What happens when you put a group of Year 10s in a hall with a group of Year 6s

I started at a new school this year.  I could write pages about this experience, but that’s not what this blog is for, I want to share things that are genuinely useful to other Maths teachers!

My new school is much nearer to my home, and one of its feeder primary schools is where my own children go.  I was Treasurer of the PTFA there some years ago so have lots of connections with the primary school.  I got talking to one of the awesome teachers there and we discussed bringing a group of my Year 10s to help with tutoring some their Year 6 pupils.

Today was our first 30 minute session.  I knew I wouldn’t have much preparation time with my Year 10s, so I took the approach of being fairly prescriptive putting together a sheet of tasks for them.

It went well; very quickly, in fact.  I gathered my group together at the end and told them how impressed I was with their coaching.  I had a fairly mixed group of 13 students, some capable mathematicians amongst them but also some students that don’t show the best focus in their own maths lessons whom I was quite concerned about.  But as soon as the Year 6s entered the hall, they suddenly took their job very seriously and made great efforts to engage the pupils.

Many of the Year 10s found that the Year 6s already had a good understanding of place value and they reported that they found the task quite easy.  As teachers, we know how to use questioning to really probe depth of understanding, but maybe this is too much to expect of a 14 year old.  What intrigued me was the variety of ways my students responded to this challenge with some of them going completely off-piste and explaining pi!  But I want to encourage this.  It’s a luxury to have no specific learning objectives to fulfil or curriculum to follow.  We are doing it 3.00-3.30 on a Friday afternoon, which I’m pretty sure means the Year 6 pupils are not missing critical learning time!

Looking forward, I want my Year 10s to take a gradually greater responsibly for planning activities.  We have agreed, that we are going to have some element of “game” in every session and we started looking at some of the huge range of Nrich activities.  I’ve put together a Google doc for next week to allow the Year 10s to collaborate and contribute ideas.  I not expecting them all to contribute, but I think a few will.

I’m also really enjoying discovering some resources and games that I’m sure will be useful in my own teaching practice.  I’m relishing not having to follow a scheme of work.  My only objective is to keep everyone engaged and learning and to “make maths fun”. If we achieve this, it’s going to make me think long and hard about how we teach maths at secondary!

If anyone has the opportunity to do this sort of partnership, or in fact is already doing it, then please get in touch by leaving a comment below.  It would be fascinating to share ideas. Also, if you have any good ideas of resources, then let me know.  I have many weeks ahead to fill!


Equations of simple Straight Line Graphs (prior to y=mx+c) using Mini-whiteboards

These slides are in groups of 4 designed to be used as a mini-whiteboard exercise for groups that need reinforcement on equations of the more basic straight-line graphs that can be determined by looking at patterns in the co-ordinates of points on the line (i.e. all points have a y-coordinate of -4 means the line is y=-4)Screen Shot 2015-09-20 at 20.25.38

The idea is that you show the line itself first and ask students to show on their mini-whiteboards the equation of the line if they know it. If they don’t, then showing them the next slide with a bunch of co-ordinates provides the scaffolding. The next slide then reveals the equation and the final slide is to make the point that the coordinates themselves are arbitrary.

Learning times tables – Number Happy Families

Anyone looking for a simple maths game for end of term Year 7 lessons? Here’s one.

mho maths

Embedded image permalinkI’ve always felt that secure knowledge of times tables at Year 7 is so important simply because it gives kids the confidence to engage in so many maths topics covered in that year.  As such any opportunity to practice is good even when it is in a simple game like this.

A Simple Factors and Multiples Team Game for 3-4 players

I came up with this idea whilst playing the traditional Happy Families card game with my family when on holiday. Kids seem to love this game – could I create a maths game as engaging?

I’ve tried this several times with Year 7 classes, playing in teams of 3 or 4 and they love it.

It takes very little preparation or explanation – in fact the students make the resources themselves!

The Cards

You need a set of 36 blank cards for each team. Anything will do.  I spent…

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Turning a Numberphile video into a lesson – Farey Addition of Fractions

I love Numberphile videos, but then I would, I am a Maths teacher. What really matters is if my students like them.  I have shown them to various classes and mostly they have gone down pretty well.  At A Level especially, they are great as an “interesting interval” in a long lesson.  This one, however, is the first time I have tried to create an actual lesson out of it.  I used it for the first time today with a fairly high attaining Year 9 class and it went pretty well. They quite liked it when I told them it was degree level! It took about 35-40 mins in total, but if you also get them drawing the circles it could be longer. Below is my description of the lesson with links to the relevant sections of the video and the resources I used.

Farey Addition of Fractions and Ford Circles

Start of video: It starts pretty quickly so make sure they are ready. Lots of opportunities to pause and ask questions in this first section.  E.g.

Pause at 0:23.  What is wrong?

Pause 1:37.  What do you think he is going to say?

Pause 4:33. At this stage, get students to create their own number line.  Today, I just let my students go freestyle in their books.  You could give them a simple number line printed out, something like this:

Screen Shot 2015-07-13 at 20.31.09

Or give them something a bit more structured with lines on it like this.

