Friday 15 March 2024

Super Curricular Activities in Mathematics











Super-Curricular Activities are activities that lie outside the classroom, beyond the school curriculum and beyond schools' extra-curricular offers. And whilst Super-Curricular participation is undoubtedly of benefit with University applications [1], the one-page of 'Super-Curricular Activities in Mathematics' collated and suggested here are done so purely for the 'more interested' young secondary school mathematician to explore, play and engage with outside of school. 

The 'Super Curricular Activities in Mathematics' to download below is a one-page collation of links to free resources and activities, from pre-school reading to University Admissions Tests. (Visits to museums, attendance at seminars and lectures, either online or in person, are not included in this collection, but of course are very much encouraged in super-curricular terms.) It includes suggested reading lists, suggested films and documentaries to watch, interviews and talks and explanatory animations to watch, podcasts and radio programmes to listen to, online courses to follow and engage with, and more. 

Once downloaded you can of course edit and adapt as you wish. The collation may complement schools' 'more able' programmes, but it is in no way designed nor intended to be restricted for exclusive use with students identified as 'more able'. Indeed, the intention is to get more students more interested in mathematics, expose more students to mathematics that would not ordinarily be visited in school curricula, and in doing so, expose more students to the power and beauty of the discipline.

Download:

  • Super Curricular Activities in Mathematics (.pdf format)
  • Super Curricular Activities in Mathematics (.doc format)
  • Super Curricular Activities in Mathematics (.png format)


Notes, References & Links:

Monday 4 March 2024

The First Equation


The 'First Equation' is a story about the evolution of the notation we use for addition (+), subtraction (–), and equality (=), which led to the first time an equation was written using the modern notation we use today, 14x + 15 = 71. Interestingly, the equals sign was introduced some two centuries after the introduction of the addition and subtraction signs, but some 50 years before the multiplication sign and a century before the division sign. 

The 'First Equation' is a story that will help students appreciate how the invention of mathematical notation fuelled the development of mathematics. Moreover, it is a story that may help students appreciate the diversity inherent in the development of mathematics; let them frame their own learning not just a function of that diversity, but also as an intrinsic part to the continuing story of mathematics. It can be used by teachers to support their teaching of setting up and solving algebraic equations to solve problems.

Downloads:

  • Lesson slides (.ppt format)
  • Lesson slides (.pdf format)


The introduction of the + and – signs

In her 2000 paper A Brief History of Algebraic Notation, Lucy Stallings identifies 'one of the earliest known symbols for addition and subtraction' to come from ancient Egypt, as seen in the Rhind papyrus (c. 1650 BC). The symbols used were 'a pair of legs walking forward [for] addition and a pair of legs walking away for subtraction' (p233). Howard Eves, in his 1983 book An introduction to the history of mathematics, describes a symbol for subtraction being used by the Greek mathematician Diophantus in the 3rd century, and the use by Hindu mathematicians of yu (यु ) as an abbreviation of yuta, meaning 'added'seen in the Bakhshali manuscript (which also featured the first recorded use of 0 for zero). 

But none of these symbols were universally adopted. The + and − signs that we use universally today were first introduced by French polymath Nicole d'Oresme in his Algorismus Propotionum (1356-61). However, as Edward Grant notes in his 1965 translation of d'Orseme's Algorismus, d'Oresme somewhat confusingly for us today called multiplication addition, and division subtraction. (For more about d'Oresme, the 'French Einstein of the 14th century', see this short biography.) 

Both the + and − signs were first used in print to indicate 'surplus' and 'deficit' ('what you add' and 'what you minus') by German mathematician Johannes Widman in his 1489 book 'Behende und hüpsche Rechenung auff allen Kauffmanschafft' (following the link will take you to the page where the symbols were first used; see the excerpted image above.) The subsequent universal adoption of + and − for addition and subtraction is evident from Heinrich GrammateusAyn new Kunstlich Buech (1521).

It is widely agreed that d'Oresme and subsequently Widman used + as an abbreviation for et, the Latin for 'and'. Eves, in describing Widman's use of +, and the subsequent universal adoption of such evident from Heinrich GrammateusAyn new Kunstlich Buech (1521), reinforces this belief 'as [et] was cursively written in manuscripts just before the time of the invention of printing' (p139). We remain unsure, however, of the reasons behind the adoption of the − symbol for subtraction.


