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
Hadi Faizal Bin Mohd Rosely is a mathematics teacher from Seri Puteri Science School (SAS) in Kuala Lumpur, Malaysia. He received his degree in Bachelor of Computer Science and Education (Mathematics) from the Universiti Teknologi Malaysia. He has been teaching mathematics at secondary school level since 2005.
Dr. Abdul Halim Abdullah is a senior lecturer at the Faculty of Education, Universiti Teknologi in Malaysia. He obtained his first degree in Bachelor of Computer Science and Education (Mathematics) from Universiti Teknologi Malaysia (UTM). He did his Master’s degree in Mathematics Education at UTM and received his PhD in Education from Universiti Kebangsaan in Malaysia (UKM).
Dr. Mahani Mokhtar is a senior lecturer at the Faculty of Education, Universiti Teknologi in Malaysia. She obtained Bachelor of Teaching English as a Second Language from Universiti Kebangsaan Malaysia (UKM). She graduated with a Master’s degree in Education and Development from Universiti Teknologi Malaysia (UTM) and received her PhD in Education from University of Bristol, United Kingdom.
Dr. Norazrena Binti Abu Samah is a senior lecturer at the Faculty of Education, Universiti Teknologi Malaysia. She obtained her first degree in Bachelor of Computer Science and Education (Mathematics) from Universiti Teknologi Malaysia (UTM). She received her PhD in Educational Technology from Universiti Teknologi Malaysia.
Prof Richard C. Larson’s specialty is Operations Research, an interdisciplinary field that uses mathematics and the scientific method to improve decision-making in industry and government. He has been involved with Technology-Enabled Education at MIT since 1995. He is principal founder of MIT LINC, Learning International Networks Consortium and principal investigator of MIT BLOSSOMS. His web site is http://esd.mit.edu/faculty_pages/larson/larson.htm.
This site, sponsored by Math Is Fun Advanced, presents a clear introduction to derivatives with many examples.
This resource, sponsored by Interactive Mathematic: Learn Math by Playing with It, provides a very comprehensive overview of differentiation (finding derivatives).
This site provides another very comprehensive overview of differentiation and is sponsored by Math Tutor.
This is the Khan Academy lesson on Calculus: Derivative 1.