Tried and Tested: GEMS – Until I Know Better
Until I Know Better

Tried and Tested: GEMS


One oddity about working  in a school that is well-known / notorious is that we are often asked about how we – that is, the maths department- approach or teach different things. I worry about saying anything, as we don’t have results yet (182 sleeps to 21st May 2019!) and our approaches haven’t been through the crucible of The Exam Process. I don’t want to give the impression of certainty as we are always changing, refining and even chucking whole strategies!

However, there is a pair of approaches we have been taking for several years that we do think are working well and I hope you will find useful too: GEMS and SMEG. I’ll write about GEMS below and its unattractively-named cousin, SMEG, in my next post.

GEMS is an alternative to BIDMAS/BODMAS, and is used more in the USA, although not widely. I can’t remember where I first saw a teacher blog about it; please let me know if it is you, so I can give credit where it is due.

GEMS stands for:


Why we use it:

(images from Ms Lopez’s blog )




If you want to make this change, please make it a whole-department change. It is a nightmare if one teacher does it and then pupils or classes move on to someone else. You may decide ‘only for Y7, and then add on a year each time,’ but ensure you have within-group consistency.


Bonus tip: introduce the order of operations after you have taught directed numbers. Children can quickly infer unintended patterns if all your examples have positive results. Ideally, early examples would be in forms such as this, to force them to preserve the order that is in question:

4 – 3 x 5

Many pupils, knowing they should ‘multiply first’, will conclude it also means ‘put the result of the multiplication first’ and write

15 – 4

for the next line. If you use only positive examples, such as 4 + 3 x 5, you won’t notice there is a growing habit of them writing 15 + 4, and so on, whereas their little leaps become obvious when negative numbers are involved.