The introduction of the equals sign

Welsh Doctor and mathematician Robert Recorde, born in 1510 in Tenby, Pembrokeshire, South Wales, was a popular author of a number of mathematical books — which he wrote, unusually for the time, in the English vernacular, thus making his writing more accessible than most scholarly books of the age, which were usually written in Latin. In his 1557 book, The Whetstone of Witte, whiche is the seconde parte of Arithmetike: containyng thextraction of Rootes: The Cossike practise, with the rule of Equation: and the woorkes of Surde Nombers [1] (which you can peruse electronically here), Recorde was the first to use the plus and minus signs in English: 'There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made – and betokeneth lesse'. In the same book, Recorde also introduced the '=' symbol, 'to avoide the tediouse repetition of these woordes : is equalle to :', which he had already used some 200 times in the book [2].

During Recorde's time, much of the mathematical notation we take for granted today was not yet in use. In designing the symbol '=' — as 'a paire of paralleles, or Gemowe [twin] lines of one length, thus: =====, bicause noe 2 thynges can be moare equalle' — Recorde's initial motivation to abbreviate was quickly overtaken by something more profound, more enduring.  As Joseph Mazur (2014) eloquently puts it, 'the concise character of the symbol came with an unintended benefit: it enabled an unadorned picture in the brain that could facilitate comprehension'.

(As an aside, neither was there an easy way in the 16th century of denoting the powers of numbers, so Recorde coined the now unsurprisingly obsolete term ‘zenzizenzizenzic' [3] to ‘doeth represent the square of squares squaredly’, or in other words to denote the square of the square of a number's square: \({\left( {{{\left( {{n^2}} \right)}^2}} \right)^2} = {n^8}\).  Recorde also used another word (which didn't quite catch on), the 'sursolid', meaning to be raised to a prime number greater than three.  So a power of five would be the first sursolid, a power of seven the second sursolid, a power of eleven the third, and so on.)


The First Equation

In The Whetstone of Witte, using his newly invented '=' sign, Recorde published what is thus the first equation to appear in the symbolic form we use today. The equation was 14x + 15 = 71. Before Recorde, mathematicians would state an equality in words. But the introduction of the equals sign was more than just a function of efficiency (or laziness!). Recorde used the equals sign to express the fundamental role of equality in algebra, namely that if we perform the same manipulations on two equal expressions, i.e., to what we now call an equation, the results must still be equal. In Recorde’s words, 'if you abate even portions from thynges that bee equalle, the partes that remain shall be equall also.'


Notes, References & Links:

Friday 9 December 2022

Mathsy Jokes and Puns



A collection of 125 of my favourite, accessible mathsy jokes and puns to tell and share (they do not need any technical knowledge to 'get' and enjoy). Many are fairly well-known, and whilst some are most appropriate for the little ones in our lives, the joy for the rest of us lies in the telling. Like much of the 'Dad joke' genre, many will invoke the most glorious of cringes. Perfect for teachers to nonchalantly drop into a lesson, or to share with loved ones innocuously over dinner. And of course, every party needs a maths joke!

Teachers may find this blog by Professor of Mathematics Education at Vanderbilt University @ilana_horn on using humour in the maths classroom interesting. And this video with Emeritus Professor of Mathematics at University College Cork Des MacHale, where he looks at the role that humour plays in the teaching and understanding of mathematics, with some hilarious illustrations.

They are arranged in no particular order, and I have sourced the writer of the joke where known, or otherwise indicated where I first heard or came across a joke. In many cases I am either unaware of the source, or have otherwise heard them from too many sources to be sure of their origin. If you know a good and accessible mathsy joke or pun for the collection, please do tweet me (@mathsedideas).




Teacher: What's the biggest number?
Pupil: 5624.
Teacher: What about 5625?
Pupil: Ooooh, I was so close!

Correlation does not imply causality, but the more I say things like that, the fewer people want to talk to me.

Did you know that Nelson had five children, but only one of them was called Horatio? That's Horatio of one to four.

I made a graph showing all my past relationships. It has an ex-axis and a why-axis.
― Source unknown

Factorials were someone's attempt to make math LOOK exciting.
― HT Steven Wright

Have you heard the one about the maths teacher who dreamed that he was addressing his class and woke up to find out that he was?
― HT Des MacHale in his wonderful book Comic Sections Plus

Not all maths puns are funny. Just sum.

5 out of 4 people have a problem understanding jokes about fractions.
― Source unknown

I've just eaten an abacus. I've always said, "It's what inside that counts."

Q: What so you get if you divide 22 sheep into 7 pens?
A: A Shepherd's Pi.

