Is this maths right?

[Rummy]

Ahh, a maths teacher! Just what we need. Is BODMAS or its variations actually on the syllabus, and how much depth are you actually required to teach it in? Given that it is just, as you said, a way of remembering orders of operations, I wouldn't imagine it would need much detail given it's not actually maths, sort of. For me as I said before it was only covered for like 20 or 30 minutes in a lesson in year 9, and it seemed to have been mentioned by the teacher more in passing than as something we were supposed to be being taught.

[KingJoe]

I could dig out the national curriculum to answer this with 100% accuracy, but as far as I know the teaching of 'BODMAS' is not mandatory, you just need to know how to do calculations in the right order. BODMAS is the easiest to teach, but not necessarily the best. Depending on the kids, I'll usually teach BODMAS in year 7 to get them used to there being an accepted order of operations (even though we usually won't have looked at Indicies/Order/Of yet) I find it better to get kids to see each addition/subtraction as something which seperates terms, each bracket as a 'bubble' containing an answer (makes it easier when they are asked to expand things like 3(x+2) later on and they can't 'do the brackets first'), multplications as single terms (so that 3x3 is a single entity, 9, which makes algebra easier later on) etc.

 

Depending on the pupils (and it really does depend on them) I would think I have covered 'BODMAS' in enough depth if they can answer 3x4-7+8÷2^2=? and 15÷ (2+1) -3 =? correctly.

[Charlie]

2 - 5 + 10 * 20 = X

2 = X + 5 + 10 * 20

-3 = X + 10 * 20

-3 = X + 200

X = -203

 

 

Or did I do something wrong there?

[Gizmo]

My faith in humanity dropped reading this thread.

 

That there is even a debate over this saddens me deeply

[Supergrunch]

Subtraction is not addition, they are different. Strongly related but definately different (one is commutative and one isn't, for starters).

Yes indeed. We asked our maths teacher if there was a binary operator that was commutative but not associative. He came up with something that worked after a few seconds, something to do with a modulus. Can't remember it though...

 

Edit: Remembered it- |x+y|. Easier than I thought...

[Zell]

2 - 5 + 10 * 20 = X

2 = X + 5 + 10 * 20

-3 = X + 10 * 20

-3 = X + 200

X = -203

 

 

Or did I do something wrong there?

 

Yeah you did. You rearranged incorrectly (2 = X + 5 - 10*20).

 

My faith in humanity dropped reading this thread.

 

That there is even a debate over this saddens me deeply

 

Yeah I know, maths is pretty much the opposite of ambiguity (well apart from maybe a bit of D1).

[Rummy]

2 - 5 + 10 * 20 = X

2 = X + 5 - 10 * 20

-3 = X - 10 * 20

-3 = X - 200

X = -203197

 

 

Or did I do something wrong there?

 

I think you did. I also see strike through doesn't work on +s, I should have realised.

[Sarka]

It's 197!

 

When you have a long row of adding and subtracting such as:

 

2 - 5 + 200

 

You go from left to right, we had a longish discussion in maths about it.

 

So:

 

2 - 5 + 10 * 20

= 2 - 5 + 200

= -3 + 200

= 197

[Rummy]

I could dig out the national curriculum to answer this with 100% accuracy, but as far as I know the teaching of 'BODMAS' is not mandatory, you just need to know how to do calculations in the right order. BODMAS is the easiest to teach, but not necessarily the best. Depending on the kids, I'll usually teach BODMAS in year 7 to get them used to there being an accepted order of operations (even though we usually won't have looked at Indicies/Order/Of yet) I find it better to get kids to see each addition/subtraction as something which seperates terms, each bracket as a 'bubble' containing an answer (makes it easier when they are asked to expand things like 3(x+2) later on and they can't 'do the brackets first'), multplications as single terms (so that 3x3 is a single entity, 9, which makes algebra easier later on) etc.

 

Depending on the pupils (and it really does depend on them) I would think I have covered 'BODMAS' in enough depth if they can answer 3x4-7+8÷2^2=? and 15÷ (2+1) -3 =? correctly.

 

Ah right, thanks for the info. Just to check, those are 7 and 2 respectively right?

 

As for everyone spouting how great they are and how stupid people are who got it wrong, I don't think it's as clean cut as that. I think this is a case of a confusing situation, for lack of a better term. It's like those wordy riddles that get alot of people(you've heard them, the ones like what do you put in a toaster, what do cows drink etc). Do people commenting as such honestly believe the people who have arrived at -203 or something other than 197 are completely incompetant when it comes to maths? I'm not looking to start an argument, so that question is rhetorical, just ask yourself if you do, and if you can't honestly 100% answer yes, then I think you should refrain from making such comments. If you do believe it, then I think you are foolish, but you are more justified in your reasoning for making your comments.

[Ginger_Chris]

I would answer 100% yes to that. Someone is only as good as they were taught, Its a failing of the education system that the government just wants to reach targets and quotas rather than teach people exactly how maths works. BODMAS is convenient as its relatively easy to teach, however it doesn't go into why its that way, which is much more important. I'm seriously considering becoming a teacher, and I'd take it as a personal failure if any of my students answered that wrongly.

