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In the 19th century, many adventurers travelled to North America to search for gold.

In the 19th century, adventurers sought gold in North America using stakes and ropes to demarcate land plots for mining. Explore how to maximize land use with only four stakes per adventurer, and discover if teamwork increases land allocation. Follow-up tasks involve assessing students' strategies for marking plots effectively.

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In the 19th century, many adventurers travelled to North America to search for gold.

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  1. In the 19th century, many adventurers travelled to North America to search for gold. Dan Jackson owned some land where gold had been found. Instead of digging for the gold himself, he rented plots of land to the adventurers.

  2. Dan gave each adventurer four stakes and a rope 100 metres long. Each adventurer had to use the stakes and the rope to mark off a rectangular plot of land. How should an adventurer place his stakes to mark out the biggest plot of land? Explain your answer. If two adventurers work together, do they get more land each – still using only four stakes? What if more than two work together? Explain your answer.

  3. Follow-up task for students • Look carefully at the following extracts of work from other students. Imagine you are their teacher. Go through each piece of work and write comments on each one. • Have they chosen a sensible method? • Are the calculations correct? • Are the conclusions sensible? • Is the work easy to understand?

  4. Alvin’s answer

  5. Bernie’s answer

  6. Chris’s answer

  7. Danny’s answer

  8. Elsie’s answer

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