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Session 3, Part D:
Number Games (35 minutes)
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Here's a number game:
• | Pick a number |
• | Add 3 |
• | Double your answer |
• | Subtract 4 |
• | Finally, multiply by 3 |
Note 5
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Problem D1 |  |
Draw a picture of this algorithm and use your picture to answer the following questions:
a. | If you pick 3, what will your final number be? |
b. | If you pick 5, what will your final number be? |
c. | If you pick 12, what will your final number be? |
d. | If you pick 38, what will your final number be? |
e. | If you pick n, what will your final number be? |
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After the first step, the result is n + 3. Close Tip |
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f. | If Mary's final result is 48, what number did she pick? |
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You will have to undo the algorithm for this and for D1(g). Close Tip |
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g. | If Joe's final result is 30, what number did he pick? |
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Problem D2 | |
Build an algorithm that lets you find the number someone picked in Problem D1 if you know his or her final result. Try it out.
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Problem D3 | |
Here's another number game:
• | Pick a number |
• | Add 3 |
• | Double your answer |
• | Add your original number |
• | Subtract 4 |
• | Finally, multiply by 3 |
Use the algorithm above to answer these questions:
a. | If you pick 3, what will your final number be? |
b. | If you pick 5, what will your final number be? |
c. | If you pick 12, what will your final number be? |
d. | If you pick 38, what will your final number be? |
e. | If you pick n, what will your final number be? |
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What would you use to represent "your original number"? Close Tip |
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f. | If Mary's final result is 48, what number did she pick? |
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This is more difficult than the seemingly identical question in Problem D1. Why? What can be done about it? Does your work in D3(e) help? Close Tip |
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g. | If Joe's final result is 30, what number did he pick? |
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Problem D4 | |
Try to draw a picture of the algorithm in Problem D3. How is it different from the algorithm in Problem D1? |
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Problem D5 | |
Here's another number game:
• | Pick a number |
• | Multiply by 3 |
• | Add 5 |
• | Multiply by 2 |
• | Subtract 6 times your original number |
• | Add 4 |
• | Finally, divide by 2 |
Use the algorithm above to answer these questions:
a. | If you pick 3, what will your final number be? |
b. | If you pick 5, what will your final number be? |
c. | If you pick 12, what will your final number be? |
d. | If you pick 38, what will your final number be? |
e. | If you pick n, what will your final number be? Can you explain why? |
f. | If Nancy's final result is 7, what number did she pick? |
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Problem D6 |  |
What strategies did you use on Problems D3(f) and D3(g)? Why are these different from the strategies used in Problems D1(f) and D1(g)? |
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Problem D7 | |
Describe another number game that has the same kind of outputs as the game of Problem D5. |
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