# GM3.7: Garden Variety

Quest Line:
Previous Quest:
Summary:

There is some leftover fence from the previous quest. Using that given amount, build a pen with the maximum area possible in order to fence in bellyweeds.

Recommendations:

This is the final quest in the quest line and can be used as a good formative assessment of whether players understand how to use area and perimeter to solve an optimization problem. Players may want to try out some initial calculations on paper, but they can also use the fence builder tool for several rounds of trial and error. This leads up to the realization that if possible, making a square always gives maximum area for a given perimeter.

Learning Objectives:
• Apply a geometric model to satisfy physical constraints
• Make a geometric construction
• Solve design problems (area/perimeter optimization)
Connecting Questions:
1. What was your strategy for figuring out the maximum area?
2. What shape was the best for maximizing area?
3. Give students practice trying out problems where they maximize perimeter, minimize area, etc.