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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:

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:

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.

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.

Essential resources for IB students:

I’ve put together four comprehensive pdf guides to help students prepare for their exploration coursework and Paper 3 investigations. The exploration guides talk through the marking criteria, common student mistakes, excellent ideas for explorations, technology advice, modeling methods and a variety of statistical techniques with detailed explanations. I’ve also made 17 full investigation questions which are also excellent starting points for explorations.  The Exploration Guides can be downloaded here and the Paper 3 Questions can be downloaded here.

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All content on this site has been written by Andrew Chambers (MSc. Mathematics, IB Mathematics Examiner).

### New website for International teachers

I’ve just launched a brand new maths site for international schools – over 2000 pdf pages of resources to support IB teachers.  If you are an IB teacher this could save you 200+ hours of preparation time.

Explore here!

### Free HL Paper 3 Questions

P3 investigation questions and fully typed mark scheme.  Packs for both Applications students and Analysis students.