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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 Stephen Froggatt.  This contains over 25 different maths magic tricks with full explanations about how to use them in a classroom setting.  As he says,

“Mathematics can be presented as a dry collection of rules and exercises (surely not!) or as a window through which can be seen explanations to many of the world’s mysteries. A magic trick provides the interest, and its explanation the demonstration of the power of mathematics to provide answers. Suddenly all that previous work on simplifying algebraic expressions comes into action when explaining why the Number You  Thought Of had to be seven.”

Magic Square Magic

As an example of one of this tricks, he describes how to ask a student his house number – upon answering, “46”, he immediately draws the following grid:

magic square

It’s then left to the students to find the connection between this grid and 46.  Each row adds to 46, as does each column, and both diagonals, and the 4 corners, and the 2×2 corner squares!  The impressive nature of this trick is the speed it can be calculated – and how it can be done with any given numbers.   The template needed is:

magic square 2

You simply need to substitute the the given value for N.  If you chose to reveal the secret it would be interesting to see if students could work out how to create their own grids with different template numbers.

Lightening Fast Multiplication

Another example from the book include how to multiply by 11 with lightening speed:

Write a large number on the board (eg. 3143221609) and race to see who can multiply this by 11 first.  The answer is 34575437699 and can be done in seconds.  Simply start with the end digit (in this case 9) and write that down, then working from right to left the next digit is 0+9 = 9.  The next digit is 6+0 = 6, the next digit is 1+6 = 7 etc.  Each time you just add the consecutive terms of the original number.  You finish by writing down the first term (in this case 3).

There are loads of other tricks in the free ebook to utilise.  The, “think of a number tricks,” are great for algebra topics, the magic cards make use of binary arithmetic and there is mobius magic for shape and space discussions.

Jan Honnens (also on TES here) has formalised some of this content into an investigation format with some great leading questions for students to follow.

Mind Reading Magic

Another example of a very powerful maths trick – which is very easy to do is given here:

And if all that isn’t enough, there’s a fantastic 96 page ebook pdf also free – available for download from here– which contains a large number of card and number tricks which make use of numerical and algebraic rules.

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IB Maths Revision

I’d strongly recommend starting your revision of topics from Y12 – certainly if you want to target a top grade in Y13.  My favourite revision site is Revision Village – which has a huge amount of great resources – questions graded by level, full video solutions, practice tests, and even exam predictions.  Standard Level students and Higher Level students have their own revision areas.  Have a look!

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IB HL Paper 3 Practice Questions (120 page pdf)

IB HL Paper 3 Practice Questions 

Seventeen full investigation questions – each one designed to last around 1 hour, and totaling around 40 pages and 600 marks worth of content.  There is also a fully typed up mark scheme.  Together this is around 120 pages of content.

Available to download here.

IB Maths Exploration Guide

IB Maths Exploration Guide

A comprehensive 63 page pdf guide to help you get excellent marks on your maths investigation. Includes:

  1. Investigation essentials,
  2. Marking criteria guidance,
  3. 70 hand picked interesting topics
  4. Useful websites for use in the exploration,
  5. A student checklist for top marks
  6. Avoiding common student mistakes
  7. A selection of detailed exploration ideas
  8. Advice on using Geogebra, Desmos and Tracker.

Available to download here.

Modelling Guide

IB Exploration Modelling Guide 

A 50 page pdf guide full of advice to help with modelling explorations – focusing in on non-calculator methods in order to show good understanding.

Modelling Guide includes:

Linear regression and log linearization, quadratic regression and cubic regression, exponential and trigonometric regression, comprehensive technology guide for using Desmos and Tracker.

Available to download here.

Statistics Guide

IB Exploration Statistics Guide

A 55 page pdf guide full of advice to help with modelling explorations – focusing in on non-calculator methods in order to show good understanding.

Statistics Guide includes: Pearson’s Product investigation, Chi Squared investigation, Binomial distribution investigation, t-test investigation, sampling techniques, normal distribution investigation and how to effectively use Desmos to represent data.

Available to download here.

IB Revision Notes

IB Revision Notes

Full revision notes for SL Analysis (60 pages), HL Analysis (112 pages) and SL Applications (53 pages).  Beautifully written by an experienced IB Mathematics teacher, and of an exceptionally high quality.  Fully updated for the new syllabus.  A must for all Analysis and Applications students!

Available to download here.

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