With the first full week of teaching done, I’ve already had some interesting discussions in Core Maths. One of the early tasks I do with my class is the classic, “How many items of luggage pass through Heathrow in a month?” I think it does a good job of showing students how Core Maths is going to be different to GCSE, is surprisingly accessible but also forces students to think about key things such as “What does this question actually mean?”

I have a couple of students in my class that got a grade 3 in GCSE. The plan is that they will retake their GCSE, with the Core Maths classes helping to support some of that and then we’ll see how things are going as to what happens next. It was really pleasing that one of these students raised a question that none of my students have done before: “When you’re counting the luggage going out, won’t you be counting some of it again when it comes back?” This is an excellent point and one that I’d not even considered in the past. I think this goes to show that a grade 4 in maths isn’t the quite the definitive answer as to whether someone can think mathematically.

**Homework**

This year, I’ve given the student A4 homework book. It’s in line with what we do at KS5 for A level classes and I’m hoping it will just keep things a bit tidier and easier to keep track of. I’ll let you know how it goes.

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I’ve shared a few of my ideas here (Tutor Time activities) and I’ve got a nice series of activities planned that I’d like to share with you. This year, I’m going to run monthly quizzes with my tutor group where I’ve given them the material in advance to learn. I’ll put them in teams of three (new team each month) and tell them when the quiz is going to be so they can plan out their ‘revision’ of the material. I’ve gone for a mixture of things that I think it’s kind of useful and/or interesting to be aware of and am aiming for a mixture of topics/subjects.

I’m also going to track the points each person gets across the year and have some sort of prize/s.

My goals are:

- Students work together/talk to people in the tutor group that they may not do otherwise
- Students may learn some general knowledge
- Students may discover some new revision technique/learn from their peers
- Give an ‘easy’ option for an otherwise quiet tutor time – “Ok, into your teams – revise for the quiz”
- Students might well question the validity of the source/s. This is a good discussion to have!

On this blog, I’ll share the material at the start of the month and then put the quiz up nearer the end of the month. I’ve got September and October ready to go with:

**September:** Monarchs and Imperial measurement conversions

**October:** Shakespeare plays and Animals’ collective nouns and young

I have some ideas for the future months but I’m very happy to hear of more/better suggestions!

Possible future topics:

*Countries – names and locations**Counties of the UK**Recipes**World cup winners and locations**Paintings – titles and artists and dates**Famous musical pieces – title, composer, date**Prime ministers and dates**Bones of the body**Key major historic dates**Rhyming slang**Average starting salaries**Dr Who actors**James Bond actors**Christmas number 1s**Olympics locations**The basic timeline of XYZ**Internet**Mobile phones*

If you have other/better ideas, please tweet me or put them in the comments!

PDFs here:

]]>I’m sure the start of a new year has been its usual mix of exciting/challenging/exhausting for you all and it certainly has been for me too. I’m trying really hard to plan my lessons further ahead this year and as this is my second year of Core Maths, I’m very pleased to have a stronger starting point. This post will reflect a little on my last year and look ahead to the coming year too.

**Results**

Core Maths entries rose from just under 7000 to over 9000 last year (MEI summary here) which is a strong indicator of its growing success. It’s no secret that I think it’s an excellent course and one that’s well worth taking regardless of the examination outcome. Having said that, I did have students taking the exam last year and these were my students’ results:

Grade | Freq |

A | 7 |

B | 3 |

C | 5 |

D | 4 |

E | 4 |

U | 7 |

Total | 30 |

I’m definitely relieved that I’ve done enough to give students the chance to get A grades and while I’m not happy with the number of U grades I think that overall, there’s a lot to celebrate. I’ve got the question-by-question break down for each student and I’ll spend some time looking for any areas that I seem to have taught particularly well or otherwise.

**Promotion**

I am very fortunate that the leadership team of my sixth form are good at mentioning Core Maths to students as they’re interviewing them and are proactive about encouraging anyone taking A levels where the course would benefit them to take it. This year we have three classes timetabled and I am even more fortunate to be teaching all of them!

In the start of year assembly for Year 12s, I asked to have a couple of slides in and I had a two minute talk reminding people to think about taking it if they hadn’t already. I explicitly said the it is for anyone with a GCSE grade from 9 to 4 because I don’t want them to think it’s ‘easier’ maths only for people with 4s and 5s. There’s still some work to be done on ‘mopping up’ some students that probably should be taking it but currently aren’t for some reason.

**Key foci for the coming year**

I know that my grade 4 students need more help, especially those coming from Foundation tier. Here’s a scatter graph of my students’ GCSE and Core Maths grades:

I’ve given the grades a ‘jitter’* to help them show the trend better. I haven’t fully thought this through but I am going to make sure I offer them additional opportunities to see things like histograms and also just more 1-to-1 time on anything they need help with.

