By Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg

Designed for the non-traditional Liberal Arts direction, Mathematical pondering and Quantitative Reasoning specializes in useful issues that scholars have to study with a view to be larger quantitative thinkers and decision-makers. the writer team's strategy emphasizes collaborative studying and demanding considering whereas providing challenge fixing in practical and significant contexts. whereas this article is extra concise than the writer team's Mathematical tours (© 2007), it includes a number of the related positive aspects and studying options, akin to the confirmed Aufmann Interactive process. an intensive know-how package deal presents teachers and scholars with a finished set of aid instruments.

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**Sample text**

Work backwards. Try to solve a similar but simpler problem. Look for a pattern. Write an equation. If necessary, define what each variable represents. Perform an experiment. Guess at a solution and then check your result. Use indirect reasoning. Carry Out the Plan ■ ■ ■ Once you have devised a plan, you must carry it out. Work carefully. Keep an accurate and neat record of all your attempts. Realize that some of your initial plans will not work and that you may have to devise another plan or modify your existing plan.

The height of this point represents the average age at first marriage for women in the year 2000, and it can be estimated by moving horizontally to the vertical axis on the left. 2 • Problem-Solving Strategies 27 age at first marriage for women in the year 2000 was about 25 years, rounded to the nearest quarter of a year. CHECK YOUR PROGRESS 8 a. S. movie theatre ticket price for the years from 1996 to 2004. b. 3 to determine the number of lane change accidents that occurred in Twin Falls in the year 2005.

She then uses the computer’s mouse to highlight the cells containing the data she wishes to graph. To create a vertical bar graph (called a column chart in Excel ) of her monthly expenditures for water, she selects “Chart” from the “Insert” menu. She clicks the “Next” button and then the “Finish” button. Note: During this process, you can select other options that allow you to enhance the graph with special artistic effects, but these can also be added later. E X P L O R AT I O N S 53. The Collatz Problem There are many un- solved problems in mathematics.