I've just put together a couple of playlists to help students studying for their IGCSE Cambridge 0580 or Cambridge 0607 Maths exams, and also their Additional Mathematics Cambridge 0606 exams. IGCSE Maths Cambridge Playlist: https://www.youtube.com/watch?v=YwTgJrE0UiY&list=PLTzMaA6R8ce0vUIWWwP_-8_tmVK4q0SeR Videos included are: 1. Number 2. Circle Theorems and angles 3. Algebra 4. Volume 5. Statistics 6. Solving equations using... Continue Reading →
The Gambler’s Fallacy and Casino Maths
http://www.youtube.com/watch?v=K8SkCh-n4rw The Gambler's Fallacy The above video is an excellent introduction to the gambler's fallacy. This is the misconception that prior outcomes will have an effect on subsequent independent events. The classic example for this is the gambler who watches a run of 9 blacks on a roulette wheel with only red and black, and... Continue Reading →
Maths Magic
https://www.youtube.com/watch?v=M4vqr3_ROIk The video above is a great example of "mathemagic" - magic through maths. Arthur Benjamin's show at TED (using a mixture of mathematical tricks and savant like numerical ability) shows how numerical calculations can still produce a sense of awe and wonder. Probably the best resource for "mathemagic" is the TES Word ebook from... Continue Reading →
The Gorilla in the Room and Other Great Maths Investigations
http://www.youtube.com/watch?v=G-lN8vWm3m0 The Gorilla in the Room and Other Great Maths Investigations These topics are a great way to add interest to statistics and probability lessons at KS3 and KS4 level, and also a good example of investigations that IB students can conduct. They also have a nice link to ToK - how can we believe... Continue Reading →
Are You Living in a Computer Simulation?
Are You Living in a Computer Simulation? This idea might be familiar to fans of The Matrix - and at first glance may seem somewhat unbelievable. However, Oxford University Professor Nick Bostrom makes an interesting case using both conditional probability and logic as to why it's more likely than you might think. The summary of... Continue Reading →
Black Swans and Civilisation Collapse
Black Swans and Civilisation Collapse A really interesting branch of mathematics is involved in making future predictions about how civilisation will evolve in the future - and indeed looking at how robust our civilisation is to external shocks. This is one area in which mathematical models do not have a good record as it is... Continue Reading →
Sierpinski Triangles and Spirolateral Investigation Lesson Plan
Sierpinski Triangles and Spirolateral Investigation Lesson Plan Leaning Objective: Students are introduced to some more complex ideas in mathematics (fractals, infinite perimeter, fractional dimensions), students explore the relationship between maths and art, students conduct an open ended invesigation into patterns and sequences. 10 minutes Start the lesson with the Mandelbrot Zoom in the background: http://www.youtube.com/watch?v=0jGaio87u3A Discussion about what... Continue Reading →
How Are Prime Numbers Distributed? Twin Primes Conjecture
How Are Prime Numbers Distributed? Twin Primes Conjecture Thanks to a great post on the Teaching Mathematics blog about getting students to conduct an open ended investigation on consecutive numbers, I tried this with my year 10s - with some really interesting results. My favourites were these conjectures: 1) In a set of any 10... Continue Reading →
Synesthesia – Do Your Numbers Have Colour?
Synesthesia - Do Your Numbers Have Colour? Synesthesia is another topic which provides insights into how people perceive numbers - and how a synesthetic's perception of the mathematical world is distinctly different to everyone else's. Those with synesthesia have a cross-wiring of brain activity between 2 of their senses - so for example they may... Continue Reading →
Imagining the 4th Dimension
Imagining the 4th Dimension Imagining extra dimensions is a fantastic ToK topic - it is something which seems counter-intuitively false, something which we have no empirical evidence to support, and yet it is something which seems to fit the latest mathematical models on string theory (which requires 11 dimensions). Mathematical models have consistently been shown... Continue Reading →
The Mathematics of Cons – Pyramid Selling
The Mathematics of Cons - Pyramid Selling Pyramid schemes are a very old con - but whilst illegal, still exist in various forms. Understanding the maths behind them therefore is a good way to avoid losing your savings! The most basic version of the fraud starts with an individual making the following proposition, "pay me... Continue Reading →
Which Times Tables do Students Find Difficult? An Investigation.
Which Times Tables do Students Find Difficult? There's an excellent article on today's Guardian Datablog looking at a computer based study (with 232 primary school students) on which times tables students find easiest and difficult. Edited highlights (Guardian quotes in italics): Which multiplication did students get wrong most often? The hardest multiplication was six times... Continue Reading →
Cracking Codes Lesson
Cracking Codes Lesson 1 Introduction: 5 minutes - Use a Morse Code Generator to play some (very slowed down) messages for students to decode. Discuss why this is was a good way to transmit data in the past. Brainstorm: 5 minutes – Why are codes important? Who uses them? Why do mathematicians go into this career? ... Continue Reading →
Wau: The Most Amazing Number in the World?
