There’s been quite a focus on kindness recently what with kindness week, my school having kindness as the ‘fortnight focus’, and this blog post from my headteacher (Chris Hildrew). It’s probably not a coincidence that my wife brought home a *kindness calendar* that she had seen on twitter from the website Action for happiness. We both really liked the idea and thought it was worth creating a similar one aimed at schools and for promotion during tutor time.

Here is our version. You’re welcome to use and/or adapt it as you wish.

pdf version School Kindness Calendar

pptx version School Kindness Calendar

We’d love to hear how you get on!

Here is a brief summary of individual talks from the Maths Jam annual conference. Thanks to Rob Lowe for writing the bulk of this and allowing me to share it.

There is a write up on its way from Maths Jam themselves and also this one from Chalkdust.

Colin Beveridge and I discuss it and have various guests comment on Wrong but Useful episode 50.

*Saturday* – Session 1a: 14:00 – 14:47

· *Colin Wright, Matt Parker and Katie Steckles: Welcome to the MathsJam Gathering*

Pretty much “what it says on the tin”

· *Tom Button: All about the base (no trebles)*

Using base 10 to prove a neat result about primes. (OK, that’s 10 in duodecimal.) Introduced the concepts of Threven for numbers in the three times tables.

· *Matt Peperell: Logical deduction games*

Introducing games where the aim of the game is to work out the rules. Sounds like a lot of fun and something I’ll be looking into more!

· A*lison Kiddle: Alison talks crap*

Alison presents and interprets the results of a fundamental poll: in fact, many fundaments were involved. Correlating number of sheets of toilet paper used with the Bristol stool scale. Used a linear correlation and log one too.

· *TD Dang: The maths in Mean Girls*

When is a limit not a limit? There’s no end to the possibilities. Looked at the mathlete’s activities in the film.

·* Noel-Ann Bradshaw: Digesting the indigestible*

On the importance of presenting data well and informatively. Wondering about the best way of presenting information about students to busy teachers.

**Session 1b: 15:10 – 15:57**

·* Zoe Griffiths: A discourse on e*

A heartfelt narration of the relationship between e and their x. You can listen to this on episode 50 of Wrong, but Useful.

· *Phil Chaffe: Maths Jammin’ – Writing a song for the Maths Jam Jam*

Hints and tips on how to write a song for maths jam. Essentially, a whole lot can be forgiven if there’s a really good line!

*· Matthew Scroggs: Big Ben Strikes Again*

How can you hear Big Ben strike 13? Why does Scroggs like Captain Scarlet so much?

· *Andrew Russell: Diabolo as a picture*

The title was an outright lie. Instead, he explained why balloon animals were semi-Eulerian graphs, and provided a counter-example. This was a talk that appealed to my inner clown.

· *Angela Brett: Mathematical poetry*

In which were reminded that it isn’t just giants whose shoulders we stand on. Available on Etsy here.

· *Adam Townsend: Stop! (or, using maths to pass your driving test)*

Where did those weird stopping distances come from? Are they even correct? (no) What should they be?

· *Elizabeth and Zeke: rat with an e*

What is 3^(1/ln 3)? More to the point, why?

**Session 1c: 16:20 – 17:07**

· *Rob Eastaway: Thinking Outside the Outside of the Box*

On drawing lines through all the dots in a grid: how far can you go? The classic puzzle of 9 dots in a 3-by-3 array. Can you join them with 4 straight lines? What about if it’s a 4-by-4 array with 6 lines? How far ‘outside the box’ can you go?

· *Rachel Wright: In A Spin*

Between sheep’s back and your back, the wool undergoes various transformations. Some of it’s a bit confusing.

· *Alex Burlton: Bags of Palindromes*

What are the chances of getting palindromes out of bags of numbers?

*· Alexander Bolton: Winning the Chalkdust Coin Game*

Why it’s a good idea not to have too similar a name to any of your peers, and why it’s a good idea to take a risk if you think you’re going to lose.

· *Vincent Van Pelt: Thank you, Mrs Holcombe*

Homophones. And, by a happy accident, an introduction to mediaeval French poetry.

**Session 1d: 17:30 – 18:17**

· *Dan Hagon: Double Negation and the Excluded Middle*

Some people aren’t happy with ¬¬P=P. Dan gives a constructive explanation of how logic works – or ought to.

· *Ben Pace: Building Successful Intellectual Communities*

Working towards a way of ranking web pages by reliability, using the Page rank algorithm (named after Larry Page and not because it ranks pages) and karma.

· *Alison Clarke: Stupid Units*

Pressure in mmHg? Volume in Acrefeet? Temperature in Fahrenheit? What were they thinking?

