Arithmagons

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Level 10 More Levels Instructions
Cross Tick

The numbers in the circles add up to the numbers
in the rectangles between them.

Check Next

Type in the missing numbers according to the rule.

You can earn a Transum Trophy for correctly completing eight arithmagons at any one level.

You are currently working on Level 7: One single digit number given in a circle and two numbers shown in rectangles. The numbers in the rectangles are the product of the two adjacent circle numbers.

You have earned a trophy for this level but there are more levels for you to try!

By working through these challenges you will discover the hidden secrets of Arithmagons. You will find the connections between the numbers in rectangles and the numbers in circles and in doing so develop strategies for solving the more difficult Arithmagon puzzles.

This activity is suitable for pupils of a wide range of abilities. It provides purposeful numeracy practice and levels that are a multiple of four (Level 4, Level 8, Level 12 etc.) encourage pupils to devise efficient solving strategies.

The subtraction or difference Arithmagons with only the rectangle numbers given (Levels 12, 24, 36 and 48) have an infinite number of correct solutions and the computer will allow any one of these correct solutions.

In his pdf eBook Rich Starting Points for A Level Core Mathematics www.risps.co.uk Jonny Griffiths says that "there is no better way to present ideas of doing and undoing than arithmogons. They have been around a long time: 1975 is the first reference I have for them, but I daresay they have been around longer than that. One of their many marvellous aspects is that they require few words. John Mason and Sue Johnston-Wilder (Designing and Using Mathematical Tasks) give a long and fascinating study of how simple arithmogons can be used in a variety of ways."

If your pupils do not have access to computers there is a printable set of Arithmagon worksheets here:

Arithmagon Worksheets

If you like Arithmagons you might also like these activities:

Challenge

Numskull

Numskull

Interactive, randomly-generated, number-based logic puzzle designed to develop numeracy skills.

The short web address is:

Transum.org/go/?to=numskull

Numeracy

Brainbox

Brainbox

Arrange numbers on the function machines to link the given input numbers to the correct output.

The short web address is:

Transum.org/go/?to=brainbox

Puzzle

Pentadd Quiz

Pentadd Quiz

Find the five numbers which when added or multiplied together in pairs to produce the given sums or products.

The short web address is:

Transum.org/go/?to=pentadd

There are many more puzzles on the Transum Puzzle page.

Transum,

Monday, June 2, 2014

"Don't be content with only completing the first level of this challenge, click the 'More Levels' tab to select more difficult puzzles. Try the 'Two digit numbers', 'Addition', 'Three rectangle values only' combination to produce some interesting arithmagons.."

Year 4, St Olave’s

Wednesday, November 14, 2018

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

Do you know the origin of the title 'Arithmagons'? This activity has been used in schools for many years but who is the person we should thank for dreaming up the idea?

Still looking for a challenge? Try one of these activities:

Ming Game

Suko Sujiko

Suko Sujiko

Interactive number-based logic puzzles similar to those featuring in daily newspapers.

The short web address is:

Transum.org/go/?to=suko

Challenge

Satisfaction

Satisfaction

This is quite a challenging number grouping puzzle requiring a knowledge of prime, square and triangular numbers.

The short web address is:

Transum.org/go/?to=satisfaction

Suggested

Magic Square Puzzle

Magic Square Puzzle

Find all of the possible ways of making the magic total from the numbers in this four by four magic square.

The short web address is:

Transum.org/go/?to=magicsquarepuzzle

There are many more puzzles on the Transum Puzzle page.

The solutions to this and other Transum puzzles, exercises and activities are available here when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

A Transum subscription also gives you access to the 'Class Admin' student management system, downloadable worksheets, many more teaching resources and opens up ad-free access to the Transum website for you and your pupils.

Levels

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 ◯ ◯ ◯◯ ◯ ▭◯ ▭ ▭▭ ▭ ▭
1Level 1Level 2Level 3Level 4
5Level 5Level 6Level 7Level 8
9Level 9Level 10Level 11Level 12

 ◯ ◯ ◯◯ ◯ ▭◯ ▭ ▭▭ ▭ ▭
13Level 13Level 14Level 15Level 16
17Level 17Level 18Level 19Level 20
21Level 21Level 22Level 23Level 24

 ◯ ◯ ◯◯ ◯ ▭◯ ▭ ▭▭ ▭ ▭
25Level 25Level 26Level 27Level 28
29Level 29Level 30Level 31Level 32
33Level 33Level 34Level 35Level 36

 ◯ ◯ ◯◯ ◯ ▭◯ ▭ ▭▭ ▭ ▭
37Level 37Level 38Level 39Level 40
41Level 41Level 42Level 43Level 44
45Level 45Level 46Level 47Level 48

Choose Your Own Options:

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Instructions

The first Arithmagon you will see is a triangle with three circles at its vertices and rectangles on its sides. The idea is to add up the two numbers in circles at either end of a side of a triangle and type the answer into the rectangle on the middle of that side.

Diagram

Click the check button when you have filled in all three rectangles. If you are correct you will see one slice of a pie chart showing your progress so far. Complete eight Arithmagons to earn a Transum Trophy.

This first level you should find very easy. It gets more difficult when you are not given the three circle numbers but are given the rectangle numbers instead. That’s when you need to come up with a strategy!

You are currently working on Level 7: One single digit number given in a circle and two numbers shown in rectangles. The numbers in the rectangles are the product of the two adjacent circle numbers.

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