If you have any suggestions, hints, tips or solutions, please leave a comment.

**Estimation**

This was a great choice to start with. It’s punchy, attention grabbing and ‘different’ to GCSE maths. It feels like it’s relevant to do and there are easy links both to real life but also to more generic ‘good skills to develop’. A lot of my students have really enjoyed the liberation of not having to focus on the **right** answer.

**Students starting late**

Due to the nature of post 16 courses, there were quite a few students who missed some of the first lessons. I need to think of a ‘catch up’ system that doesn’t take up too much of my time. This is also true for students that miss a lesson.

**Homework**

This has broadly gone well (they were expecting to get homework) but I’d underestimated the length of time it’d take to mark them. I’ll probably stick with it next year and see if just being more aware of the marking time helps.

**Resources**

There just aren’t that many out there (mine are here and updating as I go). I’m trying really hard to make mine good quality and therefore reusable so it is taking a long time per lesson.

**Twitter**

Having said that, there is a strong group of teachers that are very good at sharing and giving advice on twitter. If you’re not already on there, I’d really recommend it just for this! The hashtag #CoreMaths is well worth a look every now and again.

**Correlation/regression**

This was the first topic that really lost some of the students, particularly those with lower grades at GCSE. Unsurprisingly, their straight line graph work wasn’t secure and the complicated nature of the regression lines was a bit much. I also think that the correlation topic was a bit complex and I need to consider how to deliver this better (maybe just more slowly) next time.

**Calculators**

They don’t all have them. I want them to have the Casio fx991-Class Wiz but they’re up to £30 each! There’s the possibility of us doing a loan scheme but I do think the lack of calculators in general did not help with correlation and regression. There was, unfortunately, a correlation with those that did less well at GCSE tending to be the ones that did not have calculators.

**AMSP**

The Advanced Maths Support Programme is fantastic. They are busy on twitter and working hard behind the scenes to support maths teachers in delivering this course. They are running some CPD sessions soon and, in a pretty much unprecedented turn of events for CPD, they asked what sort of things we’d want to be included and then have actually made a course focussing on those things. What more could you want? If you’re not registered to get their emails, do it now!

So, in summary, obviously a mixed bag with this new course but lots of positives and some things to work on for next year.

]]>There were 10 of them and they’re presented here in no particular order:

*I can’t stand Russian dolls. They’re full of themselves.**When I worked as a librarian, if anyone ever asked where the books on paranoia were, I’d always whisper, “They’re behind you.”**Someone complimented me on my driving the other day. I got back to the car and there was a little sign saying “Parking: Fine”, which was nice of them.**I used to train racing snails. One day, I took the shells off to see if they’d go faster. It didn’t really work and, if anything, it made them more sluggish.**I had a job drilling holes for water – it was well boring.**Cheer leading exams are easy. You go in and shout “Give me an A”.**I got really emotional this morning at the petrol station. I don’t know why, I just started filling up.**I’ve started a business selling ejector seats to holy people. Prophets are through the roof!**Thanks for explaining the word ‘many’ to me. It means a lot.**I’ve always wanted a job putting up mirrors. It’s something I can really see myself doing.*

Assuming you’re still with me and not uncontrollably laughing, here’s a bit more detail about my survey design.

- I deliberately made it an anonymous survey and didn’t ask for any details other than “How funny are these?” I think this probably means that people are more happy to answer but it does mean I can’t do as much about drilling into the data.
- A scale of 0 to 4 allows a sensible “This isn’t funny = 0” rating and also allows enough scope for differentiating between jokes without forcing people to decide “Is this an 8 or a 7?”
- Each person that answered the survey had the jokes presented in a random order to avoid the potential issue of skewing results. For example if a mediocre joke followed a poor joke, then the mediocre one may get an unfairly high score.
- I shared my survey mostly via Twitter so it has been answered by the kind of people that follow me (and the people that follow them).
- I asked people to retweet the link just to get more responses.

There were 585 responses and you can see a spreadsheet of the raw results here. (You’re welcome to use them however you like.)

