Introduction to Problem-Solving and Practical Applications

Imagine you’re faced with a complex issue at work or in your personal life. Where do you start? The problem-solving process we’ll explore provides a structured approach to tackle any challenge. Whether you’re planning a budget for a home renovation or organizing a community event, you’ll learn to break down the problem, gather relevant information, and consider multiple strategies. By applying these steps, you’ll approach issues methodically – identifying the core problem, brainstorming solutions, and evaluating outcomes. These problem-solving strategies can become your go-to toolkit, empowering you to address challenges efficiently in any area.

Percentages are everywhere in our daily lives. When you shop during a sale, calculate a tip at a restaurant, or try to understand the interest on a loan (this will come in a later chapter as well on finances), you’re working with percentages. We’ll start with the basics of working with percentages and dive into applications, including understanding different tax systems.

Proportional reasoning helps you scale recipes, understand maps, and even how to calculate drug dosages. We’ll also explore when this method might lead us astray, ensuring you can apply it appropriately.

Finally, we’ll dive into dimensional analysis – a fancy term for a practical skill. Ever struggled to convert a recipe from cups to milliliters, convert currencies, or understand speed limits in kilometers per hour? Dimensional analysis is your solution. This technique is crucial in fields ranging from cooking to international trade, and even space exploration – remember the Mars Climate Orbiter mishap caused by a unit conversion error?

The hope is that by the end of this chapter, you’ll see math as a practical ally in your everyday life, empowering you to approach a wide range of real-world situations and not just a bunch of equations that need to manipulated or solved.

Learning Objectives

Below are the learning objectives for each section of the chapter.

1.1 Problem-Solving Process

• Identify Steps in the Problem-Solving Process
• Apply Problem-Solving Strategies to Applications

1.2 Percentages

• Solve application problems involving percentages.
• Calculate a flat tax.
• Calculate a progressive tax.

1.3 Proportional Reasoning

• Solve proportions.
• Solve application problems involving proportions.
• Identify when a proportion equation should not be used.
• Solve application problems involving similar triangles.

1.4 Dimensional Analysis

• Solve problems using rates.
• Convert between common measurements.
• Solve application problems involving conversion of units.

Attributions

• This page contains modified content from David Lippman, “Math In Society, 2nd Edition.” Licensed under CC BY-SA 4.0.
• This page contains content by Robert Foth, Math Faculty, Pima Community College, 2021.