STEM BLOSSOMS Video Mathematics Fence Up Your Equation

The wonder of mathematics is that it can apply to so many different parts of our lives. A Malaysian farmer buys some sheep and needs to create a fenced-in pen, one side of which is a pre-existing wall. He also buys 25 meters of flexible fence. The father challenges his son, who likes math, to figure out how to design the fenced-in area for the sheep so that they will have maximum grass to eat, to stay healthy. This is a lesson in mathematical modeling, geometry, quadratic equations and optimization. Students will see how to formulate a mathematical model of a very real situation and how to optimize the design of the system they are modeling. They will see clearly how math helps the farmer and his sheep! Various geometrical shapes of the fenced-in pen are considered. The optimization methods range from trial and error, all the way to differential calculus (for advanced students). The compelling farm application of this problem should take away much of the students’ perceived mystery of quadratic equations. If two class sessions can be devoted to this topic, then we recommend that the first one be the BLOSSOMS lesson by Professor Gil Strang, “The Quadratic Equation: It’s Hip to Be Squared,” located here: http://blossoms.mit.edu/videos/lessons/quadratic_equation_it’s_hip_be_squared