Function Machine

What is Function Machine?

This activity allows the user to explore simple linear functions; the function is determined by looking for patterns in the outputs. The functions available for exploration in the function machine activity have one of the following forms:

where the underline can be any integer between -10 and 10.

The notion of a function is important in higher mathematics such as calculus and in areas which use mathematics such as physics. Any rule that assigns exactly one output to an input or list of inputs can be called a function.

Here are a few examples:

• Input the number of seconds after the starting gun in a race to get an output of the number of meters the runner has covered.

  input	3	2	0	-4
  output	4	-1	2	-3

• y = x - 6, where x is the place holder (also called a variable) for the input and y is the place holder for the output.
  The rule about only one output each time is crucial and must not be violated. For example, the table below cannot represent a function because 3 has two different outputs:

  input	3	2	0	3
  output	4	-1	2	-3

Related Resources

• Activity Algebra Four
• Activity Algebra Quiz
• Activity Equation Solver
• Activity Graphit
• Activity Incline
• Activity Linear Function Machine
• Activity Number Cruncher
• Activity Positive Linear Function Machine
• Activity Possible or Not
• Activity Simple Plot
• Activity Vertical Line Test
• Activity Whole Number Cruncher
• Discussion about Functions as Processes or Rules: "Function Machines"
• Discussion about Independent and Dependent Variables
• Discussion about Multi-Step Functions
• Worksheet Four Quadrant Grid, 14x18
• Worksheet Four Quadrant Grid, 28x36
• Worksheet Function Machine Game Suggestions
• Worksheet Function Machine Game Suggestions (doc)

How Do I Use This Activity?

This activity allows the user to explore simple linear functions; the function is determined by looking for patterns in the outputs. The functions available for exploration in the function machine activity have one of the following forms:

Controls and Output

• To find out what the machine will do with a number:
  • Type a number into the X= [____] space (in our example, number 5 is typed in)
    
  • Press the Enter button:
    
  • Observe the resulting number in the Y= [____] window (in our example, number 7 is the result):
    
  • You can input as many numbers as you need to find the rule
• To check if you guessed the rule right, select an operation and type a number in the Y = X [?] [____] space, and then press the Check Formula button.
  
• To select an operation, click on the selection sign
  
  next to the question mark. You will see three operations (and a question mark):
  
  • Click on the operation you want to select, and it will appear instead of the question mark (in our example, + is selected):
    
  • Type the number that completes the rule in the space after the sign (in our example, 2 is typed):
    
  • Click on the Check formula button:
    
  • You will see one of the two messages under the picture of the machine: either Correct answer! or Try again!
• To set a new function machine (that is, a new rule), click once on the Set new function button
  
• This activity automatically keeps track of how successful you are at naming the function. To view your score press the Show Score button
  
  • To pause scoring press the Active button and it will turn into a Paused button to indicate that scoring has been paused. To resume scoring press this button again so it reads Active.
  • Every time you press the Check formula button, the score panel is updated. This panel tells you the percentage of your guesses that were correct for the current function, and all the functions.
    
  • If you want to reset the statistics, you may do so by pressing the Reset button inside of the scoreboard.
    

Because this activity randomly generates questions, a feature called Seed Random has been implemented that allows multiple users using different computers to work on the same problem. See Seed Random Help for instructions on using this feature.

Description

This activity allows the user to explore simple linear functions; the function is determined by looking for patterns in the outputs. The functions available for exploration in the function machine activity have one of the following forms:

where the underline can be any integer between -10 and 10. This activity would work well in same ability groups of two to four for about forty to forty-five minutes if you use the exploration questions and twenty to twenty-five minutes otherwise.

Place in Mathematics Curriculum

This activity can be used to:

• practice students' pattern finding skills
• introduce basic notions from algebra
• motivate the idea of a function of one variable
• practice students' arithmetic skills

Be Prepared to

• give implicit directions on what they are to do. For example, "Today we are going to learn howfunctions work. We will figure out several important facts about functions..."
• discuss the vocabulary, input, output, function rule...

Related Resources

• Activity Algebra Four
• Activity Algebra Quiz
• Activity Equation Solver
• Activity Graphit
• Activity Incline
• Activity Linear Function Machine
• Activity Number Cruncher
• Activity Positive Linear Function Machine
• Activity Possible or Not
• Activity Simple Plot
• Activity Vertical Line Test
• Activity Whole Number Cruncher
• Discussion about Functions as Processes or Rules: "Function Machines"
• Discussion about Independent and Dependent Variables
• Discussion about Multi-Step Functions
• Lesson on Introduction to Functions
• Lesson on More Complicated Functions: Introduction to Linear Functions
• Worksheet Four Quadrant Grid, 14x18
• Worksheet Four Quadrant Grid, 28x36
• Worksheet Function Machine Game Suggestions
• Worksheet Function Machine Game Suggestions (doc)