·* Belgin Seymenoglu: Donald in Mathmagic Land*

Half a century ago, Donad Duck starred in a cartoon introducing some mathsy fun.

· *Douglas Buchanan: Lowering the Tone*

Puzzles. I nearly fell of my perch at the resolution of the parrot puzzle. Possible the worst pun of the weekend, and there was no lack of competition.

· *David Mitchell: The Thereom of Trythagoras (Pythagoras is for Squares)*

Extending Pythagorean triples in triangular ways.

·* Dave Gale: Catchphrase and Coffee*

What do the ‘strength’ indicators on ground coffee mean? Why do some go from 3 to 7?Also, an (as yet) unsuccessful attempt to get the host of Catchphrase to stop calling rectangles “squares”.

*Sunday* – Session 2a: 08:50 – 09:37

·* Joel Haddley: Angle Trisection*

What are the rules? What counts as a trisection?

*· Katie Steckles: Sheeran Numbers*

What numbers can you make using (all) the operators used as titles of Ed Sheeran albums, and numbers used as titles of albums released during Ed Sheeran’s lifetime.

*· Ken McKelvie: A little ado about ‘nothing’*

Looking at where zeros occur in decimal expansions of certain numbers.

*· Tony Mann: The mathematics of competition*

Where on the beach should you put your ice cream van to maximize profit?

*· Will Kirkby: Life Beyond Binary*

Generalizing cellular automata, and some very pretty pictures.

·* Peter Rowlett: Fermi problems*

The kinds of estimating you have to do (in ‘real’ life), and the Approximate Geometric Mean as a useful tool crying out for a better understanding.

·* Kathryn Taylor: Adventures in modular origami*

How to make wonderful models, and why not to take them on the train.

**Session 2b: 10:00 – 10:47**

*· Marcin Konowalczyk: Unrolling the rolling shutter*

Trying to train a neural net to recover the original image. The dangers involved in choosing the training data.

*· Miles Gould: How Mountaineering is like Mathematics*

In every possible respect, it turns out. You can watch a video of the talk here.

·* Samuel Ball: Fake It Till You Make It*

Markov processes for constructing tweets. Also, helping people learn to code.

*· Wendy Foad: Context vs content*

Transferable skills?

· *Nicholas Korpelainen: A production line may need an arbitrarily large number of machines*

Satisfying constraints is sometimes hard.

·* Robert Woolley: Making board games fit – Numbers & Space*

How to fit several board games into one box. Clever use of the space available on playing cards.

**Session 2c: 11:15 – 11:48**

· *Glen Whitney: The Hole Truth*

Holes in a handlebody, Euler characteristic, and why a topologist is somebody who can’t tell a steering wheel from a T-shirt.

· *Sue de Pomerai: The life and times of Ada Lovelace*

The briefest of introductions: and a class in delivering a one hour talk in four minutes. Sue will hopefully be appearing in Wrong, but Useful episode 51.

· *Pedro Freitas: A programmed deck*

Programming a deck of cards to solve simultaneous equations.

· *Matthew and John Bibby: Boring log and geometrical tables*

A father and son team show us where woodwork and seaside rock meet mathematics.

· *Geoff Morley: Irrational Bases*

Looking at some of the richness of the behaviour when an irrational number is used as a base instead of an integer.

· *Adam Atkinson: Mathematics and Art: A Real-World Problem*

On the challenges facing a sculptor who wants to put a statue on top of the nearby mountain for residents of Catania to enjoy.

**Session 2d: 12:06 – 12:39**

*· Elaine Smith & Lynda Goldenberg: Multiplication: Magic or Madness*

Multiplication methods, and the ‘new’ grid method is several centuries older than the ‘traditional’ column method. Also Napier’s bones.

*· Robert W. Vallin: Maverick Solitaire and Three-Card Poker*

Probability inspired by an episode of Maverick.

*· Robert Low: Why knot?*

What do you mean, I can’t tie a knot in a piece of string without letting go of the ends? You’re not the boss of me!

·* Philipp Reinhard: From a tweet to Langnaus 4th problem in < 5min*

How to get from a relatively innocuous looking puzzle to some really deep stuff in a few steps.

*· Oliver Masters: The Fibonacci Matrix*

Coding the Fibonacci sequence in powers of a matrix, and some surprises arising.

**Whew – that’s all there was. Just a mere 49 talks!**

Thanks again to Rob for the comments. I’ll expand on some of the talks in future posts.

*nb I have undoubtedly missed some things out. I’ll remedy that in future posts.*

This weekend saw the annual Big Maths Jam in Staffordshire and once again, it was an excellent and invigorating injection of maths.

