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