# Golden Rectangles

Pupils work out how adventurers can maximise the area in which they can dig for gold given a fixed perimeter.

# Practical details

Suitability
National Curriculum levels 4 to 6 (can be extended up to level 8)
Time
30 minutes to 1 hour
Resources
Ruler, pencil, calculator and 1 cm squared paper. It may also be helpful to make available some graph paper.

# Key Processes involved

Representing
Draw various rectangles with a given perimeters.
Analysing
Find areas of rectangles.
Interpreting and evaluating
Consider different rectangles while trying to maximise the area. Find that a square is the best. Go on to find that, if the adventurers work together, they can get a bigger area each.
Communicating
Explain how they know this is the best arrangement and that working together is best.

# Teacher guidance

Check that pupils understand the context, for example with questions such as:

• How do you think the adventurers would mark out their plot of land?
• How should they share a plot that two of them had marked out?

Pupils can tackle this task in different ways, but they might be expected to:

• draw rectangles and find their areas
• collect results in a table or ordered list
• find a pattern in their data

The work could be extended to:

• finding patterns in their results and finding an nth term
• drawing a graph to clarify their results
• finding the areas of other shapes

This would take the content to National Curriculum levels 6 - 8.