The ones that didn’t get away

This week, most of Year 7 are away on a residential trip leaving 20 pupils who, for whatever reason, are in school.  I taught them on Monday and much to my relief they didn’t seem particularly aggrieved by this state of affairs.

I don’t know what they are doing in other lessons, but in Maths, well, they’re going to do some mathematics!

I actually love the freedom of not having to follow a scheme of work for a bit (although I’m sure I would eventually feel lost without it!)  I wanted to do something that was proper maths but felt a bit different from a normal maths lesson.

As luck would have it, I attended an fantastic session run by John Mason and Anne Watson on Friday.  I’m not going to attempt to write about that session. All I will say is that if you ever get the chance to meet these two, you should.  A great opportunity to reflect deeper on the nature of mathematics and mathematics teaching.

So, like all things you pick up at CPD, I decided I would use something soon before I forgot it.  And here is what occupied us for nearly an hour last thing on Monday afternoon.


This is a classic low ceiling, high threshold task.  Everyone can see some patterns in this, some will notice that the first term of the nth row is n², some will determine that the last term in every row is…

On Friday, however, I picked up something more valuable than this piece of mathematics.  I got to play around with techniques of how to present it to students.  To start with a blank board and write very deliberately and quite slowly stopping and asking questions like, “What am I going to write next?”, “What should we do now?”, “What are you thinking now?”

I really felt that we began to see the power of getting students to explain their reasoning, especially in a mixed group like this.

So, moving on.  What else can I do in the remaining lessons I have with this group?

My first instinct was to look at my own blog under investigations.  This is, after all the main reason I do this blog – as a reference for me!

Some good stuff, and it triggered memories of lessons I would otherwise have forgotten about.  And then I thought, what about those CPD events I went on in the years before I started this blog?  I looked back through my notes and found this from the 2012 ATM conference.


Factor Game

Write out numbers 1-12.

1st person choses a number.  2nd person gets all the remaining factors of that number.

1st person choses another number (but it has to be one that still has factors remaining).  2nd person gets all the remaining factors of that number.  Keep going until there are no numbers left to chose that still have factors – the second person gets all the remaining number.  Sum the totals of each – highest score wins.

Nice way to practice factors of a number as well as introduce Gauss’s trick to sum an arithmetic progression of n terms: n(n+1)/2 as you only need to calculate one of the totals, you can then take it away from the sum to get the other total.  So, in this case the total is always 78 because the sum of the first 12 numbers is 78 and that’s all we are doing.


Person 1

Person 2












Total = 46

Total = 32

Can you always win? What is your strategy?  What’s the perfect game, i.e. highest possible score.  Try it for other totals.

I tried:

    • 8.  Nice, easy one to start with.
    • 16 a bit more tricky, but the player choosing the numbers should still win
    • 20 was interesting as it was a draw – 95 each!
    • 19 was easy to win



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