What is an arithmagon? (Updated July 2015)
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 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)
Jonathan Hall’s excellent Flash Maths site includes Addagons and Productagons which will provide an endless supply of arithmagons where the operation can be addition or multiplication; it is also possible to specify the number types required and to choose which parts of the arithmagon are displayed first. This can be displayed full screen making it excellent for the interactive whiteboard.
Nrich have 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.
Mark McCourt has a lovely collection of worksheets using arithmagons on emaths. A PowerPoint is also included showing an investigative approach using number and algebra.
For more ideas to use with advanced students see Jonny Griffiths RISPs; RISP21 is on ‘Advanced Arithmagons’ (if you choose RISPs organised by topic you will see RISP21 Advanced Arithmagons under Basic Algebra).
Jonny Griffiths RISPS have been mentioned before – see the Rich Tasks resources. 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.
A whole collection from Craig Barton, several topics are covered here.
On Transum Mathematics (home of the excellent Starter a Day), the Arithmagon activity which has options for forwards and backwards problems on Addition, Multiplication and Subtraction displays very clearly on the Interactive Whiteboard.