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

# Four Fours

* Can you make statements equal to all the numbers 0 to 20 by using just four fours?* Brackets, multiplication, division, addition and subtraction are allowed for starters. When they start getting stuck you can introduce other operators such as square roots, factorial etc. Can you make all the numbers up to 100?

My year 7s had a good go at it this week, writing their answers collectively on the board:

I made a worksheet for the investigation that you can download here (Microsoft Word).

# BIDMAS Bodge Ups

To get pupils evaluating answers to BIDMAS statements you can give them some incorrect ones based on common misconceptions and get them to identify the mistakes and correcting them. Here is a booklet I made (in Microsoft Word) that covers 5 common BIDMAS misconceptions. The last one is to get across the importance of showing workings otherwise nobody knows what you have done wrong…

# BIDMAS Quiz Quiz Swap

This is a nice activity to promote focussed learning discussion in a BIDMAS lesson. Download the Microsoft Word file here and print and cut out the cards. Give each pupil one of the cards. They then quiz each other with the questions on their cards, making sure they cover the answer at the bottom of their card with their hand when they ask the question. The answers are included so they can then know if they need to have discussion if they get it wrong. The idea is that if they got the answer wrong they have a discussion between the two of them to understand why it was wrong. This leads on nicely from the BIDMAS Bodge Ups activity where they spent time identifying and correcting errors. After they have answered the questions on each other’s cards and had a learning conversation if they got them wrong, they swap cards and go find another person to quiz quiz swap with. The idea is that learning travels around the room from pupil to pupil.

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!

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

Regards

Steve Williams

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.

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

How do you get 77

4^2 +4 + 4/4

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.