Q: How are mathematicians like the air force? A: They both use pi lots. ― Source unknown

Q: What do you get if you divide the circumference of a pumpkin by its diameter?
A: A pumpkin pi.
― Source unknown

88.2% of statistics are made up on the spot.

Numbers have never been my thirte.

Student: Teacher, I can't solve this problem. Teacher: What?! Any five year old should be able to solve this one. Student: No wonder I can't do it then, I'm nearly ten!

Q: How do you stay warm in an empty room? A: Go stand in the corner — it’s always 90 degrees.
― Source unknown

I was horrible in school… I failed math so many times I can't even count.

Five ants rented an apartment with another five ants. Now they're tenants.
Infinitely many mathematicians walk into a bar. They only have enough for two beers. The first says, "I'll have a beer, please.” The second says, “I’ll have a half a beer.” The third says, “I'll have half of a half a beer." The fourth says...
― Source unknown

Q: What is never odd or even?
A: A Palindrome.

3 and 5 got married. They are an odd couple.
― Source unknown

I just realized that the word “seven” has ‘even’ in it. That’s odd.

I hired a handy man and gave him a list of things to do. When I got home, only numbers 1, 3, and 5 were done. Turns out, he only does odd jobs.

Infinity: Everyone keeps thinking I'm a number.
Me: Don't let that get you down. We all know you're bigger than that.
HT @howie_hua

My pin is the last four digits of pi.

I was in my car doing 30 miles an hour and a friend of mine phoned me. He said, “I'm 5 miles ahead of you and doing 29 miles an hour.” I said, “I'll catch up with you later.”

Me: I have a petrifying fear of the vertical axis.
Therapist: Why?
Me: Aaaaaarrrrgggghhh!!!

Q: What did the triangle say to the circle?
A: “You’re pointless.”
― Source unknown

I though I'd never understand angles, but then I did a complete 360.
Q: What did the zero say to the eight?
A: "Nice belt!"
― Source unknown

Q: What works faster than a calculator?
A: A calcusooner.
Q: Why should you wear glasses during maths class? A: It improves division.
― Source unknown

In a graph, the thickness of the curve is inversely proportional to the reliability of the data.

A policeman one evening came across a drunk who was on his knees crawling round and round a huge tree trunk which he was feeling with his hands.
    "Look Sir," he said to him, "why don't you just go home?"
    "I'd love to," said the drunk, "but I'm completely surrounded by this tree."
― HT Des MacHale in his wonderful book Comic Sections Plus

Q: Did you hear the one about the Statistician?
A: Probably.
― Source unknown

Ten maths teachers that have taught me: 1) Mr Reid, 2) Mrs Spry, 10) Mr Pink.

There’s a fine line between a numerator and a denominator.
― Source unknown

I have a scary joke about math but I'm 2² to say it.
HT @_dmarian

Q: What do you call a teapot of boiling water on top of mount Everest? A: A high-pot-in-use.
― Source unknown

Father: If I have six coconuts and I gave you two, how many would I have left?
Son: I don't know. At school we do all our arithmetic in apples and oranges.

Q: What’s a math teacher’s favourite kind of tree?
A: Geometry.
Alcohol and calculus don't mix so don't drink and derive.
Did you know that 10+10 and 11+11 are the same? 10 + 10 = twenty and 11 + 11 = twenty too.
― Source unknown

I'm not normally late for my maths lessons, he hastened to add.

Q: Which triangles are the coldest? A: Ice-sosceles triangles.
― Source unknown

My maths teacher asked me to draw a square. I drew a circle so my teacher said “You’re an idiot. Go and stand in the corner.” I said “Where’s that?"
Q: Why are obtuse angles so depressed? A: Because they’re never right.
― Source unknown

I'm a bit nervous about my maths exam. Think my chances of passing it are 40-40.

I called a local restaurant the other night and said, “Do you do takeaways?” They said “Yes”, so I said “what’s 23452 minus 345?”

Teacher: If you have £5 in you left pocket and £2.50 in your right pocket, what would you have?
Student: Someone else's trousers on.
― Source unknown

Teacher: If there are ten crows sitting on a wall and I shoot one, how many will be left?
Johnny: None.
Teacher: You don't know much about arithmetic, Johnny.
Johnny: And you don't know much about crows, teacher!
― HT Des MacHale in his wonderful book Comic Sections Plus

(P+L)(O+T) = PO+PT+LO+LT And thus the plot was foiled!

