Worksheet 4 multi step tax question

Let me know what you think.

*Edit: updated the worksheet with a couple of additions.*

Here is this year’s version – it’s great to use in tutor time every morning.

Please share with as many people as you can!

Should you prefer a different format, here are a couple of options:

School Kindness Calendar ppt – you’re welcome to adjust and adapt.

]]>I used these 5 example payslips as a starting point (all from a google search for UK payslip examples). After spending a long time getting students to look at them and see what they have in common as well as asking anything they wanted to know, we moved on to looking at some basic tax calculations using the preliminary material from last year.

Here are some questions I was asked along with (some) answers:

**What does BACS mean?**

Basically it’s a bank to bank transfer. It stands for Banker’s Automated Clearing Service.

**What does OSPP mean?**

Ordinary Statutory Paternity Pay.

**What does Attch: CSA mean?**

A court order for an ‘attachment of earnings’ from the Child Support Agency.

**Why does the tax year start in April?**

Complex. Much easier to check out this article.

**Why is the maximum for Child Tax Credits £243 per month.**

I don’t know. I can tell you it’s £55 per week and it’s separate for each parent but that’s not much help.

**Why does the gross for National Insurance value sometimes appear a few pounds less than the gross for tax?**

Not sure about this one either. Have a look at the payslips for examples though.

**In the preliminary material, it says “To calculate your income tax if your annual income is £100 000 or less” and then some instructions. What is different if you earn more than £100 000 ?**

Also don’t know yet.

**What’s the difference between Nil National Insurance and 0% National Insurance?**

Essentially, Nil means you haven’t contributed. Your benefits could be affected if there are gaps in your National Insurance record. If you fall in to the 0% band, you’re considered to have contributed to National Insurance even though you haven’t actually paid any money.

**Do you only pay tax when you are 18 years old?**

No. You’re eligible to pay tax and National Insurance from age 16 if you reach the thresholds for either of them.

**Why are the words ‘Gross’ and ‘Net’ used?**

Don’t know and am struggling to find out.

*That’s it for now. I hope you’ve learnt something and if you can answer any of the ones I couldn’t, please leave a comment!*

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**Data Handling**

I’ve gone through all of the graphical aspects that my students need to cover including box plots, cumulative frequency, histograms and stem and leaf diagrams. If I’m honest it was a fairly dry approach making use of lots of GCSE examples and questions. It was difficult to manage having students that hadn’t covered the material due to doing foundation tier while others were already comfortable having covered them at higher GCSE. It’s certainly an aspect I’ll have to talk to other teachers about and get some better ideas/approaches for next time. This is definitely the topic I’ve found hardest so far as it’s felt like there’s been a lot of material to cover in a short amount of time and I opted for the ‘here’s how to do it, now here’s some questions’. I would like to teach this through some sort of project really but I was worried that there would be very little practise of the actual skills involved. Anyone, that’s one to plan better for revision and next year.

**Finance**

I’m quite excited about teaching the finance aspects as it’s definitely one of the main topics that students have taken the course for. It’s also a major selling point for parents when I was talking about the course at the sixth form open evening.

I tend to start my planning with a mind map and I like to use a piece of software called ‘pen and paper’:

I’m not really very far through the planning yet but some sources I’ve been pointed to are:

Stella’s MEI conference notes

Barclay’s Life Skills (filter by ‘finance’)

Natwest’s MoneySense

It’s still very early days and there’s a lot to look through and filter out. I’ve decided to start with looking at payslips (it’s very hard to find convincing looking mock ones!) and then move into Tax and National Insurance using the preliminary material that seems consistently used in the AQA course.

My school has also been sent a set of these books:

I’ve had a look through and I’m sure there are some useful bits in it (the extensive glossary if nothing else!) but it does seem very text-heavy at first glance. No doubt once I’ve had more time to look through again, I’ll pull out the most useful parts.

**Some concerns**

I’ve been teaching since 2001 and in that time, there have been (many) things I’ve taught but not really understood. There have also been things I’ve taught but can’t actually really do very well (I’m looking at *you* year 13 pure maths). Usually, I’ve managed and have had a network of other, experienced (or simply better at maths) teachers to lean on, however finance is definitely an area where I feel a bit like I’m somewhat in the dark. I’m going to go out on speculative limb and suggest that might be the same for many core maths teachers. I’ll be honest, I didn’t know the difference between AER and APR (I do now and the secret is they’re basically the same but ones for saving, ones for borrowing) and I actually am not sure how to do some of the finance questions.

It is a little embarrassing (and I know how the psychology, chemistry and DT teachers that have been asking for maths help feel) but on the other hand, it’d be stupid to pretend I can do these things and hope for the best. So, here’s a question I’d like help with:

*If I use a payday loan company and borrow £100 with an APR of 4032% for a period of 15 days, paying off the full amount (with interest) at that point, how much do I actually have to pay? [and how did you work it out?]*

I have searched the interest for help and found nothing useful so any help you can give would be great! I’d be willing to bet that if I asked this question of many people working in banks, they might not be able to answer either (although that’s possibly me clutching at straws to make me feel better!)

