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:

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

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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:

farey

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.)

Neat.

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

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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.

What does “doing” Growth Mindset look like?

The first thing I need to make clear is that I am not the expert able to answer this question comprehensively – well not yet, anyway. (That’s a Growth Mindset, by the way…)

I would love you to read this and help me answer my question. I’ve read a bit myself from esteemed academics such as Carol Dweck and @JoBoaler, seen fabulous teachers like @Helenhindle1 talk about how they do it, but not really done it in my classroom yet. I’d like to think that I use a lot of the language of growth mindset routinely, but one of my targets for next year is to do more to instil a growth mindset in my students.

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What is a Growth Mindset?

My view: at its most basic it is simply students believing in themselves, having greater resilience and recognising that their abilities in Mathematics (or anything else for that matter) are not fixed and that by applying themselves consistently and working at it, they will “get better” at maths.  And it is not just about encouraging lower attaining students.  As Jo Boaler points out in in this article we need to avoid the label “smart” to prevent those kids baulking at challenging problems that they might get wrong first time round.

Getting the message across

What we are trying to do here is genuinely change students’ self-perception. Just telling students to “change their mindset” is likely to backfire. So we need to convince them why it is true. This is not easy and isn’t going to happen quickly.

Growth Mindset Maths is a great site which contains lots of resources to use.

This lesson plan that has been developed by Khan Academy and PERTS (Stanford Univ.) looks like a great way to introduce Growth Mindset for secondary students.  We all need to develop a good “Personal story” of when we overcame challenges and adopted a growth mindset. PERTS are developing a Mindset Kit which is worth keeping an eye on.

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I’m sure there are others out there who have developed resources too. If this is you, please get in touch!

So, here is my list of things I want to do next year.  What have I missed? Please let me know!

  • Specific lessons. At the beginning of the year, we can spend some lesson time doing activities such as these.  There is a need to introduce the ideas and talk about the language we will use in the classroom for the rest of the year.  Do we need to spend further lesson time on specific growth mindset tasks later in the year? I guess I will take a wait-and-see approach to that.
  • Posters. This really should be a whole school initiative.  Some of them remind me of my time in corporate life when companies went through a phase of putting up “inspirational” posters with words like “Success” and a picture of a man standing on top of a mountain looking very pleased with himself. There may be some cynical reaction to posters but I feel overall they are a useful part of the mix.
  • Celebrating success. And particularly highlighting “Success Stories” – individual students who have adopted a growth mindset, worked hard and have the results to show for it.
  • Everyday language.  Obviously using it yourself as a teacher, but also picking kids up on it every time.
  • Communication with parents.  Ultimately maybe actually trying to run sessions with parents? I don’t know successful that would be, but at the very least using parents’ evenings as an opportunity to use the right language – having a few of those posters prominently displayed will help.
  • Written feedback. Whether it is student reports / profiles or written feedback as part of marking, again being diligent to use the right language in that feedback.

Finally, I love the beginning of a new BBC programme called Kick Sum Maths.  The first 2 minutes or so of this ticks all the boxes in my view and would make a good introduction.

The question of Mixed Attainment teaching

A logical conclusion of the Growth Mindset philosophy may be that you do away with sets and this is certain something Jo Boaler strongly advocates. However, few UK schools have done this. I’ve struggled to find recent data, but an Ofsted survey from 2003-4 found that 17% of schools taught in mixed ability groups at KS3.  Tory and Labour Government policy since this time has tended to promote setting, so I can only imagine that number has gone down since. A more recent blog by Chris Husbands, Director of IoE concludes that the evidence of the effectiveness of setting is “nuanced”.  I can’t help feeling that behind all of this, there is pressure from parents to maintain sets, particularly the more vociferous middle-class parents who are less likely to have kids stuck in the bottom set.

Personally I don’t have a strong view on this. I would be interested to see mixed attainment teaching in practice before forming that view.  But I do feel that most schools and most teachers, would find it a big challenge to switch to teaching in mixed attainment groups.  Does it require a higher level of skill in teaching to differentiate more widely and use mixed-attainment group work effectively? Or is it a question of just getting used to it and adapting to a different way of doing things?

Place Value – what is 34 tens and 15 ones?

I’ve been doing a Lesson Study this week with 2 colleagues on Place Value with a lower attaining Year 7 group. I might write about that later, but in the meantime, here is one of the resources that we have developed. I think it’s hugely differentiated, fairly low threshold high ceiling task.

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In the lesson, I just wrote a few of these on the board.  It was something I hadn’t used before so I went away thinking about the range of difficulty in these types of questions and wrote a series of questions here.