Maths teachers: Help me explain why 1000-587+113=526

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My son (in Y6) is doing Schofield & Simms Mental Arithmetic 6 Section 2, test 4 for homework, and question A1 is 1000 - 587 + 133 = ?

The correct answer is 526, but he's insisting it is 280, and I'm having trouble explaining why it isn't.

The problem is he's been taught to use BIDMAS, but I'm not sure it hasn't been explained to him correctly, or at least he doesn't yet understand it correctly, so he is insisting on doing the addition (i.e. 587 + 133) first, without taking into account the fact that -587 is a negative number.

We've had the same problem before, and while I'm usually pretty confident at explaining maths, I'm struggling to get this across clearly. (I did BIDMAS in secondary school, and I'm pretty sure we did bracket expansion first, so I wouldn't have had the same problem).

How can it best be explained?

Right, I am crap at maths, so I must be massively missing something.

There is something more complex here that I don't understand isn't there?

Because 1000 - (take away) 587 + (plus) 133 is 526.

There aren't any brackets, you can't just randomly bracket questions can you?

You can randomly add brackets if they're in the correct places following BODMAS but in this case the sum would be (+1000)+(-587+133)

And what am I missing? I make it 546.

I don't know how to best explain it though...

Yes 546 here as well!

I'm lost- I get 546 too!

The multiplication and division in BIDMAS can be done in any order. That is, they come at the same 'level'.

BIDMAS should really be laid out as
B
I
DM
AS

The addition and subtraction should happen in the order they are written in the sum unless there are any other operations involved.

Isn't it 546?

Yes 21pc, that's what I did in the end - I told him that what he was actually doing to get 280 was 1000 - (587 + 113), otherwise known as 1000 - 587 -113. He did get it in the end, but he didn't seem very convinced and I felt there was a gap in his knowledge somewhere that I hadn't quite identified.

GobblersKnob/Wadingthroughsoup - yes, I think this is one of those questions that people who know less maths automatically do correctly, and those who think about it too much, because they've been taught about BIDMAS/BODMAS, tie themselves in knots over.

Can you explain it as adding together three numbers. It just that one of the numbers (587) is a negative.
So it's
positive1000 + negative587 + positive133

For anyone still wondering, OP did a typo.
The thread title said 113, which gives 526.
The text said 133, which gives 546.

Ah ok, hadn't spotted the typo.

I had exactly the same problem when I taught dd BIDMAS. PenelopePitstops's explanation was exactly what I found when I looked into it.

Yes, what Penelope said
It's not Multiplication then division then addition then subtraction; it's Multiplication/Division then Addition/Subtraction.

Does he realise the acronym BIDMAS trips off the tongue easier than BIMDSA which is a reason they are in that order?

Thanks all, and especially Penelope - that's the reminder I needed!

I've written a note to DC's maths teacher to ask her to go over BIDMAS in class to make sure they all understand it properly.

Have you tried using a number line?

Draw a horizontal line from 0 to 1000.

Starting at the far end at 1000 you draw a jump back to the left of -587 which will take you to 413.

Then from 413 you will then take a jump forward to the right of +113 which will take you to 526.

Sorry sounds a bit Rocky Horror but the physical movement might help him understand that without brackets you have two separate operations taking place!

I was taught that the sign + or - "sticks" to the number after it. So in you case if he wants to add it up first (which makes no difference here) he should add 113 to -587, ie Think of 587 as negative. Might be too complex for yr 6 though.

I agree with Pp though, maybe a number line is the way forward or to set out bodmas in levels.

When you solve algerbra you "collect terms" first, so you collect the +1000 and +133, the subtract the -587?

Can't believe I've been getting Bidmas wrong I got 280 too. OMG now I'm wondering if in calculating the sum I got into a right stew about when DS was in year 2 (now year7!) I WAS ACTUALLY WRONG!! If only someone had explained it to me like you did PenelopePitstops. I would have realised I was wrong. I would have accepted I was wrong. I don't mind being wrong. I quite like being wrong! As long as someone can convince me why I'm wrong. Which no-one ever did and I've been slagging off ds's year 2 teacher ever since.

Though annoyingly I don't think I can check as I don't think that homework book came home to keep at the end of the year... I WILL NOT TURN THE WHOLE HOUSE UPSIDE DOWN TONIGHT TO SEARCH FOR IT. WILL NOT!!

Must tell Ds. Must tell Ds tomorrow morning. I must not wake him now to tell him.

It's nothing to do with BIDMAS. The problem he's having is that he's turning a negative value into a positive value.
All the posters who are saying that it is not '587', it's 'negative 587' are correct.
I think the problem is that we teach '-' as being'subtraction', and an operation, in primary school, rather than 'positive' and 'negative' being values of numbers.
I teach my children subtraction using the Old Chinese method, with different coloured sticks for positive and negative numbers, and they cancel each other out, leaving a remainder(positive or negative) on the board.g
I find it really helps when they come to using negative numbers and in algebra.
Have a google and see if you can find some demonstrations.

Sorry, I don't know where the random capitalisation has come from!! Basically, it's just a method that was used in China, using tally sticks. It's quite good for teaching place-value too.

What about turing it into a word problem? You have £1000, you spend £587 on kittens or whatever, then you find £133 in the street. How much money do you have?

I like the word problem - it makes turning the negative into a positive impossible.
I want a maths mumsnetter to show up and tell us something interesting and enlightening.