AREA OPTIMIZATION BY PERIMETER Paul Vermilyea GOALS OBJECTIVES

AREA OPTIMIZATION BY PERIMETER Paul Vermilyea

GOALS & OBJECTIVES Goals: Students will be able to maximize area by relationship to perimeter Objectives: Given a set perimeter, students will be able to maximize rectangular area with 100% accuracy.

MATERIALS Ruler Length of string 16” long Pencil Brownies Worksheet

FORMULAS Perimeter P=2*l+2*w Area A=l*w

WORKSHEET Length: Long Side “l” Width: Short Side “w” Perimeter: 2 l+2 w Area: l*w 7 inches 1 inch 16 inches 7 sq inches 16 inches

ACTIVITY Tell the students they have the chance to choose the size of their brownie. They can have any rectangular piece as long as the perimeter is the same exact length of the string

ACTIVITY Measure the length and width and fill in the correct columns on the worksheet. Calculate the perimeter and area of the rectangle and fill in the respective columns.

ACTIVITY Students should repeat this a few more times. In doing so, they should notice that the closer the length and width get to each other, the larger the area gets and reaches a maximum area when length is equal to width(square is formed).

CHALLENGE QUESTION Farmer Joe wants to build a rectangular pen for his goats. He has 100 feet of fence, and wants as much room as possible for roaming inside. What is the maximum area he can make?

WORKS CITED Donaldson, Cindy. "Practice Brownie Perimeters. " Education. com. Web. Apr. 2012. <http: //www. education. com/activity/article/Practice_Brownie_Peri meters/>.