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To group or not to group….

… that is the question 😉

I went on a course at Swavesey Village College yesterday, basically talking about how they use mixed ability classes at KS3 to ensure they get high % of pupils making at least 3 sub levels of progress (and they do!)

They use lots of rich tasks (as you can imagine, I was VERY interested in that) and group work to ensure that everyone can communicate mathematically and gets a chance to understand the work set.  It also means that the less able have support and role models, and the more able can develop their communication, reasoning and proof skills.

The differentiation is built-in with rich tasks, but to ensure that no-one is left behind, they give out laminated ‘group role cards’, so students have roles within the group.  This seems to keep things moving nicely.

I teach only setted classes, but have quite a wide range of abilities in my AS-level group, so thought it might be good to try this with them.

We were starting the second Trigonometry chapter in Core 2, and I knew they were going to struggle, so it seemed the perfect opportunity to try this new strategy 🙂

I grouped them subtly so that each group contained 1 of my A-grade students, so there would be an ‘expert’ where needed.    I told them to assign their own roles from communicator, inclusion manager and presenter.  The communicator was the only one allowed to ask me questions, and the presenter would be the person doing the talking, either when I asked the group questions, or when I asked one from a group to go and help another group who were struggling with a concept the first group had cracked.  The inclusion manager had to ensure that everyone got their say, and that no-one got left behind.

Nrich suggest the following roles (I used an approximation for speed today)

To start them off, I set a puzzle of the week for them to do AS A GROUP.  They had to work on communication, and check their answers against other groups until we all agreed.  This done, the ice was broken, and we moved on.

The experiment was a great success, and students who would normally have struggled on in silence (I don’t know why they won’t just ask me – I’m very lovely really!?!) were discussing maths with others in the group and having lots of ‘lightbulb’ moments where they understood something new.   Those more able in the group were having to really articulate how they were doing/understanding stuff, and put it in a user-friendly way, which has forced them to really think about how they are thinking.  It also meant that I felt like I was only having to check 4 ‘lots’ of work, rather than the usual 14, as they were working in groups, so any problems to be addressed could be addressed together, with me only having to say it once per 4 people! 🙂

All in all, I was sold on the idea of group work, and am planning to implement lots of it along with my rich task work…

To the laminator, Batman!!

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Where to begin?

My task:  to rewrite our Y7 Scheme of Work so that our students get a solid grounding in the basics by the end of the year.

The overall aim:  Students leave Y7 knowing (and I mean really knowing) a method that they can use reliably every time to add/subtract/multiply/divide numbers.  They also get a healthy dose of problem-solving so that they know how to tackle problems, and aren’t afraid to do so.  Those that are capable will have looked at extending these methods to decimals and fractions, and negative numbers etc.

The problem?  Consolidation of the basic skills will involve a LOT of repetition.  How do I keep it interesting all the way through?  

If I had a ginormous budget, I’d get enough tablets (not netbooks – ours are rubbish, and take half the bloomin’ lesson to switch on/log in) for all the students to have access at least once a week to sites like mangahigh and sumdog.

These sites have done an amazing job of making learning and sums fun, offering students the opportunity to earn medals and compete with others in games or challenges that involve them practicing their basic skills.  Our students love it, although some have been put off by the rubbish netbooks that log you out when you are on your highest ever score so that it doesn’t save….

However, I don’t have a ginormous budget.  Also, I’m not the head of department, so what budget we do have isn’t under my control anyway.  

I’m currently thinking that we should use a ‘discover and do’ system.  You spend a lesson ‘discovering’ through investigations how to do something, and then a lesson or seven ‘doing’ this task.    Eg – You’d look at different methods of sharing to come up with some ways of doing division, then spend time practicing those skills.  

Students would have the opportunity to graduate to the next level of difficulty by passing a test specific to what they had been studying in their current level, and what was in the level below.  That way, they wouldn’t have to start multiplying with decimals until they had definitely mastered multiplying with integers.  Logistically this will be tricky, but we will just have to reshuffle the groups regularly based on these tests.  No-one moves down, only up, but only when they’re ready.

