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BODMAS as a first lesson

If you were to stop people on the street and ask them the answer to

3 + 2 × 4 = ?

most would give you 20, and a small minority would say 11.

I teach the convention of sequence of operations early in maths courses above level 1 (GCSE Intermediate and Access courses) as a lead into algebra. I use two activities - traditional worksheet and open ended group work. I then have a discussion about the different cognitive styles involved in the two contrasting activities. You'd be surprised how many people think that mathematics is just doing worksheets that get really hard. They have no idea of the creative side.


Just in case you have not heard the mnemonic for remembering the sequence of operations...


Whole class interactive 'exposition' on the whiteboard / Interactive Whiteboard / flip chart.

I usually go through several examples of increasing difficulty and encourage students to make up examples before moving into individual work on the worksheet. I differentiate nominated questions - can be tricky early in the year, so I keep the questions moving and refer back to the mnemonic often, ticking off the stages.

Activity 1: worksheet

Activity 2: Open ended

Next, I call the group together and write something like

                  = 7

on the whiteboard and ask for a calculation to put on the left hand side. 3 + 4 is a popular one, so then I ask for another that involves subtraction. I get 10 -3 or something so I add in 1 000 000 - 999 993 which gets people going a bit. Then I start asking for calculations that need two operations (5 × 2 - 3 or similar) and then one with brackets. People need practice chaining the calculations together and I challenge the group as a whole to check the rules...

Then I introduce the 4s activity with constraint....

4 - 4 + 4 - 4 = 0

Can you find other bodmas expressions that use the number 4 exactly 4 times and make 1, 2, 3, 4, 5, 6, 7, 8, 9??

This needs a bit of preparation (still whole class). I ask about what you can make with two 4s and build a table on the side of the whiteboard. Then...

Payoff (my word for 'meta-cognitive gain')

The answers enable me to check people's cognitive styles which is useful for future activities. I also recap the worksheet and suggest some exercises from the workbooks we use for homework. Recap in the next session usually reveals a good recall of the sequence of operations but also improved tables, and calculation.

Keith Burnett, Last update: Sun Sep 04 2011