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Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

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OK! Now Prove It

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?

Fibonacci Factors

Stage: 5 Challenge Level: Challenge Level:1

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In the Fibonacci sequence each term is the sum of the two terms before it:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...

Where do the even numbers come in the sequence?

Is there a pattern? Why?

Which Fibonacci numbers are divisible by 3?

Prove general results for the occurrence of even Fibonacci numbers in the sequence and for the occurrence of multiples of 3.