Chapter 7, page 146
Figure 7.6:
Polya’s Problem Solving Strategies
[Description of figure 7.6. This is a four-panel drawing. In each panel, the reader is looking over the
shoulder of a girl so that the readers can look at the paper that she is writing on. On the paper, there will
be a math problem and then the girl’s solution. Here is the problem: The circumference of a circle is 16.
Find the area.]
Figure 7.6a Understand the problem.
The girl has drawn a circle, writes C=16, draws the radius and labels it ‘r’.
Figure 7.6b Develop a plan for solution.
The girl has written: Solve for r using C=2ʌr.
Then solve for A using A = ʌr^2
Figure 7.6c Carry out the plan.
The girl has written: C = 2ʌr
16 = 2ʌr, r = 8/ʌ
A = ʌr^2 = ʌ 64/ʌ^2
(^) A = 64/ʌ
(^)
Figure 7.6d Look back to see what can be learned from this process.
The girl is shown thinking to her self: “In any problem when the circumference is given, you can
always find the radius and then the area.”