# Arithmagons

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 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, Irrational Arithmagons.

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.

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 have been mentioned before – see the 16+ 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.

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.

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.

From Jonathan Payne, try this Arithmagon Generator. This is very simple to use and would be an ideal lesson starter. I like the option to use fractions, also to mix the question types as you see in the image. It is possible to choose missing sides, mixed or missing vertices.

From another Jonathan you can find another Arithmagon generator on Jonathan Hall’s wonderful Mathsbot site. As always with Jonathan’s resources you have choices to create the resource you want.

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).

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.

Also on Transum, see Algebragons and Fractionagons.

# Mobile Puzzles – Algebra

Mobile Puzzles

The Transition to Algebra (TTA) project, an initiative of the Learning and Teaching Division at Education Development Center, Inc. (EDC) includes a wonderful collection of Mobile Puzzles. Visit solveme.edc.org to play SolveMe Mobiles (also available for the iPad.)

Looking at the menu, you will see categories with different levels of difficulty available from very simple puzzles to rather more complex puzzles which promote good mathematical thinking.

Students must determine the weight of each object shown which makes a good introduction to the skills required to solve equations, linear and simultaneous.

Looking at some of the Master level puzzles, you will find rather more complex puzzles:

Note the menu in the corner of each puzzle page:

Selecting ‘Information’ provides extensive help; note that various tools are available so you can annotate puzzles and / or add symbols and equations.

Note that you can then drag a heart to subtract a heart from both sides:

Note that under settings you can choose to show numbers in the mobile as in the illustration. If the solution is correct, the mobile will balance.

On the other hand….

# Number Operations

Questions such as this can make a great starter for a lesson and provide the chance to discuss number operations and the relationships between them. Manipulating numbers like this can also help with algebraic manipulation.

Looking for some more examples of this type, I came across a really useful resource on TES, “If I know this then I also know …” by Piers Butler. This would make an ideal lesson starter. As it is an Excel spreadsheet, I thought it would be simple to add another worksheet with the answers and created the Excel file CY If_I_know_this_then_I_also_know_ which is a copy of the original, but just adds another worksheet with the answers.

Thank you, Piers!