2: Mathematics and Numbers

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In previous math courses, you’ve no doubt run into the infamous “word problems.” Unfortunately, these problems rarely resemble the type of problems we actually encounter in everyday life. In math books, you usually are told exactly which formula or procedure to use and are given exactly the information you need to answer the question. In real life, problem solving requires identifying an appropriate formula or procedure and determining what information you will need (and won’t need) to answer the question.

In this chapter, we will review several basic but powerful ideas: percents, rates, proportions, conversions, and estimation. We will then focus on the problem solving process and explore how to use these ideas to solve problems where we don’t have perfect information. We will then conclude the chapter by discussing deceptive and misleading use of numbers.

2.1: Estimating the Answer
Problem solving is best approached by first starting at the end: identifying exactly what you are looking for. From there, you then work backwards, asking “what information and procedures will I need to find this?” Very few interesting questions can be answered in one mathematical step; often you will need to chain together a solution pathway, a series of steps that will allow you to answer the question.
2.2: Really Big and Really Small Numbers
2.3: Deceptive and Misleading Numbers
Numbers and figures are frequently manipulated. In this brief section we will look at how certain numbers can be presented to us in misleading or deceptive ways to give certain impressions or to change our mind.
2.4: Percentages and Proportions
2.5: Conversions

Contributors and Attributions

Saburo Matsumoto
CC-BY-4.0