November 2009, Stage 4&5

This month many of our problems focus on properties of number and calculating. 'Playing' with the mathematics of a situation is often a good way to get into a problem and several resources this month lend themselves to that approach.

Problems

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What's Possible?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

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A Question of Scale

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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Plus Minus

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

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Farey Approximation

Stage: 5 Short Challenge Level: Challenge Level:1

Use Farey sequences to obtain rational approximations to irrational numbers.

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Farey Fibonacci

Stage: 5 Short Challenge Level: Challenge Level:1

Investigate Farey sequences of ratios of Fibonacci numbers.

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Implicitly

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the maximum value of the curve defined by this expression?

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Aim High

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

How do you choose your planting levels to minimise the total loss at harvest time?

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Ford Circles

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Small circles nestle under touching parent circles when they sit on the axis at neighbouring points in a Farey sequence.

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Cobalt Decay

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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