Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Search
Follow The Annenberg Learner on LinkedIn Follow The Annenberg Learner on Facebook Follow Annenberg Learner on Twitter
MENU
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 (35 minutes)

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

When thinking about inputs and outputs, you are thinking about algorithms as functions: You input a number into the algorithm, follow the prescribed steps, and get an output. To be a function, there are two requirements. First, the algorithm must be consistent -- that is, every time you give it the same input, you get the same output. Second, each input must produce exactly one possible output.
Note 4

Some people picture the steps in an algorithm or function as little machines. An addition machine would look like this:

function machine example

If you put a 5 in the left hopper and a 4 in the right hopper, what would come out of the bottom? Take a few minutes to practice drawing your own machines.

Sometimes we want our machine to add the same thing each time. If we wanted our machine to add 3 each time, we could represent it with the 3 locked in position, like this:

function machine example

We can also connect two different machines together to make a network, so that that the output hopper from one machine goes right into the input hopper on the next machine. Consider this network of function machines:

function machine example

Try running a few numbers through this network. Remember to perform each step in order. For example, if you start with zero, you will get 3 as an output from the first machine. After running 3 though the second machine, your output will be 6, which is the output of the network.

Now try pulling a number back up through the machine in the reverse order -- that is, begin with the output and work backward to the input.


Next > Part C (Continued): Running a Function Machine

Learning Math Home | Algebra Home | Glossary | Map | ©

Session 3: Index | Notes | Solutions | Video

© Annenberg Foundation 2014. All rights reserved. Legal Policy