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New school year

As we approach the end of September, it’s getting on for 2 months since I wrote a post. I’m happy with not writing over Summer, but I’m beginning to feel bad that I’m neglecting my blogging. So, back to it! This post is just a quick set up for the coming year.

I’m teaching at the same school I have done for the last 7 years or so. I am ‘Principal Teacher of Maths’ although I’d have called it something like ‘Maths teacher in charge of the KS3 maths’. We recently got a new head teacher (Chris HildrewI blogged about that here) but otherwise, things are pretty similar.

Having said that, the two main changes for me this year are:

  1. I’m leading a whole school CPD (or CPL if you prefer) on homework. It’s still in its infancy but after one session, the group of staff are motivated to look into ways to develop independence in students’ approaches to homework. Our (clearly too ambitious) early thoughts included “ideally, we’d get to the stage where students didn’t need to be set homework as they’d independently work out how much they need to do and on what areas”. I’m sure we’ll reign that in a bit in our next meeting.
  2. I am teaching year 13s part of the Core 3 course. I taught some C1 last year and that went well. I didn’t teach any C2 though and that is making relearning the C3 stuff a little harder. I’m enjoying the challenge and I’m sure that the questions I’m asking the other maths teachers is forcing them to think carefully about their own understanding too. Next year is when the new A level course starts and at my school, I think that’s likely to mean all teachers have to teach core and applied maths but, as is always the way, we don’t know enough about it to be sure yet. Either way, brushing up on my reciprocal trigonometric functions and transformations of functions probably isn’t a bad thing!

That’s it for now. You can expect to see more frequent blog posts from me now. Feel free to encourage people to subscribe!

TES reviews – 5 star resources

Every so often, as part of the TES maths panel, I’m given a set of resources to review. The aim is to highlight the best resources to make them easier to find. Here are the ones I gave 5 stars to from my latest batch.


By William Emeny (@maths_master)

LINK here

The pdf files here are pretty straight forward and the matching activity is nice. The thing that makes this resource shine is the link to the interactive resources that show the circles theorems in action. You can drag key points and see how that affects the overall shapes involved. Great on an IWB!
GCSE Revision Topic Progression Grids

By alisongilroy

LINK here

This is a collection of sheets that allows students to a variety of different ‘levels’ of question on the same topic. A great opportunity to push students on to try the next level of difficulty once they’ve shown they can master the previous ones. I’m definitely going to be using these in lessons and also during revision time.
GCSE Shape and Measure Revision (D-A*)

By mathspo

LINK here

This was an easy 5 stars as I saw how good it was in action! I used this resource with my (top set) year 11 class during the revision weeks. It went brilliantly, keeping the class focussed for the full lesson while covering a load of topics that they may have been tempted to overlook in their revision. I certainly intend to use this again.

#TMCotham2 My take aways

Last week, my wife and I went to Cotham’s 2nd TeachMeet with the theme ‘power to pedagogy’. This evening was put together by Kelly McDonagh (@MissKMcD) and supported by Ali Goddard-Jones (@AliGoddardJones). If you’re a teacher and you’ve not been to a teachmeet before, I recommend you find one and try it out!

There were a lot of presenters (you can check out the list here) with a wide variety of themes (all presentations are available here) but I’ve picked out the ideas I’m taking away to try out. (Note: My pen was playing up so I’ve not necessarily carefully recorded who said what but I’m sure people will help me figure it out!)

Amjad Ali @ASTsupportAAli

Referred to “Comfort, Struggle and Panic” zones. You need to be in the struggle zone to learn best. This is something I’d seen before but I liked the way he related it to learning to swim. The children’s pool, where there is no danger/challenge at all, is a place where you can do a lot of lengths but won’t actually learn anything.

4 tools from Amjad that I intend to use:

  1. At the end of a lesson, get students to draw a 3 by 3 grid and fill it with the nine words they heard most frequently in that lesson
  2. Make use of to read things more quickly
  3. Going through the front page of a GCSE exam paper with the students and in (painful) detail go through each bit
  4. Red dot and Green dot highlighting. As you’re walking round a class, when you notice something that stands out as incorrect in a book, put a red highlighter dot. This is a sign for the student to check what’s written there and correct it. The green highlighter is for when you’ve looked at a page in class and know it’s good. Put a green line down the side of the page so that when you’re marking, you know you’ve already checked that work.

Chris Baker @TheEduBaker

Talking about ‘coaching cards’ for when observing PGCSE students. These are simple pictures that can give hints to the teacher AS THEY’RE TEACHING rather than waiting until after and it being too late. Link here.

