IB Maths Resources from Intermathematics
IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides
Teachers can also download hundreds of IB maths resources from my new site intermathematics.com. See below for a flavour of the type of content available! 1. Worksheets All worksheets are designed to take 40 mins to 1 hour and can be used very effectively as homework sheets or classroom activities. Worksheets are designed to hit... Continue Reading →
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? 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 →
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 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 →
NASA, Aliens and Binary Codes from the Star The Drake Equation was intended by astronomer Frank Drake to spark a dialogue about the odds of intelligent life on other planets. He was one of the founding members of SETI - the Search for Extra Terrestrial Intelligence - which has spent the past 50 years scanning... Continue Reading →
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 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 →
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 →
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 →
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 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 →
Is God a Mathematician? http://www.youtube.com/watch?v=jremlZvNDuk&feature=youtu.be That's the provocative question posed by American Physicist Michio Kaku in this fascinating 5 minute interview which takes in the ideas of Newton, Einstein and modern ideas on String Theory. It addresses the fundamental questions in maths ToK - is mathematics invented or discovered? What explains the "unreasonable effectiveness" of... Continue Reading →
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 →
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 - 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!
Graham's Number - literally big enough to collapse your head into a black hole Graham's Number is a number so big that it would literally collapse your head into a black hole were you fully able to comprehend it. And that's not hyperbole - the informational content of Graham's Number is so astronomically large that... Continue Reading →
Plus Maths has a large number of great podcasts which look at maths ToK topics: 1) An interview with Max Tegmark (pictured above) about why he thinks that the universe is itself a mathematical structure. 2) An interview with physicists David Berman about how many dimensions exist. 3) A talk with cosmologist John Barrow about... Continue Reading →
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 →
http://www.youtube.com/watch?v=PCu_BNNI5x4 What is the sum of the infinite sequence 1, -1, 1, -1, 1.....? This is a really interesting puzzle to study - which fits very well when studying geometric series, proof and the history of maths. The two most intuitive answers are either that it has no sum or that it sums to zero. ... Continue Reading →
There are a lot of good general sequence puzzles on the website Fibonicci. For example find the next term of: 1) 15, 29, 56, 108, 208 2) 13, -21, 34, -55, 89 3) 52, 56, 48, 64, 32 4) 230, 460, 46, 92, 9.2 5) 68, 36, 20, 12, 8 Answers (in white text -... Continue Reading →
There are some great telescope pictures of the universe on the Guardian Science Gallery this month. This picture shows the distorted remnants of a supernova explosion - where stars are destroyed. This particular supernova is 26,000 light years from Earth - meaning that this is a picture 26,000 years into the past. It is thought... Continue Reading →
This is another interesting maths sequence puzzle: When x = 1, y = 1, when x= 2, y = -1, when x = 3, y = 1, a) if when x = 4, y = -1, what formula gives the nth term? b) if when x = 4, y = 3, what formula gives the... Continue Reading →
This is a huge topic - closely related to some of the Theory of knowledge concepts. It also gets very complicated. Here are some of the basics (some of this information is simplified from the Stanford Encyclopedia which goes into far more detail). 1) Platonism The basic philosophical question in maths is ontological - ie concerned with... Continue Reading →
This is the first post to just link to a TES contributor rather than a specific resource, but SRWhitehouse has provided a massive number of high quality worksheets on IB (and A level) topics - there's a huge number of worksheets to choose from, everything from trig graphs to proof by induction to logs to... Continue Reading →
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 →
This is another fascinating branch of mathematics - which uses computing to illustrate complexity (and order) in nature. Langton's Ant shows how very simple initial rules (ie a deterministic system) can have very unexpected consequences. Langton's Ant follows two simple rules: 1) At a white square, turn 90° right, flip the color of the square,... Continue Reading →
Fermat's Theorem - one of the most famous and long running puzzles in mathematics is a great way to introduce proof, the history of mathematics and also to show how apparent work on an entirely abstract concept can actually drive the development of techniques which have real world applicability. The (much abridged!) story is that... Continue Reading →
This is a really interesting take on a very well known puzzle (courtesy of Ian Stewart's Cabinet of Mathematical Curiosities). The puzzle itself is pretty famous: A farmer wants to cross a river and take with him a wolf, a goat, and a cabbage. There is a boat that can fit himself plus either the... Continue Reading →
This is a really nice puzzle we looked at at the IB HL workshop: When x = 1, y = 1, when x = 2, y = 2, when x = 3, y = 3 but when x = 4, y does not equal 4. Find a sequence which describes these points. There are... Continue Reading →
Good at maths? Really good? Then maybe one day you'll be able to claim a $1million prize for solving some of the fiendishly difficult and important maths problems out there. In 2000, the Clay Institute offered the reward for any mathematician who was able to crack 7 mathematical problems. In 13 years only one of... Continue Reading →