1. Problem Solving Using the Eight Tenets
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2. It uses a systematic approach to arrive at the solution of a problem.
Introduction
The eight tenet method of problem solving lends itself well to mathematical solutions but can be expanded to other processes.
It uses a systematic approach to arrive at the solution of a problem.
This example revisits the problem solved in the video and examines the solution in greater depth.

3. The Eight Tenets of Problem Solving
Read and understand the problem statement.
Draw and label a picture that describes the problem statement.
Determine the known and unknown variables.
Examine the units and convert all units to those of the answer.
5 Determine the equations to be used.
Solve the equations.
Check the physical significance of the answer.
Report the answer with the correct units.

4. Read and Understand the Problem Statement
Tenet 1:
Read and Understand the Problem Statement
The video question was :
How many ten millimeter square chips can fit on a circular wafer that has a diameter of eight inches?
This is a simple problem and you can think of the square chips as squares and the wafer as a circle.
For this presentation the tenet will auto play but any other audio indicator will require you to click on it.

5. Draw and Label a Picture that Describes Problem
Tenet 2:
Draw and Label a Picture that Describes Problem
The purpose of this tenet is as a visual aid for solving the problem.
Usually if you can picture the problem the solution is easier to achieve.
A 10.0 mm by 10.0 mm Square
The two figures on this slide are drawn to scale with the precision afforded by Microsoft PowerPoint.
The circle has a diameter of 3.5 in and the square has a side length of 0.17 in.
An Eight Inch Circle

6. Determine the Known and Unknown Variables
Tenet 3:
Determine the Known and Unknown Variables
Known Variables :
Diameter of Circle
Dcir = 8.00 inches
Length of a Side of a Square
Lside = 10.0 mm.
Unknown Variables :
Radius of the Circle
Area of the Circle
Area of a Square
Number of Squares that fit inside the circle.
This slide lists the know and unknown variables.

7. Tenet 4:
Examine the Units Used in the Problem,
Converting all of the units to the answer’s units will save time in the end.
The units of the circle are inches.
The units of the sides of the square chip are given millimeters.
To solve this problem we need to convert the units of the problem to millimeters.

8. There are 10 millimeters per centimeter.
Tenet 4:
Examine the Units Used in the Problem.
The units of the circle are expressed in inches and must be converted to millimeters.
The conversion factor from inches to centimeters is 2.54 centimeters per inch.
There are 10 millimeters per centimeter.
The units of the squares are correct as millimeters.
Diameter of an 8 inch circle in millimeters =

9. Using the fencepost method the units can
Tenet 4:
Examine the Units Used in the Problem.
Diameter of an 8 inch circle in millimeters =
Using the fencepost method the units can
easily be converted from inches to millimeters
fencepost
8.00 inches
2.54 cm
10 mm
This slide portrays the ladder method in action while the next slide gives the result of the ladder method.
1 inch
1 cm

10. Using the fencepost method the units can
Tenet 4:
Examine the Units Used in the Problem.
How many ten millimeter square chips can fit on a circular wafer that has a diameter of eight inches?
Using the fencepost method the units can
easily be converted from inches to millimeters
fencepost
8.00 inches
2.54 cm
10 mm
This slide portrays the ladder method in action while the next slide gives the result of the ladder method.
1 inch
1 cm

11. Tenet 4:
Examine the Units Used in the Problem.
How many ten millimeter square chips can fit on a circular wafer that has a diameter of eight inches?
8.00 inches
2.54 cm
1 inch
10 mm
1 cm
(8) (2.54) = mm
(1) (1) =
203.4
millimeters
Note;
This slide portrays the ladder method in action while the next slide gives the result of the ladder method.
the units cancel to give final length has units of millimeters.
At this point in the problem the calculation contains one digit more than the correct number of significant figures.

12. Determine the Equations to be Used
Tenet 5:
Determine the Equations to be Used
To solve for the number of 10 mm by 10 mm squares that will fit in an eight inch circle one must first solve for the areas of the square and the circle,
and then use these areas to solve for the number of squares that will fit in the circle.

13. Tenet 5:
Determine Equations to be used.
Circle
Radius of a circle from circle diameter Rcircle = 1/2 (Dcircle)
Area of a circle equation.
Acircle =  (Rcircle)2
Square
Area of a square.
Asquare = (Lsquare)2

14. Tenet 6:
Solving the Equations
Solving for the Areas of the Circle and a Square

15. Tenet 6:
Solve the equations.

16. Tenet 7:
Check the Units and Physical Significance of Answer
Is squares in that circle a suitable answer?
Does the answer make sense?
Is the answer physically possible answer?
The answer to the above three questions is yes and no. To arrive at the solution we rounded values and cut corners, literally.

17. First, overlay the picture of the 324 Squares with
Tenet 7:
Check units and physical significance.
Total are of square is 32,410 square millimeters.
First, overlay the picture of the 324 Squares with
areas of 100 mm2 and the eight inch circle with an area of 32,410 mm2!
The two shapes have equal area.
Therefore it is a good mathematical solution.
Does it make physical sense.

18. Unfortunately it does not!
Tenet 7:
Check units and physical significance.
Unfortunately it does not!
In semiconductor manufacturing only the complete chips have a possibility of working. Therefore any partial chip must be discarded.
Counting the number of complete chips in the to scale diagram to the left yields a result of 289 complete squares to the eight inch diameter circle.

19. Report the Final Answer
Tenet 8:
Report the Final Answer
The unit for the number of squares is mm2 squares per 8.00 inch diameter circle.
When the area of the 8.00 inch diameter circle was matched with the area of the 100 mm2 squares number of squares the result was 324.
The final answer (with the proper units).
There are less than 324 one hundred square millimeter devices per 8.00 inch diameter circular wafer.
Notice that now there are three significant figures used for reporting the final answer!

20. If an exact answer is desired a graphical solution can be employed.
Tenet 8:
Report the final answer.
If an exact answer is desired a graphical solution can be employed.
The exact answer, solved using a graphic method, is 289 one hundred square millimeter chips per eight inch circular wafer.

21. Problem Solving Using the Eight Tenets