I’ll need more time to recall all the maths talks I saw and parts of the many discussions I had this weekend but I want to post a few thanks and highlights. I’ll expand on all of these in later blog posts but, for now…

Some highlights:

- Meeting up in person with so many people I have twitter conversations, including wrong but useful podcast cohost – Colin
- The massive range of topics in the 49 talks
- All the toys, puzzles and 3D printed goodies
- Zoe‘s poem about e
- Peter’s talk about Fermi problems
- Sam talking with me about coding and giving practical advice about getting started
- Rob giving me useful advice about juggling four balls
- Taking part in multiple competitions (and winning one)

Thanks:

- Colin for organising the event
- Katie for also organising the event
- Matt for (apparently) not really organising the event but still taking up to 1/3 of the credit
- The bake off and competition competition entrants
- Everyone that did a talk
- Anyone that laughed in the right places during my talk
- Everyone that brought an interesting thing to look at/play with

Ok. That’ll do for now (more to come I promise). If you’ve never been before, seriously consider planning to go next year. You won’t regret it!

In this month’s episode (available here) Colin and I talk with Adam Townsend of Chalkdust magazine fame. Obviously, you should go and listen to the podcast and read the magazine but here are a few tidbits and a little expansion.

Our number of the podcast is shown here:

Yes, it’s a whopper. It’s the largest left-truncatable prime. That means, as you sharpen the pencil, each number is still prime! Pretty cool. We briefly discussed the idea of a right-truncatable rival pencil brand and there’s a little more about it here.

Colin Beveridge (co-host and long time ~~enemy~~ friend) has a new book out called The Maths Behind. It’s well worth a read and contains lots of mathsy wordy bits alongside lots of mathsy pictury bits. It is very dip-into-able and once I’ve finished reading mine, I’ll probably let some students have a bit of a look. *Serious mode* It is very good and you actually should go and buy it.

Colin Wright gets mentioned for two reasons. One is that he’s the host and organiser of the annual maths jam conference which is thoroughly excellent and ideal for anyone who likes maths. I’ll be going this year and, after a gentle nudge from Colin, I’m going to give a 5 minute presentation titled *Catch Phrase and Coffee*. He’s also an expert on juggling and created the notation that is widely used now. He’s (finally) made a numberphile video about the juggling talk he does and I think I may have finally been inspired to try and crack 4-ball juggling!

I mentioned a twitter storm about a proportion question relating to an orchestra playing Beethoven’s 9th and here’s the link to that feed.

Well, that’s about it. Actually, that’s not true. We talk about a lot more in the podcast and in particular, Adam explains why mayo, blood and ketchup would all work well in a ‘chocolate’ fountain.

If you listened, let me know what you think. If you go to mathsjam, say hello!

I thought I’d share a few analogies that I use to get ideas across to students.

**The rugby player**

One I’ve borrowed from a Welsh colleague is that of a school-level rugby player. They are bigger than the other kids in their year and can comfortably smash their way through the opposition and score tries. The coach tells them they need to learn to pass the ball as they’re tackled but they don’t see the need as they can just plough through the tackles and go on to score. At county level, they use the same approach and since the opposition are now better, this player is getting successfully tackled, driven back and the team are suffering turn-overs because they haven’t learnt to pass the ball on contact. They are dropped from the team and progress no further.

This is like students that refuse to show working out in maths when they feel that the questions are easy enough. They are not developing the skills needed (think of solving equations) when the questions are straight-forward and therefore don’t have suitable strategies for when the questions are more advanced. I have seen this happen multiple times and having used this analogy, more students have started showing better workings.

**The passport**

“That homework isn’t good enough – you need to do it again.”

“Oh, but I tried some of it and I didn’t get how to do the rest.”

When you apply for a passport (or a driving license) you probably would not hand in a form when you’re not sure if it’s correct and/or with bits incomplete. If you do, it WILL get sent back to you and you’ll have to do it again. In fact, there is a post office service where you can pay to have someone check the form for you before it’s sent off to help avoid this. I offer a service where you can show me your homework before it’s due in and I’ll help you fill in the bits you’re struggling with. For free.

(You could mention that homework is like a passport to future success if you want to. I can’t quite bring myself to say it but you might like to!)

**The bath**

How do you fill a bath when the plug is out? By making sure that the taps are on fast enough to put more water in than is leaking out.

Which water goes down the plug hole first? The water near the bottom.

I use this to help describe a revision process. Of course, it is absolutely normal to forget things. The things that were learnt in year 9 are more likely to be the things that were forgotten (unless they’ve been revisited). Students can combat this by revising topics and keeping the bath topped up as they go through the course.

