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SAMDOB – mess up the order of operations

While I’m on strike, I’m catching up on stuff I’ve made but never posted about here.

At the Talking Maths in Public conference last August, I was talking with Katie Steckles and Kevin Houston about the order of operations. I think that another one of those ambiguously-written sums had gone round Twitter again. I said it would be good to have a tool where you can write an expression, then change the order of operations and see what happens.

So, on the way home, I wrote one! I’ve called it SAMDOB, which is an anagram of BODMAS.

Screenshot of SAMDOB, showing the order of operations BO(DM)(AS) on the expression 2*3/3*2+2, which evaluates to 6
Screenshot showing how with the order of operations BOMD(AS), the expression evaluates to 3
Screenshot showing how with the order of operations BO(AS)(MD), the expression evaluates to 8.

Please have a play with it. I can imagine that this could be useful to people teaching the order of operations in real life. Let me know if you have any suggestions for improvements.

The code is on GitHub.

Ask Clever Hans a question

I’ve put a very clever horse on the internet. He’s called Hans and I’ve made a little video about him.

You can ask Clever Hans your own questions! Go to and make sure your microphone is turned on. Another proviso: I think only Google Chrome supports the special technology I used to make Hans work. Sorry!

I’ll explain how Hans does his horsey magic below the fold.

Take the 30 second arithmetic challenge

My wife’s grandmother is a fearsome character. She’s in her nineties but still has all her wits about her. In fact, she’s got more than her fair share of wits. Whenever we visit her, she hits me with a barrage of questions and puzzles collected from the last several decades of TV quiz shows and newspaper games pages. My worth as a grandson-in-law is directly proportional to how many answers I get right.

One of her favourite modes of attack is the “30 Second Challenge” from the Daily Mail. It looks like this:


You start with the number on the left, then follow the instructions reading right until you get to the answer at the end. It’s one of Grandma’s favourites because it’s very hard to do in your head when she’s just reading it out!

I decided it would be a fun Sunday morning mental excursion to make a random 30 second challenge generator

Finger counting methods and their effect on cognition

Counting on your fingers may feel natural but it is not innate or universal; methods are culturally transmitted (like number lines) and may have an effect on cognition. A Guardian blog post asks you to “without thinking about it too much, use your hands to count to 10”. How did you do it?

Ability with fractions and division aged 10 predicts ability with algebra aged 16

Last week we reported that the UK Government have released a draft primary school Programme of Study for mathematics for consultation. A report from the Telegraph quoted in that article mentioned that “the use and multiplication of fractions” was “a vital precursor to studying algebra”. A piece of research published in the journal Psychological Science, ‘Early Predictors of High School Mathematics Achievement‘, investigates this area. The findings indicate the importance of learning about fractions and division by showing that these “uniquely predict” students’ knowledge of algebra and overall mathematics achievement 5 or 6 years later.

Draft UK primary mathematics changes for consultation

The UK Government have released a draft primary school Programme of Study for mathematics for consultation.

The announcement was much covered in the press, which focused on the ‘back to basics’ approach. The Daily Mail reported that “times tables are to be put back at the heart of the curriculum for children’s first years at school for the first time in decades” with other details reported including learning how to calculate using decimal places and fractions, and dealing with numbers up to ten million.