Approaching Optimization with an Engineering Mindset

The Greenhouse Project

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

Lesson Objectives

• Build models of problems• Test alternative problem solving methods:

o Analytical calculus solutionso Engineering solutions

• Compare alternative solutions to a problem

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

Story Problem Solving Methods

• In calculus: o Static drawingo Label variableso Create equation

• In engineering:o Dynamic model where possibleo Develop understanding of variables’ interactive

effects and create hypotheseso Build, test, and refine collaborative solution

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

Greenhouse

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

Calculus Solution: Week 2

• Draw diagram of problem• Identify variables• Apply appropriate formulas• Solve• Check solution

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?

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