Getting Fit & Fundraising for Cancer Charities - Completed!

May 2022's fitness challenges are now complete: the results are in!

Well... The preliminary results are in. There's still time for you to change the final figures by clicking on one (or both) of the images below and donating:

201.2 miles cycled and £355 (+gift aid) donated to Prostate Cancer UK
3,100 push-ups pushed up and £315.00 (+gift aid) donated to Cancer Research UK

Many, many thanks from the very heart of my bottom to anybody who has donated anything to either of my challenges: £670 isn't bad!

See below the jump for the original post:

Calculating Day Rates for Freelancers

This day rate calculator was created by me and is based on Paddy McNulty's advice given during GEM NE's training session ""How Much!" Know Your Value - Pay and Conditions of Freelancing", 12/01/2022. It was initially produced as a spreadsheet but this might be quicker and easier for people who don't want to download their own version to play with. It also gave me an opportunity to play around with some coding1.

A hand offers a money bag to a confused person.

To use it, just change the numbers in each of the editable fields. Totals and rates will be updated automatically as you do so. If you're not sure what to put in any of the fields, just experiment with some different numbers. and see what happens.

Annual Income

Salary (before tax, pension, etc) £
You could think of this as an equivalent salary that you'd be happy to work for if you were to go back to working for someone else.
Projected costs & expenses £
If you were working for someone else you'd expect things like insurance and work expenses to be covered by them, so estimate how much extra you'd need to cover these as a solo act.
Desired reserves/profit £
Building a business costs money; fallow and rainy days can pop up at any time, or you might just want to be able to put something in your savings. How much do you think is right?
Target Income {{ salary + costs + reserves | currency : "£" }}
This is simply the previous three numbers added together, and gives some idea of what someone else may spend on you if you were working for them full-time.

The target income above will give you an idea of what you'll need to have landing in your bank account over the course of a year to continue living in the manner to which you have (or would like to) become accustomed.
To work out what to charge people to make that happen, carry on into the next section:

Daily Rate

Working days per year: days
According to Paddy, freelancers get about 150 days of paid work per year: this needs to cover all of the income that you've stated in the cells above. Feel free to change this if you win more or fewer proposals (on average) in a year.
Holiday / sick days per year days
Everyone gets ill from time to time, and we're all entitled to days off. These need to be covered financially, though, so we've got to include them in our calculation. Paddy suggested 28 days per year is reasonable, but you may want to give yourself more holiday, or provide a larger buffer for sick days (or reduce these if you're only freelancing for part of the time).
Final Day Rate {{ ( ( holidays * (salary + costs + reserves) / workingdays) + (salary + costs + reserves) ) / workingdays | currency : "£" }}
This is your target daily rate to charge if you want to reach your target income over the working, holiday and sick days entered above.

The daily rate calculation works out how much you'd need to charge per working day to meet your target income from the previous section, and assumes that you want the same level of income for your paid sick and holiday leave. It then spreads this extra income requirement across your projected working days.
Sometimes we don't work full days in one go, though, so...

Hourly Rate

Working hours per day: hours
A standard working day is around 8 hours long. If you're happy to work longer hours, or if you want to work shorter days feel free to change this!
Final Hourly Rate {{ ((( ( holidays * (salary + costs + reserves) / workingdays) + (salary + costs + reserves) ) / workingdays)) / workinghours | currency : "£" }}
If you're not working a full day, e.g. you're delivering a session at a conference, or doing bits of work here and there, this is how much you should be charging per hour. Be aware that you should probably include time to prepare, travel, set up, etc when you're calculating what to charge in order to hit your targets set above.

All this section does is divide your calculated daily rate by the number of hours in your working day.

If you find this useful:

Get in touch with requests or issues

  1. It also helped that I had a number of far more important and pressing things to be getting on with.  

IMA Workshop (online): Python for A-Level Mathematics and Beyond

On Friday 21st January 2022 I attended an online training course hosted by the Institute of Mathematics and its Applications (IMA) and delivered by Dr Stephen Lynch. The course was titled Python for A-Level Mathematics and Beyond, and was marketed at delegates with "no prior knowledge of programming".

