1. September 2, 2011
IOT POLY ENGINEERING
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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. DRILL A: SHADOWS – ALGEBRAIC SOLUTION
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DRILL A: SHADOWS – ALGEBRAIC 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.
Height / Shadow = Height / Shadow
25 ft / 10 ft = Height / 25 ft
= Height / 25 ft
62.5 ft = Height of tree

3. DRILL B: CIRCLE GAME – _?_SOLUTION
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DRILL B: CIRCLE GAME – _?_SOLUTION
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. 1 6 2 7 5 3 8 4 9
What problem-solving strategy was used?

4. PROBLEM #5(OBSCURED BLOCKS): HOMEWORK SOL’N
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PROBLEM #5(OBSCURED BLOCKS): HOMEWORK SOL’N
Given a stack of individual blocks as shown. If all of the visible blocks were to disappear suddenly, how many blocks would remain? Write down your answer.

5. PROBLEM #5 : HOMEWORK SOLUTION (MODEL)
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PROBLEM #5 : HOMEWORK SOLUTION (MODEL)
= 17
There are 17 blocks left.

6. PROBLEM #6 (CROSSING PATHS) : HOMEWORK SOL’N
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PROBLEM #6 (CROSSING PATHS) : HOMEWORK SOL’N
Draw the following figure in one continuous action without lifting your pencil off the paper and without crossing any lines. You may begin at any point.

7. PROBLEM #7 (COUNTERFEIT GOLD COIN):
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PROBLEM #7 (COUNTERFEIT GOLD COIN):
A man is given 9 gold coins, but one of them is counterfeit and weighs less than the others. The man wants to determine which of the coins is counterfeit by using his balance scale. How can the man determine the false coin with only two uses of the balance scale? Write down your answer.

8. PROBLEM #7 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
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PROBLEM #7 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
Divide the 9 gold coins into three equal groups of 3 coins each. Call them A, B, and C.
A B C
Place A and B on each side of the balance. Leave C on the table.
This is the first use of
the balance.

9. PROBLEM #7 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
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PROBLEM #7 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
Did A and B balance?
YES NO
The light coin is in group C.
Discard the heavy group Keep the light group.
One light group has been identified with one weighing. Next, we determine which of those 3 coins is lightest.

10. PROBLEM #7 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
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PROBLEM #7 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
Divide the 3 gold coins into three equal groups of 1 coin each. Call them D, E, and F.
D E F
Place D and E on each side of the balance. Leave F on the table.
This is the second use of
the balance.

11. PROBLEM #7 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
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PROBLEM #7 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
Did D and E balance?
YES NO
The counterfeit coin is F.
The lighter coin is counterfeit.
In summary, the first weighing eliminated 2 groups of 3 coins each. The second weighing eliminated 2 of the last 3 coins.

12. PROBLEM #8 (AVERAGE SPEED):
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PROBLEM #8 (AVERAGE SPEED):
A train travels up a steep hill at a constant speed of 25 miles per hour. It takes one hour to reach the top of the hill. Neglecting the very small time it takes to turn around, how fast would the train have to travel down the hill in order for the average speed to be 50 mph for the entire round-trip?

13. PROBLEM #8 (AVERAGE SPEED): SOLUTION
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PROBLEM #8 (AVERAGE SPEED): SOLUTION
The return trip down the hill is also 25 miles. Therefore, the total round-trip will be 50 miles. For the average speed to be 50 mph for the round-trip, the train must travel 50 miles in one hour, but the train already used up that hour on the trip up the hill. Therefore, it is impossible for the train to average 50 mph for the trip.
What problem-solving strategy was used?
The train traveled 25 mph for one hour to reach the top of the hill. Average speed is equal to total distance divided by total time. 25 miles divided by 1 hour is 25 mph. Therefore, the train traveled 25 miles to reach the top of the hill in 1 hour.

14. PROBLEM #9: HOMEWORK (PENTAGON SYMBOLS):
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PROBLEM #9: HOMEWORK (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.]

15. PROBLEM #10: HOMEWORK (BLOCKED UP):
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PROBLEM #10: HOMEWORK (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.

16. September 2, 2011 HOMEWORK: (Problem Solving)
IOT POLY ENGINEERING
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HOMEWORK: (Problem Solving)
Complete any problems from today’s lesson that you didn’t already finish.
Answer problem #9 (Pentagon Symbols) and problem #10 (Blocked Up).