By the end of the year, we should have students in the sets we would have ended up with under the current system, but without those tricky gaps in their understanding that sometimes happen if you set them after one generic test.

I will still aim to cover the NC, although some will get further than others by graduating quickly.   Some may not get to algebra or probability by the end of Y7, but if they are incapable of a secure understanding of the basics of number, then I’m not sure there would be any point teaching them that yet anyway.   Year 8 would be a little bit of basics regularly, but lots of algebra, SSM and HD to make up for what we missed in Y7.  Hopefully this will be much easier to grasp when you’re not spending 30 seconds of your 1 minute working-out-time figuring out 6×7, but can actually focus on the question being asked and the process used to answer it.

I also plan to do some videos of how to do the basics, so that students can go home and watch it and practice (Flipped Classroom-style…)  If I do, they will be available via for all to use.  I shall hopefully also be able to make our SoW available to anyone else who wants to try it. 

Thoughts/suggestions/constructive criticism welcomed…..  This is currently just me thinking aloud!

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Rich tasks, or being ‘less helpful’. *Updated 6/5

Dan Meyer has a great point here:

We should be less helpful as teachers.  Our students are spoonfed pretty much everything they do in maths, and it’s made them overly dependent.   How many time have you been frustrated by a student who has just come straight up to ask how to do something, without even trying it first?

I thought it might be good to collate a bunch of tasks where we just give students a starting point, hopefully something that will intrigue them, and then just watch them go!

I’ve begun a collection of these tasks, and using the truly astonishingly splendiferous (yes, I made this word up) iBooks Author, I have put them together in a book.  I’ve got 7 tasks so far (with extensions) but here it is:

****UPDATED VERSION****  Thanks to all who have made suggestions – still a work in progress 🙂

Investigations / rich tasks v1.2

FYI:  473 sweets in the jar – will add that into next update (run out of energy…!)

There is also an iBooks version, but wordpress won’t support me sharing that type of file.  Once it’s finished, I’ll upload it onto the iBooks store for all of you lucky enough to have an iPad to teach with 🙂

The final version will have an index etc, so you can easily get to certain tasks, even in the pdf version.

I’m fairly imaginative, but I don’t think I can think of all the best ideas for this all on my own.   There are lots of you lovely clever teachers out there reading this that will have been thinking ‘I’ve got a great task for that!’, and I’d like to beg invite you to share them with me/us.

If you have a task to contribute, please pop it in a comment, or email me here: and I’ll do my best to add them all in.

I will regularly update the pdf version here, so you can keep up-to-date.  Once I think we’ve got enough, I’ll finalise it, and set up a page where you can download it (for free) and add it to the iBooks store (also free), and we can share it with the world 🙂


Puzzles, Imagination and Resilience

I read a brief summary of a paper a couple of weeks ago (in TESPro 24/2/12) about ‘mathematical resilience’.  The paper is by Sue Johnston-Wilder and Clare Lee, and in it they describe how students should learn to talk like mathematicians, possessing the language necessary to express their understanding – or lack thereof – any given topic.  The more they talk like mathematicians, the more they feel that they are capable of understanding maths.  ‘Mathematical resilience is about…confidence in what is understood and knowledge about what to do if you do not understand.  Pupil’s confidence increased, and they felt supported in answering a challenging task and knew what to do to overcome any barriers that they encountered.’

We have all felt the frustration when a student comes to you and says ‘I don’t get it’, when you know full well that they have simply looked once at the question and given up immediately.  You know as a teacher that they could have got at least some of the way by simply trying something, or asking the people around them what approaches they were taking, but they didn’t.  They just gave up.  

I want my learners to be resilient, to be unafraid to try things.  That is why I use puzzles.

I have ‘Puzzle Wednesdays’ (which is the day I see all but 1 of my classes -they have puzzle thursdays…!)