At the beginning of the workshop I started to live-tweet...

... but very soon needed to concentrate too much to be able to continue. As a handful people seemed to be interested in the content I thought I'd write up my experience here.

Redundancy: One Year On

Today marks one year since my redundancy from Bletchley Park. ⅓ of the workforce was in the same boat (notably, ⅔ of the Learning Team, following the general narrative of education being hit particularly hard with redundancies across the cultural sector). I was lucky in being able to walk straight into two part-time teaching roles within days of leaving, but many struggled to find work in a highly competitive sector with drastically reduced funding.

A hand raising a glass of Prosecco
This was taken a couple of days after my redundancy came into effect!

Since then, aside from my teaching roles (one of which I still occupy) I have completed a number of projects as a freelancer. Looking back over the year I am astonished by the range of things I have done, both independently and with my ex-BP Learning dream-team colleagues (and friends) Catherine and Kate, who were made redundant alongside me.

I've completed projects with Potential Plus UK, the University of Northampton, the Open University, Museums Sheffield and the Sheffield Industrial Museums Trust, the Leicestershire County Council Museums Service, the University of Nottingham's Museum of Archaeology and Lakeside Arts Centre, and others. I'm currently working on a project with GEM, and about to get started on another with the Motor Neurone Disease Association

Alongside all this I've presented at a conference, made new contacts and connections, and completed the first year of my Master's in Education with a Distinction grade in all assignments.

It's been a tough, busy, interesting and very satisfying year, and much of it would never happened had I not been made redundant. Choosing to go back to teaching part-time was terrifying, but it was a gamble I'm glad I committed to.

My intention, here, is not to show off (although I am proud of myself): it is primarily to record what I feel is a milestone in my own life. Secondarily, it's potentially a datapoint towards confirming the hypothesis that Things Can Change: I've broken somewhat free of the traditional nine-to-five; I am, at least for part of the week, my own boss. All it took, in the end, was the kick up the proverbial that my redundancy provided.

Thirdly, I'd really like to hear the stories of other people who were hit by the Great Cultural Sector Jobs Implosion of 2020 (especially other educators), either privately or in the comments:

  • Are you freelancing too? Feel free to describe what you do and post a website link or contact details.
  • Did you find another job? How? What and where?
  • Are you still trying to figure things out? Do you have plans that have not yet come to fruition? What are they?
  • What are the main lessons that you have learnt from the whole experience?

Calculating 5th Roots - IN YOUR HEAD!

Multiplying a number by itself (e.g. $ 6 \times 6$, or $6^2 $) is relatively easy. Going back the other way - finding out what number has been squared to get a particular result (or finding the "square root", e.g. $ \sqrt{36} $) - is tougher: you need to either just know the answer or just guess it (and, of course, square it to see if you were right, and then if you're wrong have another guess, informed by the outcome of your first one).

Cubes (the cube of 6 would be written $ 6^3 $, or $6 \times 6 \times 6$, for example) are similarly relatively simple to calculate compared to cube roots (e.g. $ \sqrt[3]{216} $), which also require a bit of trial-and-improvement (if you're working with secondary-school level maths).

Raising numbers to the 5th power (i.e. $ 6^5 $, or $6 \times 6 \times 6 \times 6 \times 6 \times 6$) is, again, fairly easy (though you'll probably need a piece of paper), but working out a 5th root (so, figuring out that $ \sqrt[5]{7776} $ is actually 6) involves quite a bit of guessing, trying, failing, and guessing again.

Except... if you're trying to work out the 5th root of a number that is the result of raising any two-digit number to the power of 5 there's a rather nifty trick that you can use to do it in your head. Indeed, with relatively little practise you'll be able to calculate 5th roots quicker than someone who doesn't know the trick can bash it into a calculator.

I described this trick as part of a 24-hour maths marathon broadcast in October 2020. You can find out more about the event here, but if you'd like to find out how to calculate 5th roots in your head really quickly, watch my section in the player below:

If you'd like me to add a readable description of the trick to this post, please let me know in the comments!

