Another ‘vary and twist’. This time on inverse proportion. Download it here.

I have added a section at the top making explicit that students should make an expectation of the answer before working it out, as I think this is where the power of these types of activity come from.

My thinking

  1. A question to start
  2. Does swapping x and y matter? If not, why not?
  3. Doubling x, what happens to y? What you expect?
  4. Doubling y in our initial relationship. Why does this differ in it’s result from doubling x from before?
  5. As above, but for x
  6. What happens if we half the value of x we want? Maybe this should be moved up in the list to question 4.
  7. A multiplication of 10 from the original. Does it hold up to more than halving?
  8. Now we’re finding x not y!
  9. We’ve doubled the y. What happens to x? Does the relationship work both ways?
  10. A decimal answer

As always, feedback would be lovely. I’m not sure I’ve correctly hit the sweet spot between making links and confusing the pupils. I’m also not sure that they flow the way they should.

I guess since I’ve done dividing in a ratio, proportion and inverse I should finish off the module. Expect simplifying a ratio and recipes (which will be a challenge to lay out) to come next.

I’m going to call these Vary and Twist.

Section A is some variation practice. Here’s my thinking behind the variations:

  1. Simple example
  2. Context change, numbers stay the same
  3. OK. Now double what we require. answer doubles
  4. Amount needed triples, answer triples. Also 6 x first one
  5. We’ve doubled the number of pens in the first one. essentially having the price…
  6. Now doubling the price
  7. Halving the price. Link between 5? Maybe 6 + 7 should be swapped around
  8. Less pens then initially. Answer will get smaller for first time
  9. Rounding introduced.
  10. Don’t just quadruple your answer from 9! You’ll introduce a rounding error!

Sections B and C add a little extension, but they use the idea of spaced practice to make students think a little more than standard blocked practice.

Worksheet is here.

Think I might be using this format for more exercises. I’ve done the table layout now. Took me ages.

I’ve found it’s a little limited, though. Tried to do a sheet with probability trees and it quickly became unmanageable with images.

Comment etc.

A worksheet attempting to combine Craig Barton’s ideas on variation theory (only changing one part at a time) and Dani and Hunal’s ideas around making students make choices. I’ve tried to build up to that.

Maybe by trying to combine both I miss the point of each.

Download the worksheet here.

Would love criticisms and thoughts.

I teach a group with low prior attainment.

One thing I noticed is that they often lack the knowledge that other students take for granted, which holds them back.

We were discussing the questions “Write  \frac{4}{5} as a decimal” and their lack of knowledge that \frac{1}{5} = 0.2 really held them back.

I thought back to spelling tests I did as a kid, learning the fact, covering up and then being tested on the word. These seemed to quite effective, and I thought I could do a similar thing with maths. So I designed some maths ‘spelling’ tests. You can download them here. At the moment, there’s only 4 of them. Hopefully by sharing the PowerPoint and format, people can adapt them. If you do this, please share your versions below.

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I collect misleading graphs. Here’s an excellent one I saw today.

What’s wrong with it? There’s more than the obvious.

How would you regraph it?

Here’s some other weird ones.

Although maybe it’s wrong to call these graphs

I went to Mathsconf13 at the weekend. It was a lot of fun. I would highly recommend attending one.

I will be the first to admit that I am not always the most well-behaved during CPD time. I often find it difficult to see the purpose, and it’s often way too generic to be useful. I’ve found this at every school I’ve worked at.

It was great to find really useful sessions that I could see the value of straight away. I enjoyed the keynote by Matt Parker, who talked about how to cube numbers easily and how we could use this to discuss the merits of expanding triple brackets, which I was teaching that week.

Ed Southall did a great session on question design, something that interests me greatly and there was an awesome session by Stella Dudzic on the large data set which I thought was superb. I always like listening to Stella speak. I once attended a session where she talked about the random walk and came away with loads of stuff to talk about and do.  I even got my picture taken with the world’s biggest prime number.

The fact that these sessions had breaks between them was even better. There were interesting stalls and lots of people to talk. I had a load of fascinating conversations.

Some of the conversations made me feel bad. I talked a little bit to Jo Morgan from resourceaholic and Jonathan Hall from the magnificent mathsbot. Both of these people are amazing. They’ve contributed so much to the profession and they have a big impact in classrooms every single day. They create and share, for free, a huge amount. I don’t.

Most of the stuff I create I keep to myself, or I hide away on TES behind a £2 paywall, thinking that one day it might earn me enough supplementary income to be able to afford a house with a proper garden. This isn’t quite right. For a start, the income that I earn from TES is minimal, and it’s also not quite fair to the wonderful people who share stuff for free. So…

I am going to start updating this blog more (I’ve said that before!). I’m going to add more resources that I’ve created than before. They’ll be up in the top menu. Most of the resources I create are called ProjectALessons (I love a bit of branding). They’re a full lesson with explanations, tasks and learning checks. I also try and add a problem solve-y bit to every lesson. I put it at that end of the PowerPoint. Don’t feel you have to do it at the end (Mr Barton had a lovely bit on his podcast where he talked about the difficulty of doing a hard task at the end of the lesson, destroying student’s confidence).

October half term I’m off to Carcassone. I’m going to withdraw my TES money to take the missus for a nice meal, and then that’s it. They’ll be gone. And all my resources will be on here. For free. Shared properly in the nav bar at the top.

I’m starting now. There’s some stuff there (and it’s only doing this that I realised I had less than I thought) if you look now. Mention if you used one and it went well. Or if you used one and it needed editing.

I’m off to plan some lessons.

My colleague and superior who doesn’t want to be named designed a Pokemon go lesson. I asked him to upload it to the TES because I thought other teachers would love it, but he’s shy and scared of the internet, so I’ve asked permission to reproduce it here.

It is a rich task talking about the time it takes to hatch eggs. I understand none of it.

A rejected Harry Potter title, that.

Artful Maths is brilliant. Some lovely end of term activities on there. We’re running Curves of Pursuit as a session. I’ll be nagging my HOD to buy fancy coloured paper next year to do some lovely folding stuff. There’s more stuff like this in the ATM book Mathematical Imagery, apparently. I wouldn’t know. I haven’t bought the book because I’m tight. Shanghai are big on representations, and visualising stuff isn’t given enough. I’m obviously going to link to Don Steward now for a great example. I might rename this blog DON STEWARD LINKS.

You could always have a go at Mandalas.

I used to do the pirate game. Kids loved the pirate game, but it’s not got a great deal of mathematical content. It is REALLY fun, though.

A few years ago I made Maths Pointless. I’m less proud of it every year. I wanted it to work like the ‘proper game’ with animations and all sorts. It kind of does but it’s stuck with the limitations of PowerPoint. At one point I thought about learning Flash or JavaScript to make a fancier version, but unfortunately that never happened. I got the idea from Mr Collins.

Resourceaholic has some stuff for the end of term. Recently they celebrated their 1,000,000th visitor and there’s some good stuff on there. Not even my mum reads this blog 🙁

You could also do some fun Rio stuff.

Just don’t do a quiz, people. I’m really bored of quizzes.