I recently sat down to plan a lesson for year 7 students about the order of mathematical operations. Here in the UK, I believe this is most commonly known as"BODMAS". The B stands for brackets, D for division, M for multiplication, A for addition and S for subtraction.

But what does the O stand for?

I've heard several different answers to the above question, none of them satisfactory. One of my colleagues told me he taught it as "Orders". This random website I found agrees. But what the heck are orders? According to the aforementioned random website, they're "numbers involving powers or square roots". I have never heard this definition before, and after consulting the oracle (Wikipedia) I found no mention of indices or powers on the page for Order (mathematics). So why on earth would we teach students the word orders when we never call them that in lessons? We in the UK usually refer to these as "indices" although I believe the Americans prefer "exponents" (but I'll get to them later).

Another colleague told me he teaches that the O stands for "of" as in "powers of", and I'm ashamed to admit this was what I was taught in school. I think this one is faintly ridiculous. Firstly, O cannot stand for "Powers of" because "Powers of" clearly begins with a P not an O. Kids may be getting dumber every generation, but I have a feeling they will notice this. Also, why does the word "powers" even need an "of"? Can we not just call them powers? It reminds me a bit of learning French when we were always taught to write the following preposition after certain words like "decider de" or "je pense que" to help you form sentences. This was actually excellent advice for learning French, but this does not dilute my point.

A third colleague (it is amazing how many of them are willing to contribute to my inane Monday-morning conversations) said that he teaches that the O stands for "Other" as in, any other operations not mentioned. This is quite nice actually, because it includes not just powers and roots but also sines, logs, factorials, etc. Very handy.

I then went into my year 7 lesson and asked them what they thought the O stood for. Interestingly, the most common response was one I had not heard yet: "operations". This is perhaps the one that annoys me the most. BODMAS is the tool we use to remember in which order we should do operations. If O stands for "operations", then we are basically saying, do the bit in the brackets first, then do the operations. Oh wait, what order do I do the operations in? Use BODMAS. So I do the brackets and then the operations. But what order do I do those operations in? etc etc. Thank you Primary school teachers. Thanks a bunch. You have just created an infinite loop in my head. You have given my eleven year-old students an acronym to learn that is actually a recursive formula. After infinite iterations they will still not have found the value of 3 + 2 x 5.

So I bet you're dying to know what I taught them in the end, right? Well I told them about the conversations I'd had in the maths office. I also told them about the American version: PEMDAS. Seriously. That's what they call it. The MDAS is obvious enough. The P is for "parentheses" which my students had never heard of but which is quite useful to know I suppose, and the E is for "exponents" as I mentioned above. My year 7s were not happy that our friends across the Atlantic do their multiplication before their Division though. "Surely they'll get different answers from us and then spaceships won't work!!" they cried. (I must have told them about the metric/imperial satellite mix up in a previous lesson). This led to a nice discussion about how those two operations are interchangeable and you would still get the same answer (or would you? I have just thought of a topic for a future post).

Anyway, in the end, I taught them the O stands for Indices. That's right, I'm on Team BIDMAS. All you BIDMAS haters out there can hate hate hate but if we refer to powers as "indices" the rest of the time why not in this? And if you have a problem with me not including trig functions or logarithms or whatever in my acronym well you shouldn't because by the time you're learning that sort of stuff you shouldn't need a mnemonic to help you remember which order to do stuff in anyway!

Over to you: what did you learn at school, and, if you're a teacher, what do you teach now?

Emma x x x

I don't every remember being taught anything remotely like a Mnemonic for operations.

ReplyDeleteI thought everybody understood "order" to mean "power" though. We talk about the order of a polynomial and numbers "in the order of 100s" for example.

The first time I saw BODMAS being used, the O was "Powers Of" - I agree Emma, pretty ridiculous and not at all pretty!

I've also seen it missed out completely (MEP in year 7 don't give it any description).

I've heard it given as Order and "Over" (in other words, the same as division).

I prefer to describe it as Operations (as in "other operations"), but acknowledge the slightly unsatisfactory infinite loop! :-)

Of course the most important thing about BODMAS/BIDMAS isn't what the O stands for but rather how we make sure that students using it get the correct answer to 6 - 3 + 4!

But we don't use the word "order" to describe powers to year 7s, 8s etc. The first time we use the word is when talking about polynomials, so year 12. We do of course say "order of magnitude" which until this very second I made no connection between the word order and the fact that order of magnitude refers to which power of 10 is involved. Weird.

DeleteI love the blank space next to the O in the MEP book - so mysterious!

I think to solve the 6 - 3 + 4 problem what would be great is if we stopped thinking about that - as being a takeaway or a subtraction and instead always think of it as the negative sign, and hence it belongs to the 3, and so we wouldn't even think of doing 3 + 4 then subtracting the answer. However, that's a whole discussion in itself! I wrote a post on that ages ago.

Why have cotton when you can have silk?. We all know that one.

DeleteI say why choose ? Have cotton and silk...

If we want students to know what this tool means, clearly identify it in full.

In short if you want students to think of the I or the O as indices but it could include other things like trig, logs etc... then use them both!

Maybe we should revamp it altogether?

BOD (MAS) and BID (MAS) are so 2014 ..

.

...could this be changed to BOIDMAS.

B:Brackets,

O Other (trig etc... )

I: Indices

D: Division

M: Multiply

A: Addition

S: Subtraction

Yep!

Wasn't that a Galaxy advert?

DeleteBOIDMAS looks good. How about BLITODMAS - brackets, logs, indices, trig, other, division, multiplication, addition, subtraction. Actually, make it SBLITODMAS - the s is for square brackets [ ] that you use when you've already used normal brackets.

I am decided that O in BODMAS as Order but I want to know about the use of O in bodmas I mean how to use Orders in a problem....I u get understood well reply me with a suitable example.....

ReplyDelete