1. Approaching Optimization with an Engineering Mindset The Greenhouse Project

2. Introduction Many students struggle with story problems They have difficulty drawing diagram of problem They have difficulty understanding how variables interact with one another Create a lesson to improve students’ ability to do story problems

3. Lesson Objectives Build models of problems Test alternative problem solving methods: o Analytical calculus solutions o Engineering solutions Compare alternative solutions to a problem

4. State Learning Goals Apply formulas in real world situations Determine how changes in one variable affects what happens in other variables Use functions to model situations Conduct experiment to test hypotheses

5. Story Problem Solving Methods In calculus: o Static drawing o Label variables o Create equation In engineering: o Dynamic model where possible o Develop understanding of variables’ interactive effects and create hypotheses o Build, test, and refine collaborative solution

6. Greenhouse Problem Home owner wants to add a triangular greenhouse addition on the side of her house. She wants to maximize usable space while minimizing cost

7. Greenhouse

8. Engineering Solution: Week 1 Build first model of problem in small group Create list of variables involved in problem Identify relationships among variables Using model and relationships among variables, hypothesize solutions Test hypotheses Refine and retest hypotheses

9. Calculus Solution: Week 2 Draw diagram of problem Identify variables Apply appropriate formulas Solve Check solution

10. Compare Solutions Students will answer following questions after completing both solutions: o What is engineering solution? o What is calculus solution? o Why are they the same/different? o Which method do you want your builder to use? Why? o What do the different problem solving methods teach you?

11. Conclusion Story problems are hard for students Applying engineering principles to math problems will help students learn to model Student will learn to visualize the dynamics of the problem through modeling