***EDIT – I’ve changed my mind about the National Insurance brackets***

I’m getting to that part of my course where it’s time to start the finance material. I always like this part but know that it is quite tricky and has a lot of complex aspects that are, necessarily, glossed over to make the material be Level 3 standard rather than an advanced degree in accountancy.

Due to the fact that tax boundaries change most years, it means that any teaching resources need updating each year and, also, we want to predict what will be on the preliminary material as the bounds to practice using in class. With a massive thank you to Jon (@last_centurion) for pointing me in the right direction and providing me with his predictions, here’s how I’ve figured out the likely ones for this year.

**National Insurance**

The first stop for this the government’s National Insurance page. We start by looking for the Primary Threshold and Upper Earning Limit in the section marked 1.2 Monthly Thresholds.

This gives us the boundaries for the monthly values that mean someone has to pay the 12% NI contributions. For the year 2021 to 2022, those are £797 and £4 189. I’ll point out that this is for up to April 2022 and when the exams are actually taken, the thresholds will have changed. However, that information is too late to be incorporated into that exam series so for the past exams, it has always been looking at the previous financial years’ boundaries.

That gives us this:

Now, the government’s website does give thresholds for weekly amounts but doesn’t give values for yearly ones. Fortunately, with a little digging, we can find them out. A useful thing to notice is that the multiplier to take the weekly thresholds to monthly ones is 4.33 (and then rounded to nearest £1). This gets round the fact that different months are different lengths.

***EDIT – I Was wrong about how to get the yearly amounts. They are available on this site here.***

That gives us:

***NB A different table appeared in an earlier version of this post.***

The yearly amounts I had worked out differed slightly from this. However, these are on the Gov website so I will be using these and updating my resources to use these amounts.

**Income Tax**

While this is a little more straight forward to find the thresholds on the government tax site there is still a minor confusion for me in the way they’ve written it:

The personal allowance for most people is £12 570. My understanding has been that if you take your personal allowance off your salary, that is called your taxable income. However, if you were to do that and use this table, you’d be taking it off twice. Due to the way the Tax Bands and Rates are written here, I think I agree with Jon that it should look like this:

With an additional rate of 45% for over £150 000 (after allowances).

The personal allowance drops by £1 for every £2 a person earns over £100 000. This means that if someone is earning £125 140 or more, they don’t get the personal allowance. This hasn’t come up in recent years so it’s a possibility for this year as a way for the exam to test the skills in a way that hasn’t been quite done recently.

**Conclusion**

The finance topics have a lot of inherent interest to them (pun fully intended). They are also quite difficult to wrap your head around so please do ask for help and, if possible, offer me help too!

In my first lesson back after half term, rather than just launch into the next part of numerical data analysis, I decided to ask my classes the following starter question:

*Estimate how many pumpkins were carved into Hallowe’en lanterns in the UK this year*.

It’s a tough question as some of the estimates are difficult to do. How many households are there in the UK? What proportion of those might carve a pumpkin? How many might carve more than one? What happens in flats?

Anyway, having had a go, the more interesting discussion came when searching for an approximate answer.

A lot of my students jumped to the bit in bold and concluded it was 17 million. However, I had some more thoughts:

- Is that 17 million just found by dividing the population of the UK by 4?
- Does the article (and my students) know the difference between the UK and “Brits”?
- Who was included in the survey?
- Was it just adults?
- How big was the survey?
- Does this assume that of those 25% that will buy a pumpkin, they will get one each?
- If 25% of people said they would buy a pumpkin, does that mean that 25% actually would?

So I clicked on the link.

I was impressed (and surprised) at the level of detail in the journalism here. The mathematical thinking is explained along with the reasoning and there are meaningful graphs too (one even has the option to switch it to a table). There is a clear effort made to show the difference between known expenditures and projected expenditures and there is a fact check section that explains how they try to ensure their information is reliable.

I won’t ruin all the fun of exploring the article about Hallowe’en with your students but I would thoroughly recommend that you spend some time on it.

It seems that there may well be some useful articles on this site – if you find some good ones, please do share!