I tried to set too much homework that became quickly unmanageable to deal with both in terms of marking and keeping track of who had done it. I’m going to slim it back to fewer, higher quality/longer homeworks and I may well use homework books to be more in line with how we deal with homework in our A level classes. I have decided/realised that they do not need homework every lesson.

This topic sticks in my mind as the one that I delivered least well. I still don’t have the answer to it yet but I will be calling on the #CoreMaths hashtag for help and suggestions.

**Other bits and pieces**

If you’re new to my blog, it’s possible that you may not know that I have some resources on TES (which I’ll continue to redevelop this year) and that I also host a maths podcast called Wrong, but Useful in which I invariably end up mentioning Core Maths.

Over the Summer, I was pleased to be involved in beginning to write resources for the Integral Maths site and I believe my first one is up. You have to register with the site to get access but (and I know this is arrogant) the Fermi Estimation resource I’ve written is easily some of my best work and I really do think that if you download it, you will find at least one thing you want to use.

**An idea for a lesson**

I think that a lot of the people that read my blog do so mainly for useful lesson ideas. This post hasn’t had any yet (although you could probably do something with that scatter graph). Here’s just a quick idea/prompt for you so you don’t go away empty handed:

Claire’s accessories have been piercing ears for 40 years. Does the following claim seem believable? Can you do a ‘Back of an Envelope’ estimate to validate your decision?

As ever, if you have any questions or comments, please do leave them below.

*I learned about adding in a ‘jitter’ to separate the points from David Spiegelhalter’s book *The Art of Statistics*

The first thing I got given was a nice bag with some goodies in it and a jam-packed list of talks to choose from. It was really very difficult to narrow it down and there were multiple cases where I’d have been happy going to 3 or 4 in the same session.

There were several stands demoing their wares and, pleasingly, none of them were pushy about it at all. I got a chance to have a chat with Jo Sibley (@JusSumChick) who I’ve met before but never who ceases to be cheerful and enthusiastic even though she was trying to plan how to introduce the keynote plenary speaker later on.

Just before the sessions started I saw Ben Sparks (@SparksMaths) who introduced me to the legend that is Jonny Griffiths (@therispguy). If someone like Jonny is at a maths event, you can be sure it’s going to be good!

**Session 1 – The Maths of Dobble – Keith Proffitt**

This was a really nice talk and opportunity to explore the world of the card game Dobble.

Keith started by showing us the Tim Gowers’ blog in which he talks his way through a problem and highlights some of the dead ends he gets himself to. It’s a good read and fascinating to get a glimpse into the thought processes of someone who is clearly very good at maths.

During the session, I sat with a few people I didn’t (previously) know and we happily talked about the way the game was constructed while seeing if we could construct some of the smaller possible sets ourselves. It was fun to explore the maths and seeing it come together nicely with some mild prodding from Keith. At the end, he then let us in to the facts that Dobble is closely linked to projective geometry and that nobody knows if it is possible to make a Dobble set with 13 images per card!

**Session 2 – Exploring Maths resources at Key Stage 3 and 4 – Jo Morgan**

Jo is curator of the amazing website Resourceaholic in which she hand selects maths resources that she recommends. As such, she is very well placed to lead a session on resources!

She started off by talking about the many aims we may have when choosing/creating resources and that very often, the go to ‘intention’ is one of practising fluency. While this is important it’s not the only thing we should be looking for.

Jo nicely summarised the way in which teachers tend to choose their resources with 4 points:

*Aim*: What is the point of this resource? What do I hope to achieve by using it with my students?*Pitch*: Is the work appropriately difficult for the class? Does it have a variety of difficulty throughout the resource?*Practical*: Is this actually going to work? Does it rely on colour photocopying or too much printing? Are there mistakes or inaccuracies?- ( ) : Do I love this resource? Am I going to go into the class buzzing about the activity I’ve got planned?

This is a sensible and pragmatic approach to choosing resource and Jo was happy to accept that the 4th point isn’t always necessary, of course, but if *none* of your resources excite you, perhaps you should be finding/making some others.

As you’d expect, Jo pointed us to some specific websites and in particular mentioned Boss Maths with its very well thought through less presentations. There’s also Cleave Books which has a variety of resources including puzzles and teacher resources.

I enjoyed this session a lot. It’s great to see someone who is enthusiastic about maths give a talk about how to thoroughly prepare lessons and resources. In my mind, there are very few people who know more about planning and resources than Jo!

