Understand the Problem Scientists have always used diagrams to understand the nature of problems. Petrus Apianus was a German astronomer and mathematician who lived in the 16th century AD. A problem he wanted to solve was using the Sun to keep track of time. Figure 2-2 shows a diagram he 2 used to help him build a successful sundial. The diagram is not accurate according to today’s knowledge. Can you see what the error is? The Sun (Solis) and all planets as well as the Moon (Luna) are revolving around Earth. Sometimes, it is very hard to solve a problem. This may be because you do not understand the problem. Here are five questions to ask to get started: • Do I understand all words used in stating the problem? • Can I restate the problem in my own words? • Can I think of a picture or draw a diagram that might help me better understand the problem? • Is there enough information to allow me to find a solution? • What do I need to find or show? If the answer to the first four questions is yes and you s can give a response to the last question, move on to the next step. The next step in the problem-solving model is to devise a plan. If you do not understand the problem, seek more information to clarify it. Goodheart-Willcox Publisher Figure 2-2. A diagram used by Petrus Apianus to create a sundial. The diagram is inaccurate based on modern science. Hands-On Example 2.1A Hands-On Example 2.1A Understand the Problem The first step in the problem-solving model is to u un derstand the problem. Use the five questions outlined in n the text to help decide if you un nd erstand the problem. 1 State the problem. The problem is: use the Sun to o tell time. 2 Do you understand a all words used in stating the problem? A sundial is a mechanical clock that uses the position of the Sun in the sky to tell the approximate time of day. 3 Can you restate the problem in your own words? ? This may be something like, “we need to find a way to use e the Sun to tell time.” 4 Can you think of f a picture or draw a diagram that might help you understand the problem? For example, you u may draw the Sun casting differe en t shadows at different times of the day. 5 Is there enough information to allow you to find a solution? You know Earth revolves around the Sun. . As Earth moves, shadows cast by y an object will change position. 6 What are you asked s to find or show? Devise a way y to tell time using the Sun. Try It! Frederick Smith founded FedEx. He recognized a problem with the way packages were delivered. His solution o was the idea around which FedEx was created. Can you identify the problem? Use the five e questions outlined in the text to h he lp decide if you understand the problem. Copyright Goodheart-Willcox Co., Inc. Chapter 2 Solving Problems 25