If you’ve been following my blog for some time, you’ll know that my school runs Core Maths on 2 lessons per week, over one year. This is not a lot of time and I have to cut some corners. In a previous post about my AMSP talk on Easy Money, I explained that I’m going to cut down how long I spend on some of the financial aspects (specifically APR and AER). This post is about me cutting down how long I spend on graphical data and some of the reasons.

Firstly, you may well be here to see what resources I’m using. They’ve been added to my TES resource collection (why not leave a 5-star review while you’re there?). A pre-warning though, a lot of what I’ve got there directs you to download a resource from somewhere else. This is actually my first real foray into accepting that I don’t have to create all the resources myself – there are plenty of other things out there that do the job so I’ve borrowed those.

Secondly, here are my thoughts on dealing with graphical data like this.

- Time. It really is the biggest factor here. I’m covering the graphical data section in four lessons (plus self-supported study).
- Scatter graphs already have their own section in the correlation and regression parts so I feel they get covered in the depth they deserve in that.
- They don’t get a huge amount of marks in exams. It’s certainly not zero but, proportionally, there are other things that will get more marks.
- A lot of graph work has at least the chance to be intuitive. I know histograms and cumulative frequency are not entirely obvious but with a few key ideas, I think students can have a reasonable attempt.
- My least favourite reason (but you’re here for honesty – right?) is that this topic is the one that is most impacted by where students took Foundation or Higher tier GCSE. I’m well aware that I haven’t got the differentiation ‘right’ here but you can see a clear attempt in the third lesson and the inclusion of some optional homeworks. If you have a good way of handling histograms with a grade 8 student that is very confident in them alongside a grade 4 student who has literally never seen them before then I’d love to hear more!

To summarise, this is far from my greatest work but I hope that the compilation of resources is useful to you and, perhaps, hearing about another teacher having to make sacrifices about the quality of their teaching makes you feel less bad when you have to do the same as well.

Ending on two positives – I think that the collation of some appropriate exam questions from multiple boards is useful and, in the resource, there are some crackingly terrible graphs that I think you’ll enjoy!

In the UK, we have a National Health Service which is funded through taxation and National Insurance. In some other countries, health care is not ‘free’ at the point of usage and patients are billed afterwards. There are stories of people asking bystanders NOT to call them an ambulance as they know they won’t be able to afford it.

It is possible to pay for medical insurance to help against these costs but, obviously, only reasonably well-off people can afford this. It might be a nice discussion point for students to think about how much they’d be willing to pay annually for a ‘Use the hospital as much as you need to’ pass. Would the amount they’d be willing to pay change if they were planning on getting pregnant soon or perhaps, if they were in their 50s?

I saw a post on twitter where someone (Seth Timlake (not someone I know)) has shown the bill they were given after being treated for a snake bite. Have a guess at the total amount.

Now, there are certainly some things to bear in mind here. I have no idea if this is a ‘typical’ bill for an emergency situation or not. This appears to be from 2015 so it could well be that things have changed since then (do students think it might have gone up or down in price?)

I’m not sure exactly what my questions would be but I have thought of these:

- How much is that in UK£ ?
- How many times the average UK salary is that?
- When considering how much students said they might pay per year, how does that compare to this bill?
- What percentage of the total bill was for the (presumably initial) Emergency Care service?
- If the dates at the bottom are correct, what was the cost per day?
- Is it possible to use this as a guide to estimate the cost of treatments in a hospital for a year?

I’d love to hear your suggestions for what you could do with this!

Just a simple idea that came up recently. I needed to buy some batteries and was genuinely faced with this choice.

What option would your students recommend I buy?

(Don’t forget to mention that your local shop was giving away dead batteries – free of charge!)

I can’t remember what I was googling but I found this claim about blood.

A starter task could be to show this image and then ask what else we’d need to know to verify this.

Things that might be useful could be the average weight of a human, whether blood weighs about the same as water (1 litre of water = 1 kg) and whether we have a sense of how much blood might be in a human (1 pint, 10 pints, 100 pints?).

