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Learning Math Home
Patterns, Functions, and Algebra
 
Session 3 Part A Part B Part C Part D Part E Homework
 
Glossary
Algebra Site Map
Session 3 Materials:
Notes
Solutions
Video

Session 3, Part C:
Function Machines

In This Part: About Function Machines | Running a Function Machine | Function Machines and Undoing

Think back for a minute to Algorithm A, which we worked with in Part B. Take a look at the following picture of Algorithm A and answer Problems C6-C10 below.

Problem C6

Solution  

Imagine dropping a 7 into this network. What comes out the bottom?


 

Problem C7

Solution  

Imagine that an 8 came out the bottom. Pull it back through the network and figure out what had to go in the top.


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Try to think of an efficient way of solving this problem. If you have Flash on your machine you can also use the Interactive Activity "Running a Function Machine" to model Algorithm A.   Close Tip

 

Problem C8

Solution  

Imagine that a 100 came out the bottom. Pull it back through the network and figure out what had to go in the top.


 

Problem C9

Solution  

Draw a picture using machines to show Algorithm B, the algorithm that "undoes" Algorithm A.


 

Problem C10

Solution  

Imagine connecting the output spout of Algorithm A to the input hopper of Algorithm B. Now you have a huge network. What does it do to a number?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Problem C10 is a lot like Problem C4.   Close Tip


video thumbnail
 

Video Segment
In this segment, Deanna and Lolita present the combined network built by connecting Algorithms A and B. Watch the segment after you have completed Problem C10. If you get stuck on the problem, you can watch the video segment to help you.

Do you think every network built by function machines can be "undone"?
Suppose a network's steps could all be reversed, step by step. Could every algorithm of this type be "undone"?

You can find this segment on the session video, approximately 13 minutes and 1 second after the Annenberg Media logo.

 

 

Problem C11

write Reflect  

Suppose someone hands you an algorithm. Describe a general process that will allow you to construct a new algorithm that undoes the one you are given. Can you imagine an algorithm for which your method doesn't work?


Next > Part D: Number Games

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