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Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
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Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
Age 14 to 16
Challenge Level
I need a figure for the fish population in a lake.
I catch 40 fish and mark a scale on each fish so that they can be identified if caught again.
The fish are then released and one week later I once more catch 40 fish and look to see which of these I caught before.
How does this help me come up with a figure for the fish population in a lake?
What assumptions does this method of estimating the fish population rely on?
How do you think you could improve the accuracy of your estimate?
Click here for a poster of this problem.
This resource is part of the collection Statistics - Maths of Real Life
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.