Golden Rectangles


Golden Rectangles

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

Practical details

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

Key Processes involved

Draw various rectangles with a given perimeters.
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.
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?
  • The adventurers need to understand your thinking, so show your findings in an organised way.

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.