I have a maths joke, but it doesn’t add up.
― Source unknown

Q: Why was 10 afraid of 7?
A: Because 7 8 9.
Q: But why did 7 eat 9?
A: Because you’re supposed to eat 3² meals a day.
― Source unknown

Approximately 3.14% of sailors are pi-rates. ― Adapted from @ThePunnyWorld

Q: Why is 6 afraid of π? A: I don't know; it’s an irrational fear. ― Source unknown

Child: My maths teacher is crazy.
Parent: Why?
Child: Yesterday she told us that five is 4+1; today she is telling us that five is 3 + 2.
― Source unknown

Q: What so you get if you divide 22 sheep into 7 pens? A: A Shepherd's Pi (approximately). ― HT @DadJokeMan

Q: Why aren’t jokes in base 8 funny?
A: Because 7 10 11.

Q: How do you make the number one disappear?
A: You just add a G and it's gone.
Q: What do mathematicians [or maths teachers] do when they are constipated?
A: They work it out with a pencil.
― Source unknown

“Take a positive integer n. No, wait, n is too large; take a positive integer k.”
Q: How do you make 7 even?
A: You take away S.
HT @pickover

Q: Why can’t a nose be 12 inches long? A: Because then it would be a foot.
― Source unknown

Doctor: How bad is your pain on a scale of 1-10? Me: π Doctor: ? Me: It's not too bad but it goes on forever. ― Source unknown

For the three o’clock race, I backed a horse at ten to one. It came in at a quarter past four.
19 and 20 got into a fight. 21.
I had an argument with a 90° angle. It turns out it was right.
― Source unknown

A shepherd said to me, “We’ve got 68 sheep. Can you round them up for me?” I said, “Sure, how about 70?”
Q: Two cats swim across a river. One is called "One Two Three", the other is called "Un Deux Trois." Which cat survives? A: "One Two Three" because un deux trois cat sank.
― Source unknown

Q: What is the volume of a pizza with radius z and thickness a? A: Pizza (or Pi-zza). ― Source unknown

Q: How do maths teachers admonish their pupils?
A: “If I’ve told you n times, I’ve told you n + 1 times.”
― Source unknown

One angle in a quadrilateral said to its opposite, ‘if you’re 37 degrees, what am I’? The other replied, ‘I don’t know, I’m not cyclic’.
― HT @cjshore

Q: Who is in favour for bringing Roman numerals back into use?
A: I for one.
Q: How many teachers does it take to do a subtraction problem?
A: One, because it only takes one teacher to make a difference.
HT @howie_hua

A Mathematician, a Physicist and an Engineer were travelling through Scotland when they saw a black sheep through the window of the train.
    “Aha”, said the Engineer, “I see that Scottish sheep are black.”     “Mmmmm”, ponders the Physicist, “you mean that some Scottish sheep are black.”     “No no no”, asserts the Mathematician, “all we know is that there is at least one sheep in Scotland and that at least one side of that one sheep is black!”
― Source unknown

I can't remember how to write 1, 1000, 51, 6 and 500 in Roman numerals. IM LIVID.
Q: What did the maths teacher say when her pet parrot died?
A: "Polygon!"
― Source unknown

Q: What did the student say when the witch doctor removed his curse? A: Hexagon.
― Source unknown

"I am, at a rough estimate, 30 billion times more intelligent than you. Let me give you an example: think of a number, any number."     "Err... five," said the mattress.     “Wrong," said Marvin. "You see?" HT Douglas Adams in The Hitchiker's Guide To The Galaxy

Q: Why was the quadrilateral late for School?
A: He got on the rhombus.

Q: Why did the student get upset when her teacher called her average?
A: Because it was a ‘mean’ thing to say.
― Source unknown

Q: What do maths teachers call retirement?
A: The aftermath.

Did you hear about the constipated accountant? He tried to work it out with a pencil — but he couldn’t budget.
Q: Why did the boy refuse to drink the water with eight ice cubes in it?
A: Because it’s too cubed!

i was arguing with π . "Get real," said π. i said, "You're being irrational." ― Source unknown

Q: Why did the Star Wars movies come out in the order 4, 5, 6, 1, 2, 3?
A: In charge of the sequence Yoda was.
To the person who invented zero: thanks for nothing.
― Source unknown

Q: How does a ghost solve a quadratic equation? A: By completing the scare.

