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

So It's 28

Stage: 1 Challenge Level:

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

Stone Age Counting

Stage: 1 Challenge Level:

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

Mrs Trimmer's String

Stage: 1 Challenge Level:

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

28 and It's Upward and Onward

Stage: 2 Challenge Level:

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

Tables Without Tens

Stage: 2 Challenge Level:

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

Which Symbol?

Stage: 2 Challenge Level:

Choose a symbol to put into the number sentence.

Neighbours

Stage: 2 Challenge Level:

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?

Sets of Four Numbers

Stage: 2 Challenge Level:

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

Going Round in Circles

Stage: 3 Challenge Level:

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

Shifting Times Tables

Stage: 3 Challenge Level:

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

Christmas Chocolates

Stage: 3 Challenge Level:

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

What's Possible?

Stage: 4 Challenge Level:

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

A Question of Scale

Stage: 4 Challenge Level:

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?

Plus Minus

Stage: 4 Challenge Level:

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

Farey Approximation

Stage: 5 Short Challenge Level:

Use Farey sequences to obtain rational approximations to irrational numbers.

Farey Fibonacci

Stage: 5 Short Challenge Level:

Investigate Farey sequences of ratios of Fibonacci numbers.

Implicitly

Stage: 5 Challenge Level:

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

Aim High

Stage: 5 Challenge Level:

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

Ford Circles

Stage: 5 Challenge Level:

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

Cobalt Decay

Stage: 5 Challenge Level:

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