1. The Art of Problem Solving
Chapter 1
The Art of Problem Solving
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2. Chapter 1: The Art of Problem Solving
1.1 Solving Problems by Inductive Reasoning
1.2 An Application of Inductive Reasoning: Number Patterns
1.3 Strategies for Problem Solving
1.4 Calculating, Estimating, and Reading Graphs
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3. Calculating, Estimating, and Reading Graphs
Section 1-4
Calculating, Estimating, and Reading Graphs
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4. Calculating, Estimating, and Reading Graphs
Calculation
Estimation
Interpretation of Graphs
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5. 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.
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6. Calculation Below are some screen shots from a graphing calculator.
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7. Example: Calculation Solution
Use your calculator to find the following: a) b) c)
Solution
a) (approximately)
b) 51 c)
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8. Estimation
There are many times when we only need an estimate to a problem and a calculator is not necessary.
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9. Example: Estimation Solution
A 20-ounce box of cereal sells for $ Approximate the cost per ounce.
Solution
Because it is an approximation, we can say that the cost is about $3.00 for 20 ounces. This works out to 3.00/20 = $0.15 per ounce.
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10. 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.
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11. 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%
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12. Circle Graph (Continued)
Solution
Notice that there were 15% A’s and 25% B’s.
For 140 students this yields:
A: 0.15 x 140 = 21
B: 0.25 x 140 = 35
which is a total of 56 students.
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13. 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)
a) Estimate the number of cups in 2004
What year shows the greatest decrease in cups?
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14. Bar Graph (Continued) Solution
a) The number of cups in 2004 appears to be about 700.
The year 2005 looks to have the greatest decrease at about 250 cups.
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15. Example: Line Graph
The line graph shows the average class size of a first grade class at a grade school for years 2001 though 2005.
Students per class
’01 ’ ’ ’ ’05
In which years did the average class size increase
from the previous year?
How much did the average size increase from 2001
to 2003?
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16. Line Graph (Continued)
Solution
a) The average class size increased in years 2002, 2003, and 2004.
b) The average class size was 16 in 2001 and 28 in 2003 which would indicate an increase of 12 students per class.
2012 Pearson Education, Inc.