]]>I’ve put together this simple list of questions as an in-class quiz. I’m planning on allowing them to look in their notes so that this task will also serve to see how organised their folders are.

Here are my questions (based on covering Fermi estimation, Correlation/Regression, Numerical data analysis).

Give a suggestion for the size of the population of a small town. |

What is “primary data”? |

What word beginning with R is another one to describe a line of best fit? |

Complete the sentence, “Interpolation is generally _____” |

What is the average life expectancy in the UK? |

How many countries are there? |

What is “discrete data”? |

What is a reasonable suggestion for the height of a house? |

What are the highest and lowest that the correlation coefficient, r, can be? |

T/F In science, a line of best fit can be a curve. |

T/F Standard deviation is linked to consistency of results. |

Briefly describe how a systematic sample is done. |

What is the average number of hours sleep per night? |

I’ve been pulling ideas from Twitter, other teachers and text books to make some resources I’m really proud of and you can download them on the TES. I felt like I wanted to make some resources for Estimation (as there simply isn’t that much around) and I knew I could adapt my numerical analysis, correlation and regression lessons from A level to suit the course.

However, it’s very time consuming and my next topic (see the scheme of work here) is graphical data analysis, which something I’ve really taught much of as it hasn’t been in the AQA S1 and S2 modules. Since these are mostly GCSE topics anyway, I’m going to go down the route of adapting resources I can find and treating this module more as a collation exercise. I’m sure I’ll be writing new material for some other topics and eventually for these ones too but I can’t do it all and there are some great resources out there already anyway!

So, I’m going to have a few posts that are simply a collection of resources, in the order I intend to use them. I’m going to teach each of the graphical methods and then tie them together into a task. First up is:

Beat the Teacher (described here by Jo Morgan)

http://www.resourceaholic.com/2014/07/stem-and-leaf.html

Stem and leaf explanation ppt (Craig Barton)

https://www.tes.com/teaching-resource/stem-and-leaf-powerpoint-lesson-6030328

Creating Stem and Leaf Diagrams (Jo again)

https://drive.google.com/file/d/0B9L2lYGRiK2bOFlobFFDMzE5QW8/edit

Stem and leaf diagram very simple worksheet (only use for very weak students if needed) (nottcl)

https://www.tes.com/teaching-resource/stem-and-leaf-diagrams-worksheets-6018092

Interpreting/reading S&L diagrams inc back to back (I’ll adapt to include some IQR) (Dannytheref)

https://www.tes.com/teaching-resource/interpreting-stem-and-leaf-diagrams-6387426

GCSE exam questions (Maths Genie)

]]>When putting together some slides for this section of Core Maths, I put in the question “What does average mean?” I realised I didn’t actually know where the word comes from so I used Google’s etymology search and found that it comes from a time when cargo ships would be transporting goods around. Sometimes the goods would be damaged and the French word *avarie* is “damage to ships or goods”. The decision as to how to **fairly share out the costs** was developed and the suffix -age from the word damage was used. Eventually, this word came to be associated with a more general sense of sharing things out as is done in the mean.

I’ve also been teaching the Standard Deviation. I made a point of going through the long calculation (even though it’s not needed for this course) as I think it’s important to try and understand *what is going on* rather than blindly use a calculator. It’s not a complex process and most students were fine with following it along. I also think it gave them an even better appreciation for the power of practising with their calculator modes (given the alternative process!)

To help come up with situations where standard deviation is important I asked Twitter to suggest scenarios and got a nice list. I’m working on putting these into a worksheet (which I’ll share once it’s ready) but I wanted to thank all those that contributed. I discussed this and the etymology of average on episode 61 of my podcast Wrong, but Useful.

In terms of comparing data sets using mean and sd, I went looking for other questions and found this one on an AQA A level Psychology paper. (Note that there’s no expectation for them to be able to calculate the sd in that course.)

I think it’s worth noting that it’s 4 marks and looking at the mark scheme is interesting too:

The Examiner’s report on this question is eye-opening too:

Although there were some strong responses, generally students found this harder than anticipated.A number failed to receive any credit due to simply defining the mean and the standard deviation. It was also far too common for students not to understand and answer the ‘justify’ component of the question. Many students simply restated information from the table or provided possible explanations or conclusions, as opposed to justifications. Although students generally saw the mean as showing a difference, there was often the claim that music hindered performance, with confusion regarding time being a higher score, meaning slower.

Worryingly, some students still have little understanding of standard deviation.

Hopefully that’s given you some things to think about regarding this topic and our course will help with that bolded section above!

]]>I’ve combined those suggestions along with some continuous and qualitative types (both of which are far easier to come up with!) and made them into a tick sheet. Students work collaboratively on the first set of examples, then, after going through those answers together, there’s another set for them to have a go at by themselves.

Thanks to all those that contributed and feel free to use this yourself.

]]>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.

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