November 2009, All Stages

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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So It's 28

Stage: 1 Challenge Level: Challenge Level:1

Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.

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Stone Age Counting

Stage: 1 Challenge Level: Challenge Level:1

What could these drawings, found in a cave in Spain, represent?

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Mrs Trimmer's String

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

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28 and It's Upward and Onward

Stage: 2 Challenge Level: Challenge Level:1

Can you find ways of joining cubes together so that 28 faces are visible?

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Tables Without Tens

Stage: 2 Challenge Level: Challenge Level:1

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

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Which Symbol?

Stage: 2 Challenge Level: Challenge Level:1

Choose a symbol to put into the number sentence.

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Neighbours

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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Sets of Four Numbers

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

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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Going Round in Circles

Stage: 3 Challenge Level: Challenge Level:1

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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Shifting Times Tables

Stage: 3 Challenge Level: Challenge Level:1

Can you find a way to identify times tables after they have been shifted up?

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Christmas Chocolates

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

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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.