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

 Problem C7 Imagine that an 8 came out the bottom. Pull it back through the network and figure out what had to go in the top.

 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 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.

 Problem C8 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 Draw a picture using machines to show Algorithm B, the algorithm that "undoes" Algorithm A.

 Problem C10 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?

 Problem C10 is a lot like Problem C4.   Close Tip Problem C10 is a lot like Problem C4.

 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 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

 Session 3: Index | Notes | Solutions | Video