**Session 3 – My first year of teaching Core Maths – Me**

I led a session about Core Maths to a mixed bunch of teachers, some of who had been teaching it for 4 years, others of whom were planning to teach it soon. I won’t actually write about my talk here as I’ve covered a lot of Core Maths in other places on this blog but I will write about the envy/jealousy I felt about the teaching station set up!

The station had a screen on an adjustable arm stand, a visualiser and lamp. The touch screen controls at the back meant that using the projector and switching between display and volume options was easy. USB and other ports were easily accessible and the whole thing was at standing height (with a suitable chair too). To top it off, there was a microphone you could wear round your neck and a camera at the back of the room so that recording the session was possible. Another interesting aspect is that the desk is set up to be at standing height (with a suitable stool) which I think is very sensible. I don’t like sitting at my desk when I have a class in the room partly because I can’t see everyone but the extra height of a stool would be very useful.

I’m sure it was a relatively expensive set up but this sort of arrangement would make my teaching easier and make me feel a lot more professional. I’m certainly going to see how much of this arrangement I can organise back in my classroom.

**Keynote Plenary – Craig Barton**

I’ve been working with Craig via the TES maths panel since 2011 and it was flipping brilliant to actually meet him in person.

His keynote was based partly around his book and broken into 3 parts:

Craig described his approach of demonstrating a mathematical technique in silence. A key aspect of this is that when you pause, students must be thinking, “what have you just done?” and “what will you do next?” He also suggested getting students to write any questions they have down (after watching carefully) and see if those questions have been answered while working through some intelligent practice.

Two very important points I took away are:

- Don’t endlessly repeat yourself. To quote Craig, “I used have the approach of ‘why say something once when you can say it 25 times?'”
- Don’t go off on tangents. You lose the thread of the lesson and some students will be completely lost.

Simply, don’t have them. They take ages to create and put up, are a massive distraction and have no effect on memory. If anything, they encourage students not to bother remembering things. Similarly, don’t have a number line on the wall. If a student needs a number line, they should have the practice at drawing one.

The memory aspect was demonstrated beautifully by showing us 6 versions of the Google logo with the colours mixed up. It’s an image that we probably see every day but still couldn’t tell you which was round the colours should be.

This is a complex topic and I can’t cover it here. At its simplest level, the idea is to have questions that vary slightly from the last one and students are then expected to think about how the question is different from the previous one and what impact that might have on the answer. There’s a lot more about it here but I’m interested to look into it more.

I have to mention the coolest presentation clicker I’ve ever seen. It basically had a spotlight tool and zoom option. It’s expensive but we were all very impressed, so….

**Session 4 – Topsy-turvey maths teaching – Debbie Barker**

Debbie works for MEI and showed us a few ways to introduce tasks to students so that by the end of the lesson, they could tell you what it was you’d intended them to learn without you explicitly telling them.

My favourite thing was simply using two pieces of coloured paper and then folding them into twelfths. Using these, it’s nice to be able to see that 1/6 + 1/2 = 8/12 without needing to resort to a procedural approach.

I also liked the activity ‘3-ish’ which is a sequences and patterns task where students are shown an image and told it’s the third one in a sequence. The key question is “what is 3-ish about this?” and then exploring what the other images in the sequence would be.

**Summary**

It really was an excellent event and I’d encourage you to look out for it next year. An additional nice touch was that a few days later, I got an email responding to the comments I’d made on my feedback form. I don’t think I’ve ever had that from a conference before but it was well received. I’m definitely looking forward to next year.

]]>It was our 6th form induction day today so as an ice-breaker activity with my new and old tutees, we played this (school friendly) version of Never-Have-I-Ever…

There’s an example question below and a link to download a ppt version (instructions included). I’ve made this with *my* tutees in mind so it’d be worth you looking through the statements first and checking they’re appropriate for your needs and age group.

Feel free to adapt as you wish!

]]>That doesn’t mean I’m not thinking about the subject though and a nice prompt was provided in this tweet from @carlosaurus :

I thought about this for quite some time and realised that, actually, I don’t think there is much in the way of prerequisites. There’s really not much of the GCSE material that is used in Core Maths and I think that in all honesty, the only really big topics that’s obviously used again are:

**1) Percentages**

Students being competent with these would be helpful and, in particular, being happy with using multipliers for percentage change and the concept of ‘reverse’ percentages.

**2) Concept of averages**

I’d like students to be more familiar with what an average actually tells us (or doesn’t tell us). Being able to compare two sets of data with averages would be handy. Being able to calculate mean averages from a grouped frequency table wouldn’t hurt.

There are a few other things it’d be nice if students were already good at but, seeing as they’re not really on the Foundation tier, I can’t call them prerequisites:

**a) Histograms**

**b) Box Plots**

**c) Cumulative Frequency graphs**

What do you think? Are there any others that should be on this list?