One main reason for doing this was to be able to look into correlation. For that, I’m going to do a statistically very dodgy move of finding the mean average rating for each joke. This is something you shouldn’t do with Likert scale data as the scale isn’t linear (ie 4 isn’t twice as funny as 2). However, I do think it’ll give a sense of which jokes were rated more highly and I’ll have to hope the Stats Gods will let me off. I promise I’ll discuss this in class.

I’ve also asked each of my classes to rate the same jokes and I’ll get them to see if there’s a correlation between the rating they gave and my followers. I’ll also get them to see if there’s a better correlation between their average ratings and those of the other class.

I did consider giving them one fewer joke to rate and use regression to predict their rating. However, I suspect the correlation will be weak and therefore the regression will be a poor predictor so I’m a little wary of showing them a scenario where regression doesn’t seem to work.

I’m also going to use the data later in the course as the basis for a discussion about the types of averages and pros/cons of each. Modal response is probably not very helpful as they’re mostly just ‘3’ (on Twitter responses at least) and Median has a similar problem.

I will also (committing the same Likert scale crime) use the data to find the standard deviation of each joke to find the most ‘marmite’ one. Those with lower standard deviations may well have been more consistent in their ratings while those with a larger sd may have been more polarising.

Here are the mean average results in case you’re interested:

Mean | Class C | Class M | |

Russian Dolls | 2.356 | 2.333 | 1.778 |

Paranoia | 2.471 | 1.889 | 1.222 |

Park Fine | 2.132 | 2.111 | 2.333 |

Racing Snails | 2.535 | 2.111 | 1.556 |

Well Boring | 2.047 | 1.111 | 1.333 |

Cheer Leading | 1.941 | 2.222 | 1.556 |

Filling up | 1.925 | 1.333 | 1 |

Ejector Seats | 2.502 | 2.111 | 2.444 |

Means a Lot | 2.55 | 1.556 | 2.333 |

Mirrors | 2.341 | 1.333 | 1.667 |

These make some fairly nice bar charts that are interesting to compare and explore/discuss. I might see if there’s anything dodgy I can do to make my favourite joke/s appear more popular than they actually were and let the students play detectives with my misleading graphs!

I may also use these as a ‘large data set’ for students to play with on computers. That’s only just occurred to me so I can’t say I’ve given it much thought but I’m sure there’s something there! Will probably be worth looking into if there are any weird results or any cases of people just rating some of the jokes and how we might deal with that.

I have done this experiment before (you can see the results here). It wasn’t all the same jokes although you’ll see that there are some repeats. There’s likely to be something we could do along the lines of “Did the jokes that featured both times seem to rank in approximately the same place each time?”

Finally, thanks to everyone that read the jokes and rated them. Thanks also to everyone that retweeted the link so it could be seen by a wider audience. If you do something interesting with this data, do let me know!

Given all of the Likert caveats I mentioned above, here’s my tentative suggestion for top three performing jokes:

*Thanks for explaining the word ‘many’ to me. It means a lot.**I used to train racing snails. One day, I took the shells off to see if they’d go faster. It didn’t really work and, if anything, it made them more sluggish.**I’ve started a business selling ejector seats to holy people. Prophets are through the roof!*

Their bar charts are below and their mean averages are above. See if you agree.

]]>

It’s pretty common for some students to be struggling with organisation and to pick up some concerns for this. One teacher commented how a student didn’t have a system at all and was simply putting their loose bits of paper into their school bag.

To help combat this while also providing course material, I’ve made a set of subject dividers for Core Maths. I created some mind maps using mindmup and copied them into publisher along with a bit more information. Our reprographics department printed each one out on to a different colour of card and then hole punched them. They look great and some of the students were very excited by them. They now don’t have any excuse for knowing exactly where to file each bit of work!

The files are aimed at the AQA course and, specifically the paper 2A option. If you’d like them, you can find them (free) in my Core Maths bundle on TES.

