Powers, answer books and Mrs Krabapple moments

There is an episode of The Simpsons* when, frustrated with her teacher’s reliance on the answer book, Lisa steals all of the “Teacher’s Editions”, denying staff access to the answers and, soon, chaos, confusion and panic reigns in the staff room. Of course, we teachers can get by without the mark scheme, but, for expediency of course, it is often easiest to turn to the answers at the back of the book.

Perhaps we shouldn’t be so swift to reach for the answers. For one, particularly with the harder A level questions, it is often better to do the question yourself, so you can more easily pick out the where and whys of student errors.

And, more importantly, it should be – and is – fun to do some maths from time to time.

And so it was, recently, that I had my own Mrs Krabapple moment, not because my answers had been nicked, but because one of my students asked a great question, for which I didn’t (immediately) have the answer.

I was working with my Year 10 (14 & 15 yr olds) class, doing some work on indices and powers. One student asked:

Which is bigger: five to the power ten, or ten to the power 5?

Although I had my suspicions, I didn’t have an instant answer, but I did immediately recognise this as a great question.

My second reaction was to stop any student reaching for a calculator – too easy to get a quick answer which would actually tell us – teach us – nothing.

So I did what any seasoned pro would do in such a situation – I threw the question back to my students.

“I don’t know” replied one girl. “But I know they can’t be the same – one will be odd and one will be even.”

This was a great answer, and we continued to explore the question some more.

We thought about how we could re-write the question, coming up with:

510 = 5x5x5x5x5x5x5x5x5x5

105 = 10x10x10x10x10

and then we realised that 10 is really just 5 x 2 so:

105 = 5×2 x 5×2 x 5×2 x 5×2 x 5×2

and re-arranging that:

105 = 5x5x5x5x5 x 2x2x2x2x2 but:

510 = 5x5x5x5x5 x 5x5x5x5x5

and writing it like that it quickly became clear to all that:

510 is bigger than 105

And we arrived at that solution without an answer book, a calculator or doing any real calculations.

What we had done was show that maths is not just knowing Pythagoras and perimeters, but that maths is a way of thinking.

A great question, a Mrs Krabapple moment that forced me and my students to think mathematically, possibly the highlight of my teaching term. Perhaps Lisa Simpson was doing us all a service when she hid all those Teacher’s Editions?!

Maths is a way of thinking

*The episode in question was “Separate Vocations”, Series 3, Episode 18 (and yes, I did have to look that up!)


Posted in Numeracy, Teaching Tips | Leave a comment

A niche joke

In the Philippines, two fifths of the band play on.

Forgive my indulgence – a rather niche joke.

Where you fall in the Venn diagram below will determine whether or not you are enjoying a quiet chuckle right now.

Posted in Uncategorized | 2 Responses

Strike one for the maths teachers …

… or how I (silently) cheered when the tables were turned.

Many is the time in my classroom (and, I suspect, in classrooms up and down the land) that I’ve had to interject, and re-focus my students when their thoughts – and more importantly – their chat has turned to football.

And so, the other day I smiled inwardly, and gave a silent cheer when, whilst stood behind a group of students watching the school’s first team footballers play an important cup tie, I heard them talking about maths. The tables had turned, and I was delighted.

The conversation began with them discussing formations: were the opposition playing 4-4-2, or 3-5-1-1? One wag (not WAG!) commented that they were playing 1-1-1-1-1-1-1-1-1-1.

Ah, you mean 110?

replied his mate, and so the conversation moved on from playing styles and onto indices and laws of powers.

Reader, I must confess that, on this occasion, I did not “re-focus” them (although I did interject to settle an argument as to whether anything to power 0 really does always equal 1. I didn’t want any trouble on the terraces.)

Posted in Numeracy | Tagged , | Leave a comment

Whimsical and self-deprecating

Forgive me for being a little self-indulgent today.

I am very chuffed and rather proud to have been featured in Mr Barton’s Podcast, as one of three recommended websites or blogs by his interviewee Rob Eastaway. Many you will know of Rob Eastaway, but for those of you who don’t, he is an author and broadcaster who is active in the popularisation of mathematics, somewhat of a celebrity in mathematical circles (aren’t all circles mathematical?!)

He describes my – this – blog as “whimsical, self-deprecating and slightly serendipitous”, and I couldn’t have hoped for a better analysis.

And to hear my website mentioned alongside FullFact.org – the UK;s independent fact checking charity  – and the BBC Podcast “The Boring Talks” puts me at exalted heights of which I could only dream.

My mention can be found on Mr Barton’s Podcast – well worth listening to the whole show, but if you want to hear my cameo mention please skip ahead to 2hr 13 mins.

I write my blog because I enjoy doing so, that others enjoy reading it is a great honour.

If you’ve never read any of Rob Eastaway’s books, I suggest you do – you can find a collection of them here , and his next book is published on Thursday:

Posted in Uncategorized | Leave a comment

June 2019 9 – 1 GCSE Grade Boundaries

For info and reference, below are the grade boundaries for the June 2019 Maths GCSE (and IGCSE) exams.

With particular thanks to https://mathsbot.com/gcse/boundaries who make it so easy to find grade boundaries for any year and board.

Higher Tier:

Foundation Tier:

Pearson EdExcel IGCSE Maths:

Posted in Exam tips | Leave a comment