Does the 7% claim match what they’ve said for babies?

You won’t need me to tell you it has been a difficult year both in teaching and elsewhere. In this post, I’m going to pick out some of my most favourite parts, share some new resources and explore some things I have planned for the Summer and next year. You probably won’t be surprised to find out the Core Maths features heavily but there are some other things sprinkled throughout too.

**Lockdown**

The lockdowns were difficult but there were some positives. My classes really made good use of Desmos and the introduction of Google classrooms to the whole school has transformed setting homework. I can’t say we’ve totally mastered it yet but it has the potential to be a great long term time saver. Another bonus to Google classrooms was that it allowed us to share our workload and collaborate on projects/topics in a way we hadn’t ever really got round to before. Because other teachers were recording their instructions for how to do something, this has the potential to be a great CPD tool when we look back at these videos in the future.

**Tutor time**

My school uses vertical tutor groups so years 7 to 11 are mixed up and year 12 and 13 are mixed. I’m a 6th form tutor so I’ve had a year 12/13 tutor group for about 10 years now. Due to Covid, we split the year groups up so I kept my year 13s and inherited some others and, we’re planning on keeping them split next year too. This is something I’ve been interested in for quite a while so I’m keen to see how this works out. There is no real doubt that the needs of year 12 and 13 in September are very, very different so I’m looking forward to having a chance to really work with my year 12 tutor group and give them a proper introduction to 6th form life.

There are two things I intend to make use of as part of being the maths specialist tutor group. One is from the Great Gatsby talk that Cat and Rachel gave where I intend to show off some other career options to my year 12s. Some of them already have some idea about what they want to do but, whether that’s the case or not, I want to show them that there are other jobs out there (like urban redevelopment) that they simply might not know about. The second thing I want to do with my tutor group comes from Catherine Madden’s talk about visualising inequality. There is going to be a competition in the first term back and I’d like to get my tutees involved. Maths/Data can be visually appealing/creative and I’d like my students (and perhaps, the school newsletter) to see that!

**Core Maths resource updates**

As a result of the AMSP’s Core Maths Festival, I have updated some of my resources and re-uploaded them to the TES. These really are some of my best work and took an exceptionally long time to improve. I’ve used ideas from Dash’s talk and Jen’s (from Uk Data service) to improve my sampling and numerical data analysis material. These now include the bullet hole problem and genuine data from the NATSAL surveys to make a more authentic resource.

As part of the festival, I was given the honour of running one of the sessions about finance. It’s a topic that teachers ask about quite a lot as it’s just beyond most of our comfort zones. One of the things I really enjoy about running a Core Maths session for the AMSP (aside from the great help you get from Cat and Tom as well as the fantastic bunch of teachers that come along) is that it gives me a real reason to think really hard about something I teach and which I do it that way. One of the great things that happened in this case is that I’ve come to the conclusion that I’ve been misusing my time on the finance aspects by focussing too much on APR and not enough on some of the other aspects. I haven’t actually got round to updating my finance modules yet but they are in the pipeline. You can read more about that talk here and I’m sure I’ll update this blog once I’ve adapted my resources.

As part of the AMSP Core Maths networks, I spent some time discussing aspects of the specific course I teach with about 20 other teachers. Three things that have come out of that are:

- Critical analysis is difficult and there’s some scope for an easier introduction. I’ve incorporated that into my scheme of work and the resource that’s on the TES. More to come on this when I build the rest of that module.
- Fermi Estimations can be at there best if there isn’t an easily Google-able answer. I’m planning to see what questions I can think of that would fit that bill.
- Histograms may have a purpose! After quite some discussion, it might be that histograms have a use in comparing sets of data. I’ll have to do some more work on this but at least I have some reason to want to use histograms now!

This year saw my first attempt at a Quibans style article (about Marcus Rashford’s book club) and while I’m pleased with how it came out, I can assure you they are harder to make than you might think!

**Summer plans**

Rest.

Spend time with the family and do some reading.

