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Flipping Y12 Further Maths

We have reached that time of the year where panic kicks in. There are only three weeks until the Further Pure 1 exam, and we are still working on the last couple of chapters.

I decided to try to maximise our class time by setting pre-homework. I’ve read about ‘the flipped classroom’, but it’s not something I’ve felt my classes were ready for yet. We have no VLE at the moment, so there is nowhere online I can leave work for them. After an attempt with emailing, I decided I needed a better plan.

I signed up to Edmodo.com, and set up a group for them. I then emailed out the group code, and asked them to sign up. On Edmodo, I have put all the links to revision sites I can find for each topic, a picture of the useful pages in the formula book that they will be given in the exam (useful to know what you don’t need to remember!) and an assignment for the next lesson.

Last week, I set them a couple of videos on the topic of hyperbolas, parabolas and ellipses. There were a couple of random pages, but it was mostly from khan academy.

Khan academy is a site set up so that anyone, anywhere can have access to lessons on all sorts of topics. It seems to cover pretty much everything in maths that I need it to!

The students had to watch the videos before the lesson on Friday, so that they had a head-start on the topic, if nothing else. It then meant that they could get cracking on the work straight away, and I was able to give immediate individual help to those that still needed it, while those that felt confident could make a start, and ask if they got stuck.

They all agree that the videos are useful (although some were more useful than others…), and I think it’s a model we will continue with.

The advantages are that each student can learn at their own pace, and can watch over and over if needed, or stop and rewind, without feeling self-conscious about not getting it as fast as everyone else.

I shall keep you posted about future developments 🙂

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Independence

I wanted to see how well my students could cope with the idea of being given a simple problem, and being ‘let loose’ to investigate it.   No spoon-feeding from the teacher, no coursework style suggestions that in order to get full marks, they would have to use algebra (hint hint…).  Just ‘go for it’.

I was pleasantly surprised!

The problem was:  What rectangles can you find that have the same area and perimeter? (from the newest version of ‘rich tasks – soon to be uploaded!)

Some predictably just spent the lesson trying out different numbers, and got no further.  Some went off on fantastic tangents about triangles, or putting together 4×4  squares to make a rectangle.  

At the start of the second lesson, I asked them what they wanted to share.  No-one shared actual measurements of rectangles that work.  They shared things like:

  • you can’t have a side that’s 1.  
  • you can’t have a side that’s 2. 
  • I think they have to be even numbers.
  • I think they have to be at least one even number.

We were able to try to figure out why the side of 2 didn’t work – there is a pattern – and then I showed them on the board with a rectangle, a 2 and an x, why the area would always be 2x and the perimeter 2x + 4.  

This sparked quite a bit of algebra in the room (okay, maybe that counted as a hint…).

The TA’s had been furiously scribbling together, and had proudly come up with some algebra to show what relationship between the numbers was needed, and that meant they were able to go and support some students with their algebra.  I deliberately stayed out of it, as I wanted them to have that sense of independence.  Having to ask a TA to check over your algebra is not the same as needing the teacher to show you how.  It meant they retained control of their work.  

I’d told them they needed some form of write-up to show me afterwards.  

They were rightly proud of what they’d achieved by the end of the two lessons, and the write-ups look very impressive – some really good, systematic approaches, and good recording techniques too.

The most important factor for me though was that they’d done it all on their own.  Maths in the big wide world after school is about seeing a problem and figuring out what to do to solve it.  No-one will spoon feed them the methods then.  More independent challenges to follow methinks!

🙂

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Finding and fixing misconceptions

Right, I’m back.  It was a very restful Easter break, due to me managing to pull/sprain an intercostal (between your ribs) muscle from coughing too hard.  As it’s not the kind of muscle you can ‘rest’, it rather jolly hurt, and I didn’t get a lot done 😦  The worst bit is that the cough is still going! (new school = new germs) grrrr.

Anyway.  

This week I have mostly been addressing misconceptions.  

I asked my Y9 (level 6-7) group to do the sum 700-182 on the board.  I even set it out for them.  It took 4 people, correcting each other’s mistakes, to finally get the correct answer.  They simply couldn’t cope with borrowing when there were two zeroes.

The original plan for the lesson had been to get them to look at any method for add, subtract, multiply or divide, and tell me WHY it works.  Why is that the algorithm that we follow, and can you explain to me why we do it that way?

The new plan obviously became for all of them to do borrowing as their method!  I gave the example of column addition and carrying to show them what I meant.

If you’re adding 312 + 59, imagine it’s in money.  HOWEVER there has been a new rule introduced that says that only pound coins, 10p pieces, and pennies are allowed.    So you have 3 pound coins, one 10p and 2 pennies.

If you add five 10p’s and 9 pennies to that, you’ll have 11 pennies, six 10p’s and 3 pounds.    Who wants to be given a whole load of pennies though?!?  It would be much better to change 10 of them for a 10p piece, and then it’s easier for everyone.  That’s where the little ‘carry 1’ comes in, as it reminds you about the extra 10p.

(This works better in numbers on my board…!)

The idea was to get them using the money analogy to identify the fact that borrowing in maths is just the equivalent of changing a 10p for 10 pennies, so you have enough pennies to ‘pay’ with.  

I told them they had the rest of the lesson to come up with their own explanation, and then the following day, I made them do a presentation in their pairs/threes to the rest of the class on what they had come up with.    I was pleasantly surprised by many of the presentations, as they had clearly ‘got’ it. Some obviously just got up and showed us the method (there’s always one) but at least they hopefully addressed their issues with the method in doing so!

I finished with showing them the original problem again:  700-182.

Imagine it’s £7 take £1.82.  How do we get change?

Lots still did borrow from H to put into T column, then borrow from T to put into U, but quite a few came up with the strategy of changing one pound coin into 9x10p and 10x1p  🙂

Y8 did a variety of methods, and we addressed lots of confused ideas about things like how to deal with remainders when you divide, so as to end up with a decimal answer instead of having to write ‘remainder 4’. Also,  I think I finally get Napier’s Bones now, so a useful lesson on lots of levels!

With my level 2-4 Y7 group, I showed them the money analogy, and got them to practice lots of sums until they were happy with it.  Some needed to have a different way of thinking about it, and my TA was explaining in terms of packets of sweets (10 in a pack – if you don’t have enough to give out, you have to open a new pack/box of packs) and ‘borrowing from your next-door-neighbour’.    They all had managed by the end to successfully answer questions, going up to 3 digit numbers, which for them is a big deal.  

It did scare me though, that my students could be so confused about a method they’ve been ‘doing’ since primary school.  Wonder what else I’m taking for granted that they can do, when they actually can’t….? 

 

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