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Session 3 Part A Part B Part C Part D Part E Homework
 
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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

Note 5

Problem D1

Solution  

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?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
After the first step, the result is n + 3.   Close Tip

 

f. 

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


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
You will have to undo the algorithm for this and for D1(g).   Close Tip

 

g. 

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


 

Problem D2

Solution  

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

Solution  

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?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
What would you use to represent "your original number"?   Close Tip

 

f. 

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


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
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

 

g. 

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


 

Problem D4

Solution  

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


 

Problem D5

Solution  

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

write Reflect  

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

write Reflect  

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


Next > Part E: Other Kinds of Functions

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