Pick a couple of topics to continue to develop. It’s likely to be the finance and critical analysis but I might need to do some thinking about the Normal Distribution.

Accept that this is not going to happen quickly. Dash was right when he said that these things take time and I think a realistic aim is to get this course, the scheme of work and the homeworks all sorted to the standard I’d like them to be over the course of about 4 years.

**A nice way to end the year**

To round things off, I received a lovely email from Tom and Cat asking if I’d like to be officially recognised as a Core Maths Advocate. More details of that to come in the new year but it was a great end to a difficult year!

If you’ve got any comments, questions, requests for resources or anything else that you think I might be able to help with, please feel free to ask. I can’t promise that I can help but it’s usually worth asking!

I hope you have exactly the type of Summer you desire 🙂

A little while ago, Kerry sent this tweet:

*Anyone got a book/website/podcast list that is suitable for students who are half way through their #coremaths course. If not a list, then recommendations please so I can compile a list, thanks!*

Well, no-one had a list so she compiled one and has very kindly allowed me to share it here.

If you have any suggestions of your own, please message @KerryDunton or leave a comment here.

Thank you Kerry!

*In this series of blog posts, I’ll summarise my take-aways from the most recent series of AMSP Core Maths Festivals. *

*The festival is finished now but there will be more in the next academic year.*

** Tom Button** (

**@mathstechnology**) is the MEI Mathematics Mathematics Technology Specialist and leading MEI’s work on the development of Data Science courses and materials for pre-university students.

MEI has developed a free set of self-study resources to introduce Core Maths students to the wonders of Data Science. This is a series of lessons including videos and programming activities in Python (though no prior experience of coding is required). The lessons are designed to be studied as an optional course alongside Core Maths.

In this session we explored the resources and how they can be used with your students.

Tom introduced himself and then asked us to discuss how our students have used technology to explore data? It didn’t take long for my group to acknowledge that we hadn’t really done this much beyond using calculators. Some people had made use of spreadsheets but it all felt somewhat limited and with a real struggle to connect the desire to use technology with our own lack of experience and the considerations of what gets asked in exams.

Before looking at the course, Tom shared that he views Data Science as being the intersection of Domain knowledge (the context), Technology skills and Statistical understanding. Society is naturally producing huge quantities of data on a daily basis and technology is more advanced than ever so is now capable of handling this vast amount of data. An interesting point is that Amazon has the computing power to use its vast database as a census rather than even needing to sample.

The Introduction the Data Science course is intentionally a short course so as to be manageable alongside 3 A levels and Core Maths. It is free and self-study (so teacher input is not needed). The course uses real data contexts and includes the A level Large Data Sets (from all exam boards).

Also, an important pragmatic point is that there is no log-in or sign up needed to do the course.

Amongst other things, the course covers:

**How to pre-process data**. Including things like actually downloading data, converting CSV files to Excel compatible formats, cleaning the data.**Visualisations.**Obviously this links to the previous session by Catherine Manning but includes technology based ways of doing this.**Predictive models**. Scatter graphs are often used as an explanatory model. This course explores ways to use the data to be predictive.**Coding**. Tom talked about the course emphasising the importance of some beginner-level coding and how crucial this is for when data sets get beyond the capacity of spreadsheets.

We had a chance to explore the modules in the course and there is a great collection of videos from real data scientists covering a brilliant variety of subject areas. They mostly follow a format of a video, then 1 or 2 activities, then maybe another video and another activity. In each module there is a further reading section and a ‘meet a data scientist’ video.

In the second part of the talk, Tom gave us a brief introduction to coding in Python. This language is free, comparatively easy to get started with and also commonly asked for in job adverts. The Data Science course uses Python through a web-based coding environment called Kaggle. If desired, it is possible for students to share their Kaggle notebook with teachers.

Again, we had a chance to play with this tool and while I didn’t get enough time to look thoroughly, the parts I saw seemed pretty intuitive and easy to use.

Finally, Tom showed us how Kaggle can do things that spreadsheets can’t with a data set containing **all **of the national house sales from 1995 to 2020. The data set contains over 22 million pieces of data (!) which would obviously break Excel but was handled with ease by using coding in Kaggle. It was an impressive demonstration and has certainly made me think about what could be done with coding.