I challenged 1 to a fight.  He brought 3, 5, 7 and 9 with him. I knew the odds were against me.
― Source unknown

Eating too much cake is the sin of gluttony. However, eating too much pie is OK because the Sin of Pi is 0.
Did you know Irish people are really good at maths? It's because they love Dublin.
― Source unknown

Teacher: If I had eight flies on my desk and I swatted one, how many would be left?
Student: One: The dead one.
Q: Where do mathematical fish live?
A: Indices.
― Source unknown

Q: Why should you worry about a maths teacher holding a piece of graph paper?  
A: Because they are definitely plotting something.
― Source unknown

I had a hen that could count her own eggs. She was a mathemachicken.
There are three types of people in this world. Those who can count and those who can't.
― Source unknown

There are two types of people in this world: 1) Those who can extrapolate from incomplete data.
― Source unknown.

People who do binary jokes are the first thing I would put in Room 5.
― HT @paulsinha

There are 10 types of people in the world. Those who understand binary, those that don’t and those that weren’t expecting this joke to be in base 3.
 
The vector was walking down Cartesian drive when he bumped into a confused Scalar. The vector asked him what was wrong, and he replied, "Help, I have no direction."
― Source unknown

Q: What sound does a drowning mathematician make?
A: ‘log log log log log log log …’

Knock.
Knock.
Knock Knock.
Knock Knock Knock.
Knock Knock Knock Knock Knock.
Who's there?
Fibonacci.
― Source unknown

Do you want to hear my latest joke about the Fibonacci sequence? It’s as good as my previous two jokes about the Fibonacci sequence put together.
― Source unknown

Q: Is the Fibonacci sequence hard to understand?
A: No, it’s as easy as 1, 1, 2, 3.
― Source unknown

Q: What did the circle say to the tangent?
A: "Stop touching me!"
― Source unknown

Q: Why did ⅕ go to the masseuse?
A: Because it was two-tenths.
Old mathematicians never die. They just lose some of their functions.
Source unknown

Q: How can you tell if a mathematician is extroverted?
A: When talking to you they look at your shoes instead of theirs.
― Source unknown

Q: What does the "B" in Benoit B Mandelbrot stand for? A: Benoit B Mandelbrot.
― Source unknown
― [Explainer: Mandelbrot was a mathematician well-known for his work on fractals, a word he coined. A fractal is an infinitely complex geometric pattern that is self-similar across different scales. Interestingly, Mandelbrot added the middle initial 'B' himself, which actually stood for nothing. Perhaps he did it to facilitate this joke!]

When you keep missing maths class it starts to really add up.

Q: Why isn’t every man in a red suit with a beard Father Christmas?
A: Because correlation doesn’t imply Claus-ality.

Q: Why do sets only have one median?
A: Because if there were two, they would be called comedians.
HT @howie_hua

Q: How many seconds are there in a year? 
A: There are 12 seconds in a year: January 2nd, February 2nd, March 2nd….
HT @cruz4thought

Q: Where are mathematicians buried?
A: The Symmetry.

Approximately 3.14% of sailors are pi-rates.
Adapted from @ThePunnyWorld

Jesus and his disciples were walking one day, when Jesus said, "The Kingdom of Heaven is like y²=4ax."  The disciples were puzzled, and asked Peter, "What does Jesus mean - the Kingdom of Heaven is like y²=4ax?  Peter said, "Don't worry.  It's just another one of his parabolas."
 
Many things in math make me feel numb, but divisibility by 2 makes me even number.
― HT @archernikov

Q: Why do mathematicians always confuse Halloween and Christmas?
A: Because 31 Oct = 25 Dec.
― [Explainer: 31 in base-8 (Octal) = 25 in base-10 (Decimal). In base-8 31 means 3 × 8 + 1, which is 25.]

If I had to describe myself in three words, I would say: “Not very good at maths.”
― Source unknown.

Q: Where can you go to practice math on New Year’s Eve? 
A: Times Square. 

Teacher: 874362, 874361, 874360...
Pupil: What are you doing?
Teacher: I am determined to count backwards from one million; I will stop at nothing.
Adapted from @geoff_tibballs

A statistician got soaking wet trying to cross a river. He thought he could cross, because it was one-foot deep on average.
― Source unknown.

I knew a mathematician who couldn’t afford lunch. He could binomials.
― Source unknown.

Q: Why should the number 288 never be mentioned?
A: Because it's two gross.
― Source unknown.

Exponentiation isn't my favourite mathematical notation... but it's definitely up there.
HT @howie_hua

Q: How did the number feel when it lost 1/3 of itself?
A: numb.
HT @howie_hua