On Puzzle Wednesdays, each class, regardless of ‘ability’ will have a go at some puzzles.  I  set a puzzle of the week (which I now upload into the POTW section on this blog) which contains two puzzles.  One is usually visual/spatial, and one is more numerical in nature.    The level of arithmetical understanding I know a class possesses will normally determine which puzzle I give them to try, but those that get the answer sooner will be given the other to do as well. Students often choose to work together, which is one of the best bits for me.  They are talking like mathematicians without me even needing to ask 🙂

I also have a class set of puzzle cubes ( which I think teach the following skills:  perseverance, logic, reasoning, spatial awareness, and the understanding that just because you think you are good at maths does not mean you can automatically solve this the fastest…. (e.g. humility!)  I use these occasionally, although I always end up being the one to put them back together!  The students have not got bored of them in all the time I’ve been using them, as there are 32 different ones to try, and you don’t tend to remember how you did them anyway.

I have a large collection of puzzles on the site too – 

Puzzle Wednesdays takes up a lot of my teaching time with each group.  I sometimes only do it for half a lesson, but that is still 12.5% of their maths lessons for the week.   I don’t do this because of the new emphasis in the syllabus on problem solving, and the new styles of question that are appearing in exam papers (although it helps!)  I do this because I believe that being a mathematician is not about being able to do the hardest arithmetic, but about being an incorrigible problem-solver.  It should bug you if there is a problem you can’t seem to solve.  It should be eternally present in the back of your mind until you can crack it.

I use the analogy with students that you could have a large toolbox, full of tools like a saw, hammer, drill etc, all of which you know how to use.  Having this toolbox does not mean you can automatically build a garden shed.  You probably couldn’t build the shed without them, but more is required.  How should the bits fit together?  How will you make sure it doesn’t leak?  All of this requires thought, and a whole different skill set. 

You can learn all the tools of arithmetic, and possess all those skills, but unless you are unafraid to try out problems with different approaches (without someone telling you what steps to take), you are not a mathematician. 

To be a mathematician, I would say that the most important skill you need is imagination.  

What happens if I…?  But what if I changed this bit…?  How can I model this situation…?


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Similar Triangles to measure the height of a student…

Well, today’s Y9 lesson was very ‘creative’…  We have been looking at similar triangles, and I found a useful resource on TES (that I now can’t find at home… will add link later).  The resource asks students to match up the shape that is similar to the one given.  It then leads on to show similar triangles like this:


We discussed why they are similar (angles all the same) and that therefore one was an enlargment of the other.

We worked out the scale factor, and therefore the missing sides on a couple of examples, which was the level 8 skill I wanted them to at least try.

I then had a moment of stupidity brainwave…

We’ll measure the height of Bradley!

I got a student to lie on the floor, and positioned Bradley across the room, and the metre ruler at the correct position so that the person-on-floor(D) had lined up the top of the ruler(E) with the top of Bradley’s head(A).    We then measured the distance from person-on-floor to Bradley’s feet(BD), and from person-on-floor to the bottom of the metre ruler(CD).

I drew up the diagram (as above) on the board, and we worked out the scale factor of the base of the triangle, and used that to work out how tall Bradley was 🙂

We discussed how it might have been easier to just measure him, but that we could use the technique for other stuff that wouldn’t be so easy.

Discussion ensued about measuring the height of the Eiffel Tower etc, or simply a tree or lamppost, and how you could make it work without having to lie down on the floor too….!

Very productive lesson, and most seemed to grasp the concept well.   Hopefully they’ll remember it!

