1. September 20, 2010 IOT POLY ENGINEERING I1-12 DRILL A: SHADOWS – During the day, a 25 foot tall telephone pole casts a 10 foot shadow on the ground. At that same time, a tree casts a 25 foot shadow. How tall is the tree? DRILL B: CIRCLE GAME – Place the numbers 1 through 9 in the nine circles below such that the sum of any three circles connected vertically, horizontally, or diagonally is equal to 15.

2. IOT POLY ENGINEERING I1-12 DRILL A: SHADOWS – SOLUTION During the day, a 25 foot tall telephone pole casts a 10 foot shadow on the ground. At that same time, a tree casts a 25 foot shadow. How tall is the tree? This problem can be solved by setting up a ratio. (POLE) Height / Shadow = (TREE) Height / Shadow 25 ft / 10 ft = y / 25 ft 2.5 = y / 25 ft 62.5 ft = y 10’ 25’ y

3. IOT POLY ENGINEERING I1-12 DRILL B: CIRCLE GAME – Place the numbers 1 through 9 in the nine circles below such that the sum of any three circles connected vertically, horizontally, or diagonally is equal to 15. 5 1 9 2 8 37 4 6

4. IOT POLY ENGINEERING I1-11 PROBLEM #3: PENTAGON SYMBOLS: This pentagon is divided into 5 equal parts. By coloring in one or more parts, how many unique patterns can you form? [A pattern is not unique if it can be achieved by rotating another pattern or if it is a mirror image of another pattern. Use only one color.]

5. IOT POLY ENGINEERING I1-11 PROBLEM #3: PENTAGON SYMBOLS Sol’n: GIVEN There are 7 unique patterns that can be formed.

6. IOT POLY ENGINEERING I1-11 PROBLEM #4: BLOCKED UP: Arrange the blocks into three equal columns so that the sum of the numerals on the blocks is the same for each of the three columns.

7. Columns add up to 15. IOT POLY ENGINEERING I1-12 PROBLEM #4 : BLOCKED UP – SOLUTION This problem can be solved by “trial-and-error” along with the following strategy: 1+2+3+4+5+6+7+8+9=45, and since each of the three columns must have the same total, that total must be one-third of 45, namely 15.

8. IOT POLY ENGINEERING I1-11 PROBLEM #1: POWER PLANT LOCATION Constellation Energy will build a nuclear power plant along the Susquehanna River to provide electricity to city A and city B. They are located on the same side of the river, but at two different distances. The river is used to provide cooling water and the power plant must border the river. At what location along the river should the power plant be located so that the TOTAL LENGTH of power line connecting the two cities to the power plant is MINIMIZED?

9. A B The power plant must be located along the river’s edge. Three possible power plant locations are shown below. IOT POLY ENGINEERING I1-12 PROBLEM #1: POWER PLANT LOCATION SOLUTION The TOTAL LENGTH of power line connecting the two cities to the power plant must be MINIMIZED. How can we be sure that we have chosen the location that minimizes the power line?

10. IOT POLY ENGINEERING I1-12 PROBLEM #1: POWER PLANT LOCATION SOLUTION A B Let’s pretend for a moment that B is on the other side of the river, but at the same distance. B The shortest distance connecting A and B is a straight line. Since the line connecting A and B touches the river’s edge, this is the ideal location for our power plant!! Once the plant is located, we run the power lines to the real city B, not the imaginary one.

11. IOT POLY ENGINEERING I1-12 PROBLEM #2 : Prime Numbers Determine all prime numbers between 100X and 100(X+1) where X is the number of the class period in which you attend IOT class. Develop a strategy first. Write down your answer.

12. IOT POLY ENGINEERING I1-12 HOMEWORK PROBLEM #1 : SPIDER & FLY Given: A spider and a fly are in a room whose dimensions are 25 feet wide by 15 feet deep by 8 feet high. The spider is on the CEILING and the fly is on the FLOOR. If one corner of the room represents the origin (0,0,0) of an x-y-z coordinate system, then the spider is located at (20,8,-11 ) and the fly is located at (5,0,-7 ). See the given diagram. Problem: What is the MINIMUM DISTANCE that the spider must travel to reach the fly?

13. IOT POLY ENGINEERING I1-12 HOMEWORK PROBLEM #2 : SPIDER & FLY Given: A spider and a fly are in a room whose dimensions are 25 feet wide by 15 feet deep by 8 feet high. The spider is on the FLOOR and the fly is on the CEILING. If one corner of the room represents the origin (0,0,0) of an x-y-z coordinate system, then the spider is located at (5,0,-7) and the fly is located at (20,8,-11 ). See the given diagram. Problem: What is the MINIMUM DISTANCE that the spider must travel to reach the fly?

15. September 20, 2010 IOT POLY ENGINEERING I1-12 HOMEWORK: (Problem Solving) 1.Complete any problems from today’s lesson that you didn’t finish. 2.Complete the Spider & Fly problems.