# BIDMAS order of operations- Four Fours, Bodge Ups and Quiz Quiz Swap

### 8 Responses

1. Tom Whittaker says:

Four Fours is a great idea – it worked really well with my year 7s. They loved coming up to the board to write up ones they had found.
Thank you for sharing all these ideas!

2. Very useful thanks! Your website is great, thanks for making so many resources available to all of us who teach maths.

Regards
Steve Williams

3. Claire Brown says:

I gave this investigation to my Year 4/5/6 children who are level 5/6 and they absolutely loved it! There was no giving up until every answer had been found. Thanks for all your great ideas.

4. Emily says:

this was extremely helpful but does anyone have the answer to 21 using four 4’s???

• Joseph says:

How do you get 77

• Sam says:

4^2 +4 + 4/4

5. leonard ferris says:

When I was at school I learnt BOMDAS which would be translated as BIMDAS in your terms. The question I pose is why has the order of operations been changed for division to precede multiplication? Is it because of the commutative law, and if so why doesn’t subtraction also precede addition? Wouldn’t it be more accurate if the order of operation was BIDMSA?
Now I want you to think about this without immediately dismissing the idea. If you are thinking of responding by saying that addition and subtraction are complimentary than that would be an argument against the change from BIMDAS to BIDMAS in the first instance. When I was taught, multiplication and division were considered complimentary and thus to be performed as read from left to right in order to maintain integrity, and the same procedure was applied to addition and subtraction. For example: 4 x 3 divide 2 x 6
=(4 x 3) divide 2 x 6
=(12) divide 2 x 6
=(12 divide 2) x 6
=(6) x 6
=36
If multiplication is done order prior to division errors may be introduced to the divisor of the divisions. Thus division should be done prior to multiplication to alleviate this risk.
Similarly with addition and subtraction for example: 3-2+1
=(3-2)+1
=(1)+1
=2
If addition is done in order prior to subtraction errors can be applied to the subtrahend of the subtractions.
Strictly speaking, I believe BIDMAS to be misleading to students. If we name this procedure as an ‘order’ it needs to be explicitly an order of operations without any ambiguity or special considerations that need to be applied to some aspects of the order and not to others. This may well contribute to students failing to grasp the fundamentals of arithmetic law in middle school. Why not simply replace the non commutative operations of division and subtraction using the multiplicative inverse (turn divisions into multiplications of the multiplicative inverse i.e. 4 divide 3 = 4 x 1/3 = 4/3, and turn subtractions into additions of the additive inverse i.e. 4 – 3 = 4 + negative 3). Now the order of operations can be simplified explicitly to BIMA as there are no longer non-commutative subtractions or divisions. This means that special consideration no longer need to be applied to series’ of multiplications and divisions or series’ of additions and subtractions that need be performed ‘as read from left to right’. Wouldn’t the ability to utilise the commutative law to simplify the process of rearranging formulae in algebra? If we take for granted the processes we have been taught, without question then how can we progress? I would value any constructive feedback on this topic as I am about to enter the teaching profession as a maths teacher.

1. 17/02/2013

[…] BIDMAS order of operations- Four Fours, Bodge Ups and Quiz Quiz Swap | Great Maths Teaching Ideas. […]