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Centre for Research in Mathematics Education (CRME)
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Maximizing area: gold rush
This is a problem solving lesson, designed to help you access how well students are able to:
- Interpret a situation and represent the variables mathematically
- Explore the effects on a rectangle’s area of systematically varying the dimensions whilst keeping the perimeter constant.
The initial problem is set in the context of gold prospectors marking out rectangular plots of land using four wooden stakes and a rope measuring exactly 100 metres. Students must find the optimum rectangle to maximise the area that can be marked out.
There is then a proposal that ropes be joined together. The problem is to find out if this leads to a greater area for each prospector.
This is a problem solving lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.
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