Session 3, Part D:
Number Games (35 minutes)

Here's a number game:

 • Pick a number • Add 3 • Double your answer • Subtract 4 • Finally, multiply by 3

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?

 After the first step, the result is n + 3.   Close Tip After the first step, the result is n + 3.

 f. If Mary's final result is 48, what number did she pick?

 You will have to undo the algorithm for this and for D1(g).   Close Tip You will have to undo the algorithm for this and for D1(g).

 g. If Joe's final result is 30, what number did he pick?

 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.

Problem D3

Here's another number game:

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?

 What would you use to represent "your original number"?   Close Tip What would you use to represent "your original number"?

 f. If Mary's final result is 48, what number did she pick?

 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 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?

 g. If Joe's final result is 30, what number did he pick?

 Problem D4 Try to draw a picture of the algorithm in Problem D3. How is it different from the algorithm in Problem D1?

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?

 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)?

 Problem D7 Describe another number game that has the same kind of outputs as the game of Problem D5.

 Session 3: Index | Notes | Solutions | Video