Some possible ways to use this course are:

- An optional summer project for students
- As preparation for any data-based Extended Project Qualification (EPQ)
- Working with teachers/students in other subjects

As a finisher, Tom told us that there are plans for a data science taught course in the Autumn term. It will be aimed at year 13 students that have completed the self study course and looks to be an exciting opportunity for students to really stand out from the crowd! More information on that is available here.

This was an excellent way to finish this series of sessions in the Core Maths Festival and it was great to have a change of pace/approach/style. Thanks to Tom for this session and to all those that have helped to make the Festival come together.

**My take aways:**

- I want to complete this course myself. I’ve already completed the first module and am looking forward to working through the rest over this Summer.
- I intend to offer this to my current year 12 students as I think some of them will enjoy the challenge.
- I am going to share this course with some colleagues at school. There are certainly some other maths teachers that would love it and I think there may be some teachers of other subjects that would benefit from it.
- This course does seem like a good way to provide some differentiation for the top end students that take Core Maths. A little bit of extra work that they could sink their teeth into.

*In this series of blog posts, I’ll summarise my take-aways from the most recent series of AMSP Core Maths Festivals. *

*The festival has finished now but there will be a 4th Core Maths festival in the new academic year.*

This one is a special guest blog post from James Maloney – thanks very much! It also has the slightly weird aspect of being about the talk that I gave. I’ve added my comments and thoughts throughout in *purple italics.*

As we entered this session of the Core Maths Festival with @reflectivemaths, the talk was of England’s first knockout game of Euro 2020. There seemed to be an even split between those who cared and those who were working out what rule changes would be necessary for them to even begin to register a picogram of investment.

**Cake Emergency**

Dave knows what motivates Core Maths teachers though, and attention was swiftly on his session, with a question involving delayed payment for a cake from a parents’ evening.

(It might have helped my atrocious guesstimate had I properly noted the date of the parents’ evening!) Of course, it was very large number and Dave then talked about where he took the discussion then, revealing some of the questions students have asked in the past:

• How big is this?

• Compare it to the UK national debt

• What would happen with regards to payment etc?

• At what point does a debt become untenable?

• Could Dave go to prison?

• Was the brownie nice?

• Are Jaffa Cakes cakes or biscuits?

I really like how Dave acknowledged the seemingly more frivolous comments that may be dismissed as being pointless to explore, as these can often lead to deeper and different types of understanding. For example, asking whether the brownie was nice could lead to discussions about value, and that a lot of human decisions are not made on numbers alone but in conjunction with aesthetic or risk judgments. Similar approaches were discussed around Phone Emergency which led into Payday Loans and how Dave went through loans with his students. We had a quick discussion about how to use payday loans in Core Maths, now that legislature has limited the extent of the debt a person can build up. They have lost a little of their impact on student engagement due to this, but remain a useful hook. This year I have added in a discussion about the ‘Brighthouse’ model of buying electrical goods and appliances on credit, as I felt this business model had grown as the payday loan business model was curtailed by the legislation. Incidentally, I’ve also used this example for GCSE resits as instalments are common in exam questions there. **I’d be interested to hear more about this!**

**Timing** **and What is a Financial Question?**

We then had a poll on when we taught financial maths in our schemes of work. Dave revealed he allocated a lot of time for financial maths and noted that it wasn’t the first topic, preferring to start with estimation. I was really interested to hear how Dave and the other attendees approached this as I wanted to compare it to my college’s first year of teaching AQA option 2B, with a focus on different elements to our previous exam board.

Dave then focused in on APR, on which he spent a lot of time (showing his powerpoint to illustrate this) and wanted our views and ideas on whether it was worth spending so long on it. His grade 8/9 students liked doing the APR formula as it ‘felt mathsy’ and challenging but those with lower grades, well, not so much! So Dave went through his analysis of the syllabi of the exam boards. APR was only mentioned specifically in AQA and NCFE, though it was not ruled out from being examined in the other boards. A series of polls asked us what percentage of marks we thought were allocated to financial questions and whether we thought two examples of exam questions counted as financial questions.