]]>*… thoughts on 0 being even or neither!! Some of my dept say neither I say even as a multiple of 2 sorry?!?!?*

Here’s my thoughts about what makes something even as it’s something that comes up in my classes often when I’m doing the caterpillars investigation.

**Even numbers end in 0, 2, 4, 6 or 8**

This one often comes up with students and I’d agree with the caveat that we’re talking about integers. I wouldn’t want to have to say that 1.2 is an even number for example.

**Even numbers are (integer) multiples of two**

Passes this test. 0 = 0 × 2

**Stacking up a pile of blocks**

If you stack up the blocks into two piles, the top is level (even). This works with 0.

**Sharing it out**

When you share an odd number of things equally between two people, you have an odd one left over at the end (remainder one). That doesn’t happen with two.

**It fits the pattern**

-3, -2, -1, 0, 1, 2, 3

odd, even, odd, even, odd, even, odd

So, in conclusion

*******************************************

**In other 0 related news:**

0 is neither positive nor negative

0 may be a natural number or not, depending on which definition you use!

]]>

Soon, I’ll be moving on to the topic of correlation and regression with my Core Maths classes. It’s a topic that I think often makes intuitive sense (you can have a feeling of what correlation you might expect) while also being something that it’s easy to see as being useful.

For me, it’s important in Core Maths lessons that they are more than ‘just about the maths’ when possible so this seems like a good time to talk about spurious correlations and also to have some fun. I’ve made four scatter graphs that relate to some well-known sayings. See if you can figure out what saying each one is!

They’re just meant to be a bit of fun and a nice way in to the topic. (I’m well aware they are bending the exact meanings of the sayings in some case.)

I’ve been talking to a couple of the science teachers in my school (this one and this one) about some of the things we do differently in maths in science. It turns out that are just some different phrasings that are used and I don’t think we are going to get a collective agreement. So, it makes sense to explicitly point these out to students so that they just get the idea that we deal with things differently. Here’s a slide from from my correlation and regression lesson notes. You can find the whole powerpoint over on TES. (Along with some other resources.)

]]>Great for projecting on to the screen for the class to do and is even useful for tutor time.

The link is here http://christianp.github.io/30secondchallenge/

]]>The classes have 18 students and 12 students which is a good take up rate and, although there will likely be some fluctuation as they finalise their A level choices, this is promising! It is less than the amount originally signed up so I’ll do what I can to try and find out where those other students have gone.

So, what did I do in my first lesson? I really wanted to start with something that is different to what they’re used to. Estimation seemed to fit the bill and note that you don’t need to know the answers to be able to put these in order, just a sense of the size:

It went well and there was a good ‘buzz’ in the class. People were willing to suggest ideas and I got an early chance to encourage participation with things like “Obviously, you don’t know the answers here – who would? But, you’ve got an idea of how old a really old tortoise might be haven’t you?”

Things I’ve learnt and to bear in mind next time:

- Having the two distances in different units was unnecessary and confusing
- Students often didn’t know where the river Severn was
- It wasn’t entirely clear that students definitely knew where Edinburgh was
- EVERYONE was able to get involved in this. It seems like a good starting point

Next, we went in to the main task of the lesson:

We spent a long time on this (longer than expected) and I made good use of Lily Tang’s (Twitter: @cvcltang) framework for breaking down a Fermi problem. The structure was very helpful in getting students not to panic and to also make them think they could do these kinds of things.

Things I’ve learnt about this:

- Students often know things I don’t (how are runways used for example)
- I did this twice and got pretty different answers with both classes
- Students were expecting me to ‘know’ the answer. I had to explain to them that’s not how these questions work
- I can probably push this forward more quickly and model ‘not getting bogged down with detail’

Next, I showed them the following slide.

It’s easy to forget that just a few months ago, these were GCSE students. They have not magically learned how to take notes so I’m going to help make sure they have decent things to look back on in their course notes. To signpost this, I’m making slides with notes on have a different background to them. Hopefully that will help!