Ali Goddard-Jones @AliGoddardJones

Reminded us that we should always “Begin with the End in Mind”. I think this is very easy to forget! She also mentioned a TED talk by Derek Sivers on How to Start a Movement which I intend to watch soon.

Danny Dignan @DrDanNicholls

Say to your students, “Who did something great today? There are 30 of you and only 1 of me. If you saw someone else doing something good, tell me about it.”

The importance of ‘thank you’ and assertively asking for it.

Danny doesn’t like using sweets as rewards (which I agree with) partly because I don’t think they help students struggle with problems for long periods of time.

Chris Baker @TheEduBaker (part 2)

Talked about the effect of dopamine and the need for regular, small opportunities to feel successful. He mentioned people who make checklists are ‘dopamine-addicts’ and freely admits that he falls firmly into that camp. Chris also pointed out that there is a tension with the desire to create patient problem solvers but I’m sure there’s some element of middle ground to be found. I especially liked the idea of using a post-it note to praise a piece of student’s work in the classroom as you’re walking around. I have done this occasionally in the past but this has reminded me to make use of it again.

Dave Gale @reflectivemaths

I talked about tutor time activities. It was great. They are here.

One of the things I really enjoy about TeachMeets it the opportunity to meet other teachers and see them sharing ideas while having a chance to share mine too. I’m looking forward to the next one! Thanks again Kelly.

Contingency Tables

Our year 12s are back in school getting a good head start on their year 13 studies. One of my tutees asked why Contingency Tables (from the S2 course – goodness of fit test) were called that. I didn’t know but it seemed like a question worthy of exploring.

I asked twitter and got these responses:

@michiexile My guess would be because they give you quantified risks for systematic outcomes, to plan from.

@tslumley Pearson coined ‘contingency’ to mean ‘deviation from independence’ (with this link)

@MsGreenMaths  I don’t know, but always assumed it was because some values are contingent on others … ?

@BetterMaths i suppose as it’s a relationship between two or more categorical variables – they are ‘contingent’ on each other.

So, I now know that this was certainly a term created by Karl Pearson (or PMCC and other fame) in 1904. It appears that the name was chosen mainly because it’s a system for checking whether some entries in the table are contingent on others.

Let me know if you have more to add.

Real-life Packing Problem

I came across a problem that I want to solve. I assumed that maths would have an algorithm for this but it turns out that it might not be as straight-forward as I thought.

This is a genuine issue that I’d like help with (and discussed on the latest Wrong, but Useful) so please do help out.


I play a collectable card game called Magic: The Gathering. There are a variety of ways to play: some involving building a deck and taking it with you to a tournament, another involves going along, being given a selection of cards and building your deck with those. I’m organising an event where the cards are provided as you turn up but this is a slightly unusual version called a chaos draft. Essentially, 8 people will arrive and they’ll get three packs of cards each. The ‘chaos’ part is that all these packs are different and have different values. I’d like the players to have a roughly equal total values of packs and therein lies the problem.

More mathematically

There are 24 objects of varying values.

They are to be split into 8 groups of 3.

How can this be done so that the total value of each group has the least variation possible?

What I think so far

Some people on Twitter have pointed me towards bin-packing problems. These are on the right lines but don’t seem to quite do it as they’re concerned with packing a number of objects into the fewest number of bins possible.

Colin Wright said: “This seems to be a small example of a more general problem known to be NP-Complete. In light of that, why do you ask?” (This is what prompted this to become a blog post.) Brief, simplified description of what NP-Complete means.

Colin Beveridge mentioned the ideas along the lines of equal/fair sharing of cakes. That’s probably worth investigating further too.

It’s at times like these that I wish my computer programming skills were better (ie they actually existed) as I’m sure there’s ways to make progress. 24 items isn’t a huge number so it’s plausible to do this by brute force.

My best so far

Having placed the 24 items into 8 groups of three packs, I’ve calculated the standard deviation of those 8 values to be 1.84. My method wasn’t random but is not very systematic either. Can you do better?

If you fancy a go, here are the 24 values:


Thanks for looking. Thanks for any help you can give and, if there are any questions, please ask!

Learning Walk findings

I did a learning walk (pedagogical perambulation) recently in subjects that I personally have rarely seen taught with the main intention of finding out what else goes on in the school. This post just highlights some of what I saw and whether I think I can take anything away from it to use in maths. My take-aways are at the end.