I also point out that if the plug is mostly in (this could be effective revision strategies that make forgetting the stuff less likely) then a steady drip over time will fill the bath too. It’ll also be a lot less stressful than trying to slosh bucket loads in just before bath time.

Hopefully you might find these useful and can use them with your classes!

One of the persistent misconceptions I come across as a teacher is the question of what exactly is it that makes a shape a rectangle? This is something I mentioned briefly on episode 48 of Wrong but Useful (coming soon here) but I think it’s worth getting to a wider audience.

Chances are that if I ask you to imagine a rectangle, something like this will come to mind:

I suppose it’s fair to say that if you’re reading this then maybe it might be more like this one:

I think the reason the first rectangle I showed is most likely is because that’s how they usually appear in ‘my first shapes’ books. Note that they almost always have their edges parallel to the sides of the book and certainly have “two long sides and two short sides”. However the necessary requirements for a shape to be a rectangle are:

- It’s a closed quadrilateral (a 2d shape with four straight sides and no gaps)
- It has four right angles

That’s it.

Easy.

However, in our Equable Shapes project, students are asked to explore shapes where the perimeter and area have the same numerical value. We start with rectangles and sooner or later, someone finds that 4 by 4 works (area and perimeter both 16). At this point all hell breaks loose and the two sides are formed with the “you can’t have that because sir said it had to be a rectangle” gang squaring* off against the “squares are special rectangles” crew.

Inevitably this leads to a lot of unpicking and most students believe they have been told explicitly at some point in the past that reactangles have two long sides and two short sides. Obviously I delicately correct this by going through what I mentioned above but some students still struggle to get that all squares are rectangles but it doesn’t follow that all rectangles are squares. The most effective way I’ve found to help illustrate the point is with furniture.

“Do you know what the word furniture means?”

“Yes”

“Are you happy that all wardrobes count as furniture?”

“Yes”

“Are you also happy that not all furniture is a wardrobe?”

“Yes”

“Then you can understand about the squares and rectangles.”

“Oh. I think I get it now.”

So, there we have it. Squares are rectangles, rectangles might be squares and oblongs are something for another post.

Why not try asking people you work with whether a square is a rectangle? The

*pun very much intended

It’s been ages since I’ve blogged. You know what it’s like! Anyway, I intend to do some more so, here goes!

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

What do you do in your first lesson with year 7? Rules? Expectations? I certainly do mention those things but usually, I like to do some maths and the investigation I choose is Caterpillars. I’ll explain it first then discuss why I like it.

**What is ‘Caterpillars’?**

Caterpillars have three simple rules:

- Stop when you get to 1
- Even numbers – halve them
- Odd numbers – add one

and that’s it. I demonstrate with 14 like this:

and then just say things like “I wonder if you can get a caterpillar as long as mine”, “Can anyone get one longer? or shorter?”. Then I let them try some of their own recommending (strongly) that their starting number is under 100.

After a short while, I ask people to make comments on what they’ve noticed and it’s often:

- They end 4,2,1
- They all get to 1
- Odds are better than evens

Amongst other things. This is a project that will comfortably take the first lesson.

**So, why do I like it?**

The actual operations are very straight forward as they are just halving and adding one. This investigation quickly show you who your weaker students are as they struggle to halve.

The project introduces a clear set of rules to follow. Which students bother to check whether the number is odd/even and which simply alternate the rules?

Who ignores the suggestion to start under 100? Why have they done that? It’s a great chance to tackle the misconception that picking higher numbers shows that you’re cleverer.

What numbers do they start with? Are they being remotely systematic in their choices?

Who can articulate a conjecture clearly? Who can do it concisely?

There’s frequently a chance when someone’s conjecture is contradicted by someone else and we get a chance to discuss how to handle this. The conjecture is wrong now, but *it wasn’t at the time*. Such a crucial way to show that someone has learnt something is that they’ve found something that doesn’t work!

Also in this project, you’ll eventually end up discussing whether decimals are odd or even. Is 5.2 even? What if it was? How do you know a number is even/odd? There’s a lot to discuss here and you will uncover misunderstanding about what odd and even means.

Someone might choose a negative number, presenting you with an early chance to think about adding one to a negative. A student may well choose zero and the infinity discussion to follow is always a nice moment!

Finally, I like that the longest caterpillar is fairly surprising. I won’t spoil it here but I honestly think this project starts the year with an air of curiosity and a chance to show determination while telling a lot about the students in front of you.

Let me know what your starting lessons are in the comments!