Finally, I set them some homework. Because of the length of time I have to teach the course, I think homework is necessary. None of the students questioned it so I’m guessing they were expecting it!

The homework includes some of the facts people should know and also two estimation questions. We’ll see how that goes!

All in all, a really great start with a positive buzz about all the questions so far. Looking forward to the next lessons.

]]>However, it’s not a topic I’ve ever taught before and it very much seems like the sort of thing that lots of varied practice would help with so I set about finding a list of questions. I could find some but not as many as I wanted so I set about collating a list and creating some more. Lots of people on twitter helped contribute ideas too so thanks for that.

Questions like these are included:

It’s a little rough at the moment and I will do some fine tuning later on but, it’s a good starting point. At the time of writing, there are 61 questions and, if you have any more ideas, please let me know so I can add them!

]]>**Why have you chosen AQA?**

Primarily because I was a proof reader for a book called AQA Level 3 Certificate in Mathematical Studies by Hodder and Staughton which was tied to the AQA course.

I also like the fact that there are different options and although I’m starting with 2A (the stats option) this year, I’m excited about the possibility of running different classes as appropriate for different students with maybe those taking Geography and Psychology doing 2A while the Business students can take 2B (featuring critical path and cost benefit analysis).

**Are you teaching the course over 1 or 2 years?**

1 year.

A big driver here was wanting to make sure that the exam did not happen at the same time as the A level exams at the end of year 13. It has been a good ‘selling’ point and will also be something concrete to put on UCAS application forms.

**How many hours per week have you been allocated?**

2.

I’m aware this is very tight and I will be making use of homework to help with this. If it is looking to be too short then I’ll talk to the 6th form team and see what we can do additional sessions. I will be upfront with the students and say that they’ll simply have to do additional work.

**Are you accepting anyone with at least a 4?**

Yes.

The course is designed for anyone who got a 4 or higher so there’s no reason not to allow those students to take the course. It looks like we will also be having students who got grade 7s as well.

**Have you written your own sow or using aqa/other ones?**

My head of faculty has a friend who is teaching core maths already so she kindly let me have that as a starting point. I’ve adapted it a little as I really wanted to make sure the course starts with something new (Estimation). The scheme I’m going to start with is this but it’s obviously open to adaptation if needed.

Any more questions, please ask!

]]>

This sparked a thought along the lines of what things it might be helpful to prompt students into finding out just so they feel more confident about answering these questions. What is the population of the UK? How long would a car be? And so on.

Next, I realised that this isn’t really something that would only be useful to Core Maths students and I also thought that other people would come up with good ideas too, so I turned to Twitter. Unsurprisingly, there were plenty of good ideas and here’s my collated list. The ordering is somewhat arbitrary and you may well decide that some aren’t that important for your needs. That’s fine – use it as you wish. Perhaps these could also spark tutor time discussions!

Thank you to everyone who contributed ideas.

*Population of the UK*

*Life expectancy in the UK*

*Average adult height*

*Average adult weight*

*Average UK temperature*

*How many countries are there?*

*Weight of an apple*

*Height of a house*

*Height of a door*

*How many people fit on a bus?*

*What temperature would be gloves and scarves weather?*

*Diameter of the Earth*

*How far away is the sun?*

*Population of a large town*

*Population of a small town*

*What temperature would be t-shirt and shorts weather?*

*Population of the world*

*Average hours of sleep per night*

*Weight of a melon*

*Average car length*

*Average car width*

*Width of the UK*

*Length of the UK*

*How many primary schools in the UK?*

*How many secondary schools are in the UK?*

*How many teenage pregnancies were there last year?*

*What proportion of the UK are over 65?*

*Volume of water in a bath*

*Water used per shower*

*Days in a year*

*How many people can a theatre hold?*

*How far away is the moon?*

*Average car petrol tank capacity*

*Average car miles per gallon*

*Average distance an electric car can go on a full charge.*

*Average family size*

*Weeks in a year*

*How many people are unemployed?*

*How many people fit on a train?*

*How much water does a flush use?*