Mathematics Teaching in Indonesia

My first assignment for my Master's course was to "look at a chosen aspect of education in one country and comment on the socio-economic, political and cultural influences on this aspect of education [using] an infographics tool to present [my] findings."

The country was a largely random choice: I didn't have a particular country in mind so I just sort of broadly read around until I landed on something that struck me as interesting. Could the aspect I chose really have been anything else?

I completed and submitted the assignment at the end of November and have just received my grade* so here it is:

Mathematics Teaching in Indonesia

The Third Reich Is Listening

As Bletchley Park's "Enigma Man*" I was often asked the question "... but what were the other side doing?" The museum doesn't cover this side of the story other than very fleetingly and in passing so it was always tricky to answer, but it is nevertheless a very pertinent - and thoroughly interesting - question.

This is my copy of The Third Reich is Listening and you can't have it (but you're welcome to buy your own, or borrow it from a library, of course)
This post is, essentially, a review of Christian Jennings' The Third Reich is Listening.

Its subtitle "Inside German Codebreaking 1939 - 1945" tells you the main focus of the book, but the story does start earlier than that, summarising work done by key characters in World War I and the inter-war years.

BP's story is utterly fascinating whether you have the briefest of overviews or a more in-depth understanding. As you wade deeper you find that every part of it is much more complicated and involved, from a historical perspective, than you had ever thought possible. Every aspect of allied operations in World War II has the site's work somewhere in its background and the story has an almost fractal nature to it: pick any part you like, zoom in, and you'll see it explode into so much detail you'll wonder why nobody has started a museum dedicated to just that bit.

You'll also notice, as you learn more and more, that almost every aspect of the story is steeped in myth and misconception. So many things that are common knowledge, routinely-told anecdotes when scratching the surface turn out to be simplifications, half-truths, or downright incorrect as you pick apart the evidence.

One such myth is that the codebreakers were working to reverse-engineer an almost completely unbreakable cipher. This, when dipping your toe into the story, is not incorrect: Enigma** is a tough nut to crack. But as you wade into deeper waters you find there's an unspoken caveat: if it's used properly. Bletchley's codebreakers had a helping hand, and not just from the Polish mathematicians who figured so much of it out before the war even started: Germany itself proves very helpful in the fight against Enigma. At the lowest level, mistakes were made by Enigma operators that were of great aid to their counterparts in the brick blocks and wooden huts of Bletchley Park; as were many features of the procedures put in place at much higher levels.

One key theme in favour of allied codebreaking was Germany's disbelief that its ciphers had been (or could be) broken. As Jennings puts it, "the Third Reich might have been listening but increasingly it had its fingers in its ears."

All this is just a very brief, very anglocentric view of what was going on in Germany.

Whilst there are still many and varied parts of allied codebreaking in World War II still to be uncovered, clarified or corrected in the public mind, the mirror within which we may see Germany's point of view is cloudy and smudged, and hasn't been dusted in a long time. Jennings' book takes a damp rag to it and does a surprisingly good job of clearing away some of the grime.

And what we can see is just as fascinating as the story we already know. There are parallel figures in that world, characters even more forgotten than the codebreakers of Bletchley Park, such as Wilhelm Tranow, and internal fights against an oppressive and militaristic regime to rival those depicted in The Imitation Game. There are revelations of mistakes made by British encryption procedures and communications staff that equal those made by Germany, and which similarly aided German cryptanalytical victories. There are disastrous decisions that reduced its effectiveness and eroded the viability of what could have been a genuinely effective rival to Bletchley Park.

If you're interested in secret messaging during World War II and, so far, you have only read about Bletchley Park you have restricted yourself to less than half of the story. The Third Reich is Listening is a surprisingly comprehensive introduction to the parallel world that is German codebreaking in World War II. It takes us out of the narrative that they're just the Bad Guys in the Bletchley Park story and shows us the human ingenuity, struggles, victories and defeats of a whole new, largely unexplored dimension of the history of cryptography and cryptanalysis.

* I used to visit schools (and other places) with an Enigma machine on behalf of the Bletchley Park Trust. I would often introduce myself at reception, with the response "oh, you're the Enigma man!"

