What is an arithmagon?
Clearly, the numbers in the rectangles are the sum of the numbers in the adjacent circles. Of course, there is no need to use addition and no need to use triangular arithmagons!
These could be used with students of all ages. Young children could practice basic skills or students studying advanced Mathematics could look at Calculus or Complex Numbers for example.The challenge is, of course, to go backwards…(Going backwards in Mathematics really helps understanding).

Colin Foster has written a suggested lesson plan on Arithmagons with full commentary.

Nrich Irrational ArithmagonNrich has some very useful resources including this introduction to arithmagons which includes an interactive allowing numbers to be changed and would work well on an interactive whiteboard. See also these further Nrich resources – this on multiplication and for older students a rather more advanced multiplication arithmagon using complex numbers. Also on Nrich, Irrational Arithmagons.

Algebra1 Alan Hodson

Arithmagons by Alan Hodson on emaths

From Mark McCourt’s emaths, the Teacher Resources include Investigations, Rich Tasks and Puzzles; these include a small collection of Arithmagons by Alan Hodson covering Number and Algebra. The Algebra resources include simplification using like terms and solving linear equations. A PowerPoint file showing an investigative approach using number and algebra and notes are included as is a useful sheet of 15 blank Arithmagons for students to record answers.

Don Steward

Expressions Arithmagons – Don Steward

From Don Steward, try his Expressions Arithmagons. Note the very efficient use of space here! Also from Don Steward, have a look at Directed Number Arithmagons.

For ideas to use with older students see Jonny Griffiths RISPsRISP21 is on ‘Advanced Arithmagons’  (if you choose RISPs organised by topic,  you will see RISP21 Advanced Arithmagons under Basic Algebra).

Jonny Griffiths

RISPS – Jonny Griffiths

Jonny Griffiths RISPS have been mentioned before – see the Rich Tasks resources for Older Students. Another site included in the Rich Tasks resources is the New Zealand Maths problem solving site; a resource on that site uses arithmagons to form and solve linear and simple quadratic equations.

Arithmagons - TeacherLED
Noting this tweet from Spencer Riley (I really like his TeacherLED site which has free high-quality teaching and learning resources compatible with desktop and mobile devices.) I had a look at his Arithmagons resource and can verify it worked very well on my phone as well as on the desktop.

Spencer Riley - Arithmagons

Arithmagons – Spencer Riley on Teacher

Craig Barton - Index & Factorising Quadratics
Arithmagons Collection – Craig Barton

From Craig Barton, we have a complete collection, covering Number, Algebra and Shape and Space. Each resource includes a PowerPoint File with clear instructions and a selection of challenges to really make your students think.

One of the many free resources (do a search on ‘free’) on the excellent MathsPad is this interactive – Negative Arithmagons. (MathsPad is a subscription site, but very low cost and good value for schools – see details).


MathsPad – Negative Arithmagons

Transum - Arithmagons

Transum – Arithmagons

On Transum Mathematics (home of the excellent Starter a Day), the Arithmagon activity has options for forwards and backwards problems on Addition, Multiplication and Subtraction at various levels.

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