In this lesson, Kat was helping the students explore human dignity. Four things struck me:

  • Liberal use of pictures. This just is more engaging/eye catching.
  • Very clear and explicit use of key words.
  • This was clearly part of a series of lessons. Students knew what they’d done previously and also where they were heading to while being able to make links between the different topics they’d looked at.
  • Kat was able to get emotional responses from students in the sense that they could feel empathy towards the people in the pictures. The students wider experiences of life (and TV) were directly useful to them in class.


This class had recently rotated in design tech groups and Kim was working on a ‘Jitter Bug’ project with them. I’ve seen students with the finished products previously (in maths) and I know that they like to show off what they’ve made. Kim had incorporated some changes to this project from previous years and was looking into increasing the challenge by (for example) including more use of formal circuit diagrams. She told me that this was at least partly to do with allowing students to develop their electronic skills earlier on in their school career (these were year 8s) because otherwise, when they pick up electronics later on, they’ve not encountered them.


A BTEC group was sitting and discussing the current theme of motif development. Shelley was excellent at asking questions and then probing the responses further and allowing students thinking  time. The students then moved onto developing the performance pieces and it was clear that they were all doing obviously useful things.

Whilst they were working, Shelley showed me some folders of their work and explained some of the structure of the course. I was particularly interested in the letter of application they’d written and the way that everything they were working on was clearly leading to a specific outcome. The idea that all the time they were building towards a culmination of work was evidently really motivating.

Food Tech

Wow! Sarah has warned me it’d be chaotic but I had no idea of what to expect. It was a whirlwind of activity with students all up and about doing something useful. They were making wraps in their zoned areas and some were washing up and/or putting away as well. The level of organisation was immense and there was a real sense of Sarah being everywhere and ‘juggling’ everything with super-clear routines. Again, there was a sense that everyone knew what to do and they were clear on why they were doing the things they were doing. There was a clear sense of ‘end goal’.

I liked the fact that students were developing practical skills (grating, chopping, julienning) but all within the context of making a wrap.


This was an interview lesson so there were several interviewees taking the lesson. I won’t comment on their lessons as I don’t have their permissions but I did learn something interesting from talking to the PE staff. They all told me that the head of faculty (James) was very clear on one thing: “Have as many students doing something as often as possible. No sitting around unnecessarily.”

It started raining so I left. Apparently I’m a “fair weather observer.”


Key words are something I could do more about. I’ll have a think about that.

A fairly easy thing to try to incorporate into my lessons is a greater use of pictures. I should be able to do that although I’m going to be careful to only use ones that are relevant. (I’ve seen maths lessons with pointless pictures for no reason!)

From Electronics, could we improve some of our projects to be more explicit about some of the skills we are developing for later years? I think we can.

PE’s take away is simple enough: Students should be mathsing as much as possible.

A bigger issue that was recurrent across all of these lessons was the theme of ‘working towards something bigger’.  This was incredibly clear in Dance and Food (and PE) – you’re working towards a performance or you’re working towards making a wrap. No questions, everyone got it. In Electronics, although it wasn’t necessary to be looking at the circuits to make the jitter bug, it was obvious to all students why you would be doing that. It seems natural enough that if you’re learning how to make something, you should be looking at how it works. RE was a little less obvious but Kat had done a good job of working together a variety of concepts into a bigger project and there certainly wasn’t any ‘why are we doing this?’ I suppose there is some element of natural curiosity for people to want to know how other humans think and feel but there still considerable skill employed in bringing this together.

In maths, we do work on projects in key stage 3. There is a ‘bigger picture’ there but it’s far less obvious than in the lessons I saw. I suspect that students often get lost in the exploring of the maths and aren’t really clear where they’re going or what the overall outcome should look like so I’m beginning to think if we should start off by showing them some examples of good maths work. We don’t do that at present and I think I will change this in future.

The best project we do from the point of view of a ‘clear outcome’ is the juice drink box project. It’s obvious to all what the point is and why the various aspects matter. I’ll have to talk to the other maths teachers about what else we should do to improve the other projects.

So, all in all, I learned and experienced loads. I actually spent about 50 minutes in these lessons in total and it was well worth it. I’d encourage you to go and see some other classes and my thanks to all the teachers involved.

Revision tool – GCSE Maths

I stumbled across this great set of flashcards from Ben at Tanner Maths (@tannermaths) while looking for revision ideas for my top set year 11s. I always worry that they spend too long working at the A and A* grade material and just assume they will be fine with the D, C and B topics.

I think this set is a good way to ‘check off’ these things by just having students look through them and any that they had to think about need to be kept and revised.

You can find the full sets here.