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Puzzle of the Week

22/6/15 POTW

15/6/15 POTW

1/6/15 POTW

24/3/15 POTW

17/3/15 POTW

9/3/15 POTW

23/2/15 POTW

9/2/15 POTW

2/2/15 POTW

26/1/15 POTW

19/1/15 POTW

12/1/15 POTW

8/12/14 POTW

1/12/14 POTW

24/11/14 POTW

17/11/14 POTW

10/11/14 POTW

3/11/14 POTW

20/10/14 POTW

13/10/14 POTW

6/10/14 POTW

29/9/14 POTW

22/9/14 POTW

15/9/14 POTW

8/9/14 POTW

14/7/14 POTW

7/7/14 POTW

30/6/14 POTW

22/6/14 POTW

15/6/14 POTW

8/6/14 POTW

2/6/14 POTW

19/5/14 POTW

12/5/14 POTW

6/5/14 POTW

28/4/14 POTW

22/4/14 POTW

30/3/14 POTW

23/3/14 POTW

17/3/14 POTW

10/3/14 POTW

3/3/14 POTW

24/2/14 POTW

10/2/14 POTW

3/2/14 POTW

27/1/14 POTW

20/1/14 POTW

13/1/14 POTW

6/1/14 POTW

15/12/13 POTW

8/12/13 POTW

1/12/13 POTW

24/11/13 POTW

17/11/13 POTW

10/11/13 POTW

20/10/13 POTW

13/10/13 POTW

6/10/13 POTW

30/9/13 POTW

22/9/13 POTW

15/9/13 POTW

15/7/13 POTW

8/7/13 POTW

1/7/13 POTW

24/6/13 POTW

17/6/13 POTW

10/6/13 POTW

3/6/13 POTW

20/5/13 POTW

13/5/13 POTW

6/5/13 POTW

28/4/13 POTW

21/4/13 POTW

15/4/13 POTW

25/3/13 POTW

18/3/13 POTW

11/3/13 POTW

4/3/13 POTW

25/2/13 POTW

18/2/13 POTW

4/2/13 POTW

28/1/13 POTW

21/1/13 POTW

14/1/13 POTW

7/1/13 POTW

16/12/12 POTW

9/12/12 POTW

2/12/12 POTW

25/11/12 POTW

18/11/12 POTW

11/11/12 POTW

4/11/12 POTW

21/10/12 POTW

14/10/12 POTW

7/10/12 POTW

30/9/12 POTW

23/9/12 POTW

16/9/12 POTW

10/9/12 POTW

13/7/12 POTW

6/7/12 POTW

29/6/12 POTW

22/6/12 POTW

15/6/12 POTW

25/5/12 POTW

18/5/12 POTW

11/5/12 POTW

4/5/12 POTW

27/4/12 POTW

30/3/12 POTW

23/3/12 POTW

16/3/12 POTW

9/3/12 POTW

5/3/12 POTW

How will you use yours?

I email this out to staff every Friday to have a go.   For students, Wednesday is Puzzle Day – it might only be the starter, but we do a little bit of problem solving each week to keep our brains working 🙂

Answers at bottom of ppt (in notes section) – no cheating now…! 😉


Self-assessment by topic


Self-assessment by topic


So this week I have had to admit that my assessment (particularly comments in books etc) could be better…

Being a bit lazy, I decided that I couldn’t be bothered to research the levels for each topic each time I do a new topic, so instead I have spent the whole weekend making an online resource that does all that for me in one place 🙂

Check it out, and let me know what you think!  KS4 to follow when I get another burst of energy….!

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Teaching bias without teaching bias…

So, in the spirit of early-onset enthusiasm, here is my next post 🙂

This week, I have tried a new approach to teaching questionnaires.  I normally go with the whole ‘let’s find out about what TV programmes people like’ *yawns* and write up our results’ approach.  Not this week.

I decided to try something completely different with my Y8 top set  – I wrote a (terrible) questionnaire entitled ‘Mrs Hughes’ awesome survey’, and gave them a copy as they came into the room.  I then read out the questions, and got them to vote (hands up) for each answer, choosing the most popular answer as the one I would list on the board.

The questions were classic examples of bias, poor wording, totally nonsensical questions, and overcomplicated language.  

For example, question 1 was – Who is the best maths teacher in the whole school?  

A) Mrs Hughes (that’s me)         B) *a PE teacher’s name         C) *the Principal’s name         D) other

I went through the first 5 questions before they really started to openly criticise the questions, and at that point, I feigned surprise that they were confused by my questions – you mean my survey isn’t awesome?!?

I gave them 1 minute in pairs to talk to each other and answer the question ‘what do you think of my survey?’

