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Theres Gold in Them There Hills A GEMS Lesson

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A tour of Mars surface http://www.nationalgeographic.com/mars/

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Imagine that it is year 2100, a rare and precious metal has just been discovered on the planet Mars. You and hundreds of other adventurers are traveling to the planet to stake your claim. Each new prospector is allowed to clam any piece of land that can be surrounded by 20 meters of laser fencing. You want to arrange your fencing to enclose the maximum area possible.

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The Mars colony adds the restriction that each claim must be a rectangle. 1. Sketch several rectangles with a perimeter of 20 meters. Include some with small areas and some with large areas. Label the dimensions of each rectangle. 2.Make a table showing the length of a side and ht area for each rectangle with a perimeter of 20 meters and whole- number side lengths. 3.Make a graph of your length of a side, area data. Describe the shape of the graph. 4.If you want to enclose the greatest area possible with your fencing, what should be the dimensions of your fence be? How can you use your graph to justify your answer? 1. Sketch several rectangles with a perimeter of 20 meters. Include some with small areas and some with large areas. Label the dimensions of each rectangle. 2.Make a table showing the length of a side and ht area for each rectangle with a perimeter of 20 meters and whole- number side lengths. 3.Make a graph of your length of a side, area data. Describe the shape of the graph. 4.If you want to enclose the greatest area possible with your fencing, what should be the dimensions of your fence be? How can you use your graph to justify your answer?

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How are Parabolas used in the real world? http://www.analyzemath.com/parabola/parabola.html

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