 

@ Rummy and anyone else: if you need any help with maths work/concepts/general stuff, just pop into the homework thread. There a bunch of us who are happy to answer anything you have, and then explain how you get the answer. Thats the important part that I feel the education system is lacking, the explaining, especially with maths and sciences.

[Rummy]

My point was that some people have simply posted in here with a post that basically says

"-203? Wrong. It's 197."

No real explanation of why, to try and help those who end up with -203 to understand why or where they've gone wrong. The only reason I can see for not trying to explain it in a way they can understand, is if you believed that they were completely incompetent in maths, and therefore trying to explain it would be futile.

[Ginger_Chris]

Ok,

 

If we take the example:

2 - (2 + 5 * ( 3 + 5) - 3 + 6 * 4 ) + (4 * 2^2)/(2) = X

There are a good range of mathematical operators there. An operator is simply an action that you perform. Without any rules or guidance, the above equation could have many different answers, which is why there are a set of rules that determine what operators act upon, and in which order they are performed.

 

When something is placed in brackets it means that the whole bracket is treated as a single object.

2 * (5 + 3) = 2 * (8) = 16.

This is because the bracketed numbers are treated together, and so its usually best to work out the brackets first.

2 - (5 +3) = 2 - (8) = -6

 

Multiplication and Division are treated equally. This is because they are technically the same operator. Dividing something by 5 is exactly the same as multiplying it by a fifth (1/5) (also known as its reciprocal (the reciprocal of 3 is 1/3 etc)). This is why;

6*5/3 = (6*5)/3 or 6*(5/3) or (6/3) * 5 or 6*5*(1/3)= 10.

 

A similar thing happens with addition and subtraction. Subtraction is really the addition of a negative number.

2 - 3 = 2 + (-3)

This is where the mistake in the question was made.

2 - 5 + 200 = 2 + (-5) + 200 = 197

What people did was 2 - (5 + 200) = 2 - (205) = -207

 

Operators such as * / + and - act only on what is directly after them. -5 + 200. The - acts on the 5 only and the + on the 200 only. in the case of -(5+200) the minus acts on the object after it, the (5+200), because everything in the brackets acts as a single object.

 

The ^ (to the power of) operator is slightly different. It raises what ever object is directly before it, to the power of what is directly behind it. (simple examples)

3^2 = 9

(2+1)^2 = (3)^2 =9

3^(6/3) = 3^2 = 9

Again brackets are used to designate what is designated as a single object.

 

The order in which operators act are brackets (as they determine objects), then ^, then /and* (equally) and finally +and-. They are the rules that were decided, they could have been different, in which case we would write equations differently. The reason we have this convention is so that everyone does the same thing, and like we saw, when given a problem everyone should give the same answer if they follow the same rules.

 

Going back to the first equation. This is how I's solve it (step by step):

X = 2 - (2 + 5 * ( 3 + 5) - 3 + 6 * 4 ) + (4 * 2^2)/2

Firstly sorting out the brackets. There are a set of brackets nestled within another set. As brackets are treated as single objects to operators the first bracket we would solve is the (3+5)=8.

X = 2 - (2 + 5*(8) - 3 + 6*4) + (4 * 2^2)/2

we can now solve the two sets of remain brackets. Taking the first (longer) one:

(2 + 5*8 - 3 + 6*4)

The multiplications are performed first.

(2 + (40) - 3 +(24))

Then the additions and subtractions:

(2 + 40 + (-3) +24) = (63)

This gives us:

X= 2 - (63) + (4 * 2^2)/2

For the last bracket the 2^2 is calculated first 2^2 = 4

X = 2 - 63 + (4*4)/2

technically the brackets at the end aren't needed because multiplication and division are equal. However it's usually best to work out the numerator and denominator separately because they might contain additions or subtractions(*).

 

X = 2 - 63 + (16)/2

X = 2 -63 +8

X = 2 + (-63) + 8

X = -53

 

(*) - something like (5-2)/(2+3) the brackets are calculated first, giving (3)/(5)=0.6.

 

Anyway, I ope that helps a bit. You didn't really say which bit was confusing you (which makes it hard to help) so I did everything, If anything sounded condescending it didn't mean to be. Most problems people have, (especially us uni students) are not wit the hard bits but a small simple mis-understanding of a something fundamental. Anyway. If theres any typos, or silly mistakes I've made, let me know and I'll change them. Typing maths is hard.

[Rummy]

I wasn't confused, I know where I went wrong, but that looks pretty handy for anyone who still doesn't understand how it comes out at 197. I think if alot of people just saw the second line;

2 - 5 + 200 = ?

Most of them would get 197, but when they see the first line they think BODMAS, which they then follow in exact order, and gives them the wrong answer of -203, that's why I think it's more a trick of the mind than a failure at maths.

[Cube]

Something more interesting:

 

x = 1

x^2 = x

x^2 -1 = x - 1

(x + 1)(x - 1) = x -1

x + 1 = 1

x = 0

Therefore 1 = 0

 

[Supergrunch]

Thats the important part that I feel the education system is lacking, the explaining, especially with maths and sciences.

Very true. I feel like killing people who say "it goes positive when you move it to the other side"...

Why use parts, when the answer is lnx (+ c)? Wait, that maths makes no sense whatsoever. Was that the joke?