Dave didn’t get the answer he was expecting for either one, ** (I don’t really think this is a finance question)** but it was generally felt that any questions with money involved should be considered as financial in the exam. A table showed that AQA would consistently have 15-20% of marks related to financial maths while Edexcel and OCR were less predictable.

**APR or AP Aren’t?** *(This could have been the talk title!)*

A discussion in break out rooms about how we’d covered APR this year, led to comments from attendees and Dave that we probably should not spend too long on APR and perhaps it could be thought of as more of an extension opportunity. * (I do want all students to be aware of APR and what it means but I’m not convinced the technical breakdown of the algebra is useful for the majority of students.) *The year it came up on the AQA exam, it was a very poorly answered question according to the examiner’s report.

*(Although it is fair to point out that it was a fairly tough variant of the topic.)*At this point, I was reflecting on having now taught AQA for one year, I’ll be reducing how long I spend on APR. In preparation for assessments, I had told students, if only from a timing point of view, any question on APR was likely to be involving only 1 or 2 years, or one of the simpler substitutions. My focus for next year will be more substitution into financial formulas in a broader sense (mortgages etc). Seeing past paper questions this year, I’ll be treating APR and AER as specific examples of the skills involved in substitution. Past papers questions have shown that AQA like to test the ability to work with any financial formula and sometimes they are linked to spreadsheets and iterative formulas. Students need to be prepared to use a financial formula they have never seen before, so I’ll be emphasising noting time periods and expressing percentages as a decimal and those skills that are common to financial formulae.

**Financial Maths Bucket List**

Dave’s next question was, ‘So what financial aspects should a Core Maths course cover?’ Dave gave us his list (see below,) based on what he’d like his children to know.

Crucially his list wasn’t just about topics that were specifically on the Core Maths specification and brought in other areas from the course such as critical analysis. I completely agree with Dave here, and it mirrors comments I suspect we’ve all had from CM students along the lines of, ‘I wish we’d done this at GCSE!’

Then we came to the section where Dave’s considered analysis set about inspiring tasks and problems he’s used in his lessons along with the beginnings of ideas that are not yet fully-formed. They definitely got me thinking! As so often during the Core Maths Festival, my brain and muscles were scrambling to get the smorgasbord of ideas filed away for future reference, attached to a lesson from last year I wanted to change, or noting down how I was going to use them. These included

- Monthly budgeting
- “Car or Moped” (about students’ college transport
- Raising the pension by £10
- Gapminder’s Dollar Street
- Mortgages vs rent
- Claiming Expenses
- Food poverty
- Pay slips
- Student loans

We closed with a snapshot of Dave’s alternative SoW with new titles to the lessons to create a more interesting sounding Scheme of Work. **(I know this needs some work but it feels far closer to how popular science books organise their chapters compared to how a text book would.)**

I like this idea, and I’m going to see how it goes down with my students. The Core Maths teachers in my department preferred to stick to our traditional topic listings however! *I’m a little surprised by this!*

A tiring but inspiring final section then, leaving me needing time to process everything. Any time I’ve attended a session with Dave, there’s been a wealth of ideas and resources presented. From there it’s up to us to analysis, use and adapt what we feel will work best with our students. Dave always has a fresh and unique perspective and the common topics all of us spend our time thinking about and teaching. Thanks for another inspiring session, Dave and the Core Maths Festival! **Thanks. This is a very kind summary.**

**Main Takeaways**:

- Don’t spend too long on APR!
- Teach substitution into financial formulas generally rather than specifically AER/APR.
- Students will be most engaged with financial situations most relevant to them.
- They still appreciate covering topics they won’t encounter immediately, like mortgages.
- Remember students will likely know less of the world than you expect!
*Finance is a good opportunity to cover some of the social inequality aspects that will crop up.**Anything that makes students realise how much money it costs to be an adult is time well spent!*