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Chapter 1

Chapter 1. The Art of Problem Solving. Section 1-4. Numeracy in Today ’ s World. Numeracy in Today ’ s World. - Objectives:. Be able to use a calculator for routine mathematical operations. Be able to use estimation techniques.

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Chapter 1

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  1. Chapter 1 The Art of Problem Solving

  2. Section 1-4 • Numeracy in Today’s World

  3. Numeracy in Today’s World - Objectives: • Be able to use a calculator for routine mathematical operations. • Be able to use estimation techniques. • Be able to interpret information by reading circle, bar, and line graphs. • Be able to use writing skills to convey information about mathematics.

  4. Calculation • There are many types of calculators, such as four-function, scientific, and graphing. • There are also many different models available and you may need to refer to your owner’s manual for assistance. Other resources for help are instructors and students that have experience with that model.

  5. Calculation • Below are some screen shots from a graphing calculator.

  6. Example • Use your calculator to find the following: • a) • b) • c) Solution a) 3.14159265 (approximately) b) 51 c) 5.0625

  7. Estimation • There are many times when we only need an estimate to a problem and a calculator is not necessary.

  8. Example: Estimation • A birdhouse for swallows can accommodate up to 8 nests. How many birdhouses would be necessary to accommodate 58 nests? Solution Divide 58/8 = 7.25. This cannot work because you cannot have a fractional birdhouse. Round up. 8 birdhouses

  9. Interpretation of Graphs • Using graphs is an efficient way to transmit information. Some of the common types of graphs are circle graphs (pie charts), bar graphs, and line graphs.

  10. Example: Circle Graph (Pie Chart) • Use the circle graph below to determine how many of the 140 students made an A or a B. Letter Grades in College Algebra F 10% D 10% A 15% B 25% C 40%

  11. Circle Graph (Continued) • Solution • Notice that there were 15% A’s and 25% B’s. • For 140 students, this yields: • A: 0.15 × 140 = 21 • B: 0.25 × 140 = 35 • which is a total of 56 students.

  12. Example: Bar Graph • The bar graph shows the number of cups of coffee, in hundreds of cups, that a professor had in a given year. Cups (in hundreds) 2010 2011 2012 2013 2014 • a) Estimate the number of cups in 2013. • What year shows the greatest decrease in cups?

  13. Bar Graph (Continued) • Solution • The number of cups in 2013 appears to be about 700. • The year 2014 looks to have the greatest decrease at about300 cups.

  14. Example: Line Graph • The line graph shows the average class size of a first grade class at a grade school for years 2011 though 2015. Students per class ’11 ’12 ’13 ’14 ’15 • In which years did the average class size increase • from the previous year? • How much did the average size increase from 2011 • to 2013?

  15. Line Graph (Continued) • Solution • a) The average class size increased in years 2012, 2013, and 2014. • b) The average class size was 16 in 2011 and 28in 2013, which wouldindicate an increase of 12 students per class. ’11 ’12 ’13 ’14 ’15

  16. Communicating Mathematics through Language Skills • Research has indicated that the ability to express mathematical observations in writing can serve as a positive force in one’s continued development as a mathematics student. The implementation of writing in the mathematics class can use several approaches.

  17. Communicating Mathematics through Language Skills • One way of using writing in mathematics is to keep a journal in which you spend a few minutes explaining what happened in class that day. The journal entries may be general or specific depending on the topic covered, the degree to which you understand the topic, your interest level at the time, and so on. Journal entries are usually written in informal language.

  18. Communicating Mathematics through Language Skills • Although journal entries are for the most part informal writings in which the student’s thoughts are allowed to roam freely, entries in learning logs are typically more formal. An instructor may pose a specific question for a student to answer in a learning log.

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