Screen Shot 2015-07-13 at 20.32.29

Give them about 10 mins on this task.  They don’t need to measure anything, they can just do it by eye. It provides good opportunity for asking questions like “is 3/5 bigger than 2/3?” “How do you know?”  Put a timer on and see who can do the most in 10 minutes.

Then start the video again. He looks at all fractions where q<=234. This might be worth explaining.  There are 20,000 of them, apparently. Again, might be worth touching on briefly why is it 20,000. We just look at a section of these around 1/3:


Pause 7:10.  Give them out the sheet of numbers, in order to hunt the Farey additions.  This isn’t the best resolution as I have screen-grabbed from the video, but it worked well enough as a print out 4 per page.  Give them 5-10 mins (with calculators).  If they feel like they have done enough, ask them to investigate the ones that don’t work.  If they are really thinking they might get the next bit on their own.

The video then shows an explanation of examples where it doesn’t appear to work, but if you cancel them down…

Then move onto drawing circles on the number line.  The explanation in the video at this point isn’t brilliant and it would be nice for students to discover that when they draw the circles they get this, with the big circles on the end just touching the other circles. However, I shied away from this as the circles soon get very small and maybe too hard to draw. But it might be good to provide a print out with the two big circles at 0 and 1 and then get them to draw the circles at 1/2, 1/3 2/3, ¼, ¾, etc.  You’d have to think carefully how you scaled it.  Alternatively you might want to work out how do it on Geogebra if you have access to tablets / computers.  Let me know how you get on!

Using a quadratic and a straight line to do simple multiplication

So, here’s something cool that Johnny Ball showed me that I hadn’t seen before.  I love it when this happens although I fear that as the years roll on and I become a wizened old maths teacher it may happen less and less…

Anyway, here’s a picture to explain, click on it to move the points:

Screen Shot 2015-07-10 at 07.12.35Multiply the moduli of the x-coordinates of the two points where the line intersects the curve and you get the y coordinate where the line intersects the y-axis. (Or another way of looking at it, multiply the x co-ordinates and you get the negative of the y-axis intersect.)


The proof for this is very satisfying and would make a nice extension exercise for Year 12 C1 class. Here are my scribbles. Enjoy!


Initial thoughts on More than the Sum of Their Parts

There was an impressive line-up of Maths “celebrities” on the programme for the inaugural conference of the 6 London Maths Hubs “More Than The Sum Of Their Parts Conference 2015: Raising Standards Together” held in Chobham Academy including Johnny Ball, Rob Eastaway, Matt Parker.  Interesting though it is to meet these people, I’m generally more interested in meeting other maths teachers and doing maths together. I couldn’t help feeling that today was about Maths Hubs trying to find a way to spend their money.

Maybe it was my choice of sessions, but I didn’t find myself doing as much maths as I would have liked.  In my book, successful CPD contains 2 things:

  • Me getting engaged in some maths I haven’t seen before
  • Having something I can take back to the classroom

Overall I had an interesting and inspiring day even though not all of it ticked both these boxes.  I’m out of time now to write about the individual sessions.  There are quite a few things I want to now explore further which is a sign of a successful day. Never enough time though…

Lesson Study – the best type of CPD you can do in school!

Last week, I joined two colleagues to carry out a Lesson Study looking at Decimal Place Value with Year 7.  The actual resources we used are here, this is just a quick reflection on the process.

There are various ways you can do lesson study, but ours looked like this:

  • 3 consecutive lessons taught to one class by their normal teachers (this happened to be me)
  • 4 reflection / planning sessions: 1 before the lessons, 2 in between and 1 straight after the 3rd lesson. These were about 30 mins each.
  • The 2 other teachers arranged cover for the 3 lessons they missed and they both observed all 3 lessons.
  • Before the 1st lesson, we identified 3 students in the class whom they were to observe closely and have a quick chat with at the end of each lesson.

It was intense, but highly rewarding.  It also had quite a high impact in terms of lessons requiring cover.  I have done lesson studies in other formats before, e.g. over a longer period of time where each teacher teaches the same single lesson to their own class over a number of weeks with the others observing.  My experience was that this was the best for a number of reasons:

  • Seeing a series of lessons is how we actually teach and it is useful to see the learning building from one lesson to the next
  • The observing teachers get to know the students and observe and understand their learning needs
  • There is no such thing as a “perfect way to teach Topic X” as every class is different and so comparing the “same” lesson between different classes is not as instructive as watching the learning develop over a series of lessons.

Of course, another reason this worked so well was my excellent colleagues who had so many interesting things to say about the lesson.  I learned a lot.

I’m sure we have all sat through INSET sessions where you simply feel like you are not likely to use the ideas any time soon in your classroom, because they are generic whole-school sessions. It’s looking like a lot of next year’s twilight INSET time at my current school will be allocated for Lesson Study next year.  I reckon that’s the best CPD you can do.  It’s an effort to set it up, but well worth it.

Ideas for better maths teaching