# Problem Solving Ks3

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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If I just give you the three square numbers, can you always find the circle numbers?

When testing out their conjectures, one student could invent three circle numbers, work out the square numbers (carefully!

), and then give just the square numbers to the person next to them to see if they can recreate the original circle numbers.

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.

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 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.

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