** Of course, another myth is that Enigma was the only, or toughest, cipher being broken at BP.

The Most Important Thing in Your Pencil Case, or Calculators Ain't Bad

I have a friend who's starting secondary school in September. Her mum sent me this:

I need your opinion on something. B is laughing at me because I said that choosing a new pencil case is THE MOST IMPORTANT thing about a new school year. I messaged my English dept, but she said they’re bound to agree and I needed to message a Maths teacher. Thoughts?

I responded with:

I nearly agree... THE MOST IMPORTANT thing is assembling your pencil case kit, which includes choosing a new pencil case, but you have to make sure the right kit is in there - non-exploding pens, for example. The stuff that goes inside is important because that will help to inform which pencil case is the right one. It might feel right for a moment, but if it doesn't fit what you need, or allow you to arrange it how you want to then it's not the right one.

Two calculators that have stood the test of time from my own school days. I've just noticed that the batteries haven't, though.
Two calculators that have stood the test of time from my own school days. I've just noticed that the batteries haven't, though.

I then listed my essential pencil case kit. That's not really what this post is about, but of course I have included it at the bottom for all and sundry to disagree with. 

The final thing on the list, THE MOST IMPORTANT thing to go in your pencil case, is a calculator.

And that's something I really do believe.

Calculators are not the enemy

Teaching to the Void

Following a conversation sparked by one of their training events GEM, the professional network for people interested in learning through museums and heritage, asked me to write a guest post loosely based upon (and an expansion of) the ideas in this post. It's here:

    Teaching to the Void at

Is Zero Odd or Even?

It's been a while since I posted something mathsy, but I've seen a few people being wrong about this one lately, so here goes...

Let's start with the popular-but-wrong response; the one that would get the QI alarm awooga-ing: "it's neither!"


Now I've lit the blue touchpaper for a few ranty comments or tweets, let's look at the facts. A good place to start is to take a step back and ask...

What exactly is an even number?

The first port of call for almost all questions must surely be the great* Wikipedia, which says that "an even number is an integer that can be divided by two and remain an integer or has no remainder."

Wikipedia isn't the best source for dissuading ranty comments, though.

Wolfram|Alpha, possibly a more reliable source of mathematical information in many eyes, says "an even number is a number in the form $n = 2k$ where $k$ is an integer."

Does zero fit here?

Wikipedia first:
  • An integer is a number with no fractional part (i.e. no decimals; a whole number): ✓
  • If we divide zero by 2 we get zero (with no remainder): ✓
And Wolfram|Alpha:
  • If we can find an integer $k$ such that $0=2k$ that means $0$ is even:
    $k = \frac{0}{2}$, so $k = 0$. ✓
Both Wikipedia and Wolfram|Alpha agree:
$0$ is even.

Need some more?

  • Back at primary school you may have learnt a quick way of identifying whether a number of any size is even by glancing at its units digit: any whole number that ends in $0, 2, 4, 6$ or $8$ is even, $0$ ends in... $0$. So it's even.
  • Additionally, you might also recall the rule that if you add two even numbers together the result is always even, for example: \[2+2=4\] \[120 + 346  = 466\]
    Well, $-2 + 2 = 0$, so $0$ is even.
  • It's also true that two odd numbers added together ($3 + 7$, for example) give an even number ($10$).
    What's $-3 + 3$? Oh, it's $0$, so that's even.
  • Multiplicatively, any even number multipled by any integer results in another even number, e.g.:
    \[2 \times 3 = 6\] \[84 \times -37 = -3,108 \]
    $28 \times 0 = 0$, so $0$ is even.
  • We're all familiar with the number line, stretching from $ -\infty $ to $ + \infty$ . Let's look at a section of that line with $0$ in it:
    ... , -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, ...
    And let's colour in the even ones:
    ... , -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, ...
    Without $0$ included there's a big hole and the pattern is broken. Why would we do that to a perfectly decent pattern?

Still not sure?

Many a maths fan's bible, the On-line Encyclopedia of Integer Sequences (OEIS) naturally includes an entry on the nonnegative even numbers and this begins with $0$. Are you going to argue with the OEIS?

* And often, I admit, fallible

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