The golden rectangle, the golden ratio, and the Fibonnaci sequence provide rich sources for investigation. There are several good websites that provide information in these areas, including:

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
Fibonnaci numbers and the golden section. Comprehensive and accessible with plenty of information, activities and links to other areas of the curriculum. Over 200 pages of interesting and stimulating ideas and activities.

http://www.geocities.com/CapeCanaveral/Station/8228/
The golden ratio, Fibonnaci series, and links to art, biology and Ancient Egypt.

http://www.mathsoft.com/asolve/constant/gold/gold.html
The golden ratio.

A method for constructing a golden rectangle is given below.

1. Draw a square. Divide it through the centre into two rectangles.

2. Draw a diagonal across one of the rectangles.

3. Using a pair of compasses draw an arc of a circle centred on the point A passing through the point B.

4. Extend the base of the square to intersect the arc. Draw a line at right angles from this point and extend the top of the square to complete the golden rectangle.

The golden rectangle has the property that if you take away a square you are left with another golden rectangle:

...and so on!

Mazes

Students may enjoy constructing their own mazes. A method is shown below.

1. Take some squared paper and mark on it an entrance on the outside and a goal on the inside.

2. Draw a winding route from the entrance to the goal.

3. Draw some 'false' paths leading off the main path. Ensure that every square has a path through it.

4. Place a sheet of tracing paper over the squared paper, and on it draw the walls of the mazeover the lines of squared paper that are not crossed by a path.

‘Old’ Money

The words ‘pound’, ‘shilling’ and ‘penny’ and the symbols £, s, d date back to Roman times.

‘Pound’ is from Old English ‘pund’, from Latin pondo. £ is the initial letter of the Latin word libra (pound). The dash through the middle of the L is a relic of the Gothic script from which German script developed, which survived until the Second World War.

The symbol d is the initial letter of the Latin denarius, which was a small silver coin. Penny is an Anglo-Saxon word, penig or pening in Old English.

The symbol s is the initial letter for both the English word shilling and the Latin word solidus for a Roman coin introduced by the Emperor Constantine. The stroke (/) means ‘solidus’ or ‘shilling’, and 7/6d should be read as ‘seven shillings and six pence’.