is it?

If you mean kids trying to rote learn the types of questions out there, yeah, of course that's not going to work. It's inevitable that some questions will be repeated from year to year (even with numbers modified), but it's naive to think that all of them will, especially the more difficult ones. Unless the Victorian school board is that lazy.

So it took me longer to get the answer - but I did get it rather easily. Again, I don't see why it's made the rag - they could have chosen so many other tougher questions, or at least a selection of them.

His comment was with respect to thinking outside the square (or dodecagon), instead of following some standard process "because that was what they were taught".

 

[sinophile888]

Today, I picked up a new Year 8A Maths class for the rest of the year. A couple of students finished all the set work early and asked what they should do. So I gave them the 50 cent coins problem. One said “Well, the internal angle of polygon with 12 sides is 150[SUP]0 [/SUP]” and the other said “So that makes x equal to 60[SUP]0[/SUP] ".

 

[incumbent]

THREE minutes! Jeez, what were you doing for the remaining 2:55? Trivial maths.

I still want to hear the five-second solution.

 

[TheRealTMA]

I still want to hear the five-second solution.

See above.