*You could conclude the lesson with a plenary in which the students talk about what they have found out.They may notice patterns to do with odd and even numbers and interesting results, such as that the sum of the square numbers is always twice the sum of the circle numbers.Please use the attached curriculum review sheets to access further details of the maths curriculum in KS3.*

*You could conclude the lesson with a plenary in which the students talk about what they have found out.*They may notice patterns to do with odd and even numbers and interesting results, such as that the sum of the square numbers is always twice the sum of the circle numbers.Please use the attached curriculum review sheets to access further details of the maths curriculum in KS3.

This makes sense, because each circle number is counted twice by contributing to two different square numbers.

Students could try to explain this carefully, perhaps with a diagram showing why it will always work.

Although the problem is equivalent to solving three simultaneous linear equations in three unknowns, it is not necessary for students to use algebra to make sense of the structure.

Some careful reasoning enables them to solve the general problem and see why it will always work. Each time the square number is the sum of the circle numbers on either side of it. The first one should be straightforward, the second involves subtraction and the third and fourth are more difficult. The last one may be particularly challenging, given the halves in the answers.

Year 8 students should expect questions on all content studied to date, so we recommend looking through the year 7 sheets in addition to the year 8 ones.

Maths revision works most effectively as a relatively short, regular, daily commitment.

This is a useful result, because one way to solve an arithmagon in which you are given just the three square numbers is to start by adding these together and halving the answer, to give you the total of the three circle numbers.

You can write this in the middle of the arithmagon.

There is no reason why a good calculator, purchased now, should not last through to the end of GCSE.

Students should also have a geometry set containing pencil, ruler, eraser, pair of compasses and a protractor.

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