**A nice thing about the course**

I can honestly say that a nice thing about this course is that it really doesn’t have much of the specific requirements that many level 3 courses do have. I’ve enjoyed taking students from whatever their starting point was and showing them several new and interesting topics.

]]>Before that, I’ll mention that I have applied to be an examiner for this paper and was turned down last year (due to not having the relevant experience) and I think I must have missed the window for this year. I’ll try again next year as I think it’d be a great insight into some aspects of teaching this course.

Obviously, I’m not going to reveal any of the questions because people will be using these for mocks next year although if any students read this, they will get a sense of what to expect. I will assume you have access to a copy of the paper so you can see what I’m talking about! If you don’t teach AQA, you might want to skip to the end section.

**Level 3 Certificate – Mathematical Studies**

I have to say that I was somewhat relieved and surprised to find that this paper was pretty much **exactly** what I’d expected. I had (wrongly) predicted that the first question would be a percentages one but otherwise, the paper was very close to what I’d told my students to expect.

*Question by question break down*

- Totally fair. Part a is easy but part b will have caught some out. I’ll be interested to see the mark scheme for that.
- Some of my students were a little worried about how spreadsheets would be asked so I think they’ll have been happy with this one. Seems to be a fairly straight forward set of questions. I wasn’t expected the Student Loans question to be asked by itself and I think the marks for this seem a little more than I’d planned for.
- Fully routine and very similar to a past question. A bit tedious finding the median and I’m sure some of mine will have made mistakes. Part b is a gift of 3 marks. The comparison *should* be straight forward but I think a lot of students find this difficult.
- Pretty easy and should be a guaranteed 1 mark for all really. A lot of my students should get 3 but we’ll wait and seen.
- In my opinion, there’s too much detail in this question. It feels a bit too much like students are being lead through this and I’d expect (hope that) most of mine to get the 4 marks here.
- Straight forward and I can’t see how this is 4 marks rather than 3.
- I was expecting a little twist on the Tax/NI question and seems to fit the bill. One extra little wrinkle in what should otherwise be a fairly routine question.
- Part a is as straightforward as possible and could easily be on a GCSE paper. Part b is awkward enough that it will have put some of mine off (although I know it shouldn’t have). I’m curious to see what is needed to get 1 or 2 marks here. Part c: Easy, easy, easy.
- All of the students I’ve talked have said that the motorway question was very nice and more or less exactly as anticipated. “You didn’t even have to worry about the thickness!”, I was told. 9b is a classic.

Anyway, on balance, I am pleased it feels like it’s gone well. That’s much better than having students come back saying they didn’t feel prepared for it.

I’ll end with a quick note: There were no APR/AER questions on paper 1 but they could still be on paper 2. It wouldn’t hurt to mention this to your students.

*What were your thoughts? Leave a comment!*

**Overall thoughts**

This exam has put my students in a very positive frame of mind. They think it went well so they think they stand a good chance of getting a good grade overall. I’m inclined to agree with them. I can’t believe I’m saying this, but, I actually think it was **too** easy. I’m a little disappointed that these questions were quite as predictable as they were and I don’t think it will have stretched my very top end of students. I think the estimation question should have been a little more ‘open’ and I also think that some of the skills (sampling, histograms, box plots) were asked in a manner that was too routine. Why does this matter? Well, my concerns are:

- This will have lulled some of my weaker students that didn’t revise too hard for ppr1 into thinking they don’t really need to. ‘Winging it’ is a legitimate strategy.
- Paper 2 may simply be harder to compensate.
- The grade boundaries may need to be noticeably higher to accommodate the fact that many students will probably have done well this time.
- In terms of preparing students for next year, it will be tempting the think that exam questions have become ‘predictable’ and teachers/students will be caught out by relying on past papers too much.

I’m off to let my students know when I’m available this week (as they’re on study leave). I’ll write a similar reflection on paper 2 once I’ve got to see it.

]]>Normal distribution layout practice Just some very basic questions but designed to help get students used to laying the work out clearly. Assumed they’ll be using the Casio fx991.

(Questions are adapted from Exam Solutions)

Another few rounds of Calculator Drills. If you spot any errors, please let me know!

Calculator Drills 1 (posted this one before but it’s here for completeness)

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Calculator Drills (updated with correct answers!)

Example slide:

The other resource is a work in progress and will be a series of calculator drills on the main things that students should be able to just do without really thinking too hard. I’m intending to have enough that students can time how long they take and then, on another occasion, see if they can beat their time. I’ll try to think of a way to incorporate the importance of accuracy too!

Let me know what resources you’re using.

]]>Please share with your students and recommend the flashcards and matching games.

If you have a computer room or students with phones, then using quizlet live is *very* engaging! (Quizlet Live guide here)

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