Wau: The Most Amazing Number in the World? This is a fantastic video from Vi Hart of Khan Academy. Watch it first and marvel at the properties of this amazing number: https://www.youtube.com/watch?feature=player_embedded&v=GFLkou8NvJo Once you have watched it, watch it again - this time thinking about what number Wau might be - and why you have... Continue Reading →
Cracking ISBN and Credit Card Codes
Cracking ISBN and Credit Card Codes ISBN codes are used on all books published worldwide. It’s a very powerful and useful code, because it has been designed so that if you enter the wrong ISBN code the computer will immediately know – so that you don’t end up with the wrong book. There is lots... Continue Reading →
Benford’s Law – Using Maths to Catch Fraudsters
http://www.youtube.com/watch?v=vIsDjbhbADY Benford's Law - Using Maths to Catch Fraudsters Benford's Law is a very powerful and counter-intuitive mathematical rule which determines the distribution of leading digits (ie the first digit in any number). You would probably expect that distribution would be equal - that a number 9 occurs as often as a number 1. But... Continue Reading →
Simulations -Traffic Jams and Asteroid Impacts
Simulations -Traffic Jams and Asteroid Impacts You can study the mathematics behind traffic flow using this simulator. Why do traffic jams form? How does the speed limit or traffic lights or the number of lorries on the road affect road conditions? You can run a number of different simulations - looking at ring road traffic,... Continue Reading →
Time Travel and the Speed of Light
Time Travel and the Speed of Light This is one of my favourite videos from the legendary Carl Sagan. He explains the consequences of near to speed of light travel. https://www.youtube.com/watch?v=lPoGVP-wZv8 This topic fits quite well into a number of mathematical topics - from graphing, to real life uses of equations, to standard form and... Continue Reading →
Even Pigeons Can Do Maths
Even Pigeons Can Do Maths This is a really interesting study from a couple of years ago, which shows that even pigeons can deal with numbers as abstract quantities - in the study the pigeons counted groups of objects in their head and then classified the groups in terms of size. From the New York... Continue Reading →
One Direction Maths Song
A maths song sung by current flavour of the month One Direction - follow the lyrics to arrive at the total. http://www.youtube.com/watch?v=gIpdV9jSpXU Some of the best maths songs are by Learning Upgrade, such as, videos on circle formulae, fractions, exponents, the quadratic formula and the one below, "Mean, Median and Mode": http://www.youtube.com/watch?v=uydzT_WiRz4 Some other good maths songs:... Continue Reading →
Finger Ratio Predicts Maths Ability?
Finger Ratio Predicts Maths Ability? Some of the studies on the 2D: 4D finger ratios (as measured in the picture above) are interesting when considering what factors possibly affect mathematical ability. A 2007 study by Mark Brosnan from the University of Bath found that: "Boys with the longest ring fingers relative to their index fingers... Continue Reading →
Amanda Knox and Bad Maths in Courts
Amanda Knox and Bad Maths in Courts This post is inspired by the recent BBC News article, "Amanda Knox and Bad Maths in Courts." The article highlights the importance of good mathematical understanding when handling probabilities - and how mistakes by judges and juries can sometimes lead to miscarriages of justice. A scenario to give to... Continue Reading →
Does it Pay to be Nice? Game Theory and Evolution
Does it Pay to be Nice? Game Theory and Evolution Game theory is an interesting branch of mathematics with links across a large number of disciplines - from politics to economics to biology and psychology. The most well known example is that of the Prisoner's Dilemma. (Illustrated below). Two prisoners are taken into custody and... Continue Reading →
Premier League Finances – Debt and Wages
Premier League Finances - Debt and Wages This is a great article from the Guardian DataBlog analysing the finances for last season's Premier League clubs. As the Guardian says, "More than two thirds of the Premier League's record £2.4bn income in 2011-12 was paid out in wages, according to the most recently published accounts of... Continue Reading →
Why Study Maths? Careers Inspiration
This is inspired by a fantastic website - we use math - which has a massive amount of information about different careers using mathematics in a really well laid out format. According to a comprehensive careers survey by Careers Cast - which looked at over 200 different jobs and ranked them for stress, pay, job... Continue Reading →
Michio Kaku – Universe in a Nutshell
Michio Kaku - American Professor of Theoretical Physics and fantastic populariser of mathematics and physics takes us through a 40 minute journey on the importance of physics in explaining the universe: http://www.youtube.com/watch?v=0NbBjNiw4tk Great stuff - well worth watching!
Fun Maths KS3 and GCSE Quizzes
One of my favourite resources is the Jeopardy quizzes. For those not familiar with the game (I think it's American), it's a gameshow, where you get to choose questions of different levels of difficulty, from a range of categories. I downloaded the template from TES - it's a ready-made powerpoint which you can click on... Continue Reading →
Maths Pictionary
This is a great resource from Mr Collins - Maths Pictionary. What I like about this is that it can be incorporated into a large number of classroom activities - from Jeopardy games, to starters to topic revision. It can also be easily adapted to everything from KS3 to IB - and can be a... Continue Reading →