At the end of the minute I dinged my little bell (like you find on old-fashioned hotel front desks – every teacher should have one!) so they would know to stop.  I got them to tell me their answers, and without even trying, I’d got them talking about bias, and basically listing all the things you shouldn’t do on a questionnaire. 😀

They then worked in their pairs on a specific question, different for each pair, to tell me what was good/bad about it, and where it could be improved.  Instead of telling me at the end of the 5 minutes (*ding!*) I got them to join up with another pair and explain their answers to each other.  The mathematical language being used was brilliant, and they were all actively involved in articulating their thought processes.

We shared ideas as a class discussion, and I held my tongue as far as possible and left them to be the leaders of their own learning on this (really really really hard!)

Next job was to discuss uses of questionnaires in real life, and I set them the challenge of finding some information from other students about their thoughts on our current BSF project (we are getting lots of new bits and refurbishing all the old bits) or the fact that we are in the process of becoming an academy.  I wanted it to be an evocative topic that might inspire some debate/controversy.

They were to write one question each, but to write two versions of the question: one fair, one biased.   This allowed me to see who really understood the concept and who didn’t.  They also had to give some thought to the data collection process – would their question be an easy one to ‘graph’ afterwards?  

After the allotted time (*ding!* – I love my bell..) I got them to join again with another pair, and this time to swap books and peer assess the others’ questions.  They had to give 2 things they liked, and 1 possible improvement (written, ideally).

At the end of the lesson, I reminded them that I hadn’t written the objectives on the board as I wanted them to work them out themselves.   They were given 1 minute to discuss what they thought the objectives were, then I asked several students to feed back.  

Here’s what they said:  

“You wanted us to learn how to write good questions.”

“You wanted us to learn to work out what questions to ask.”

“To know what bias is about and how to write fair questions.”

“To be able to plan how to collect our data.”

I then popped up my IE window on the IWB, and showed them the level 7 descriptor for HD:

‘Explore problems using statistical methods, frame questions, identify possible sources of bias and plan how to minimise it’.

I love it when that sort of risk pays off 🙂


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Do something that scares you!

Hello, good evening, and welcome to this, my inaugural blog.

My name is Emily Hughes, and I’m a maths teacher, mum, website creator ( and current Twitter addict.

I’ve only recently started using Twitter after realising quite how many inspirational maths teachers are on there, sharing ideas and resources, but over the last couple of weeks I have seen so many inspirational blogs by others, sharing ‘outside the box’ teaching ideas, that I found myself thinking “I should do that too…”

As soon as the thought hit me, my scaredy-cat brain kicked in with a million reasons why I shouldn’t do it – it’ll take up too much time, I’ll have to actually start doing these innovative lessons that push boundaries on a regular basis, not just when a moment of inspiration happens to hit, etc, etc.  I’ve obviously decided however to overrule my common sense nerves and go ahead and do it anyway!

My thoughts on Maths teaching:

  • If students enjoy it, then they are more likely to want to learn, and less likely to mess around .
  • If I enjoy it, I’m more likely to stay (relatively) sane, and happiness tends to be infectious 🙂
  • If I always do things the way I’ve always done things before, then I’ll always get the same results I did before… How on earth can I improve like that?
  • Students are people too – we’ve all had bad days, where we carry our mood round with us – someone having a go at you is not likely to snap you out of your mood, but a smile might…
  • Even the most motivated, enthusiastic of us will struggle to concentrate when someone is talking at us for ages and ages and ages… (as one student explained to me – “when Mrs X talks, it’s like Homer Simpson – I get the little monkey clanging his cymbals in my head!” – and he’s an A-level student!)
  • You learn more by discovery than by instruction. (“Give a man a fish…” and all that.)

I could go on for a while (ask any of my colleagues…) but I shall stop there.  For now.   I’ll be back soon with some tales from the classroom – the tale of Y8 and the biased questionnaire perhaps…  Before I go though, I’d like to encourage you to do something that scares you too – it might turn out to be less frightening than you thought!

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