Function Machine

Give me some of that input/output! – Give me some of that Math! Introducing your advisory to the concept of variables early helps them see algebra in their LTI projects.  Also, the concept of a variable will make discussing budget equations, compound interest, credit card debt, and car loans much easier in future advisory activities.
Advisory Activity:
Start by putting the following charts on the board:
You Say… The Machine Says…
0                     6
1                     7
3                     9
4                     10
7                     13
Explain the chart.  Ask your students to call out a number. “The machine” responds with a number. The machine is, well, a machine—it has some sort of rule it uses to figure out its response.  What’s the rule in this case?  (Answer: Add six to the number you say.)Here are a few other examples:
x    y
2    5
3    7
5    11
8    17
The machine doubles the number, then adds one.You could write that as y = 2x + 1.  The 2x means two times x.
x     y
2    0.5
5    0.2
10    0.1
12    .083
The machine divides one by the number you give.You could write that as y = 1/x.Ask your students to write the rule as a function (a formula). “The number that you say” we call x.  “The number the machine responses with” we call y.  So we add six to x to get y. You can write this using algebraic notation as y = x+6.  It is standard to use x for the input and y as the output. Now, turn the machine idea into a game.  Have someone come up with a rule and stand at the board, acting like the machine.  (Ask a student to come up with a function, or use one you suggest)Have other people give “the machine” a number.  “The machine” then responds using the rule.  The group then has to figure out the rule and devise a formula that represents the rule.Students can take turns trying to stump each other.  Make sure everyone gets a chance to be the function machine (this can be a fun game to play for a few minutes a week – your students will be pros!)
The more times you can come back to this activity, especially during those five or ten minutes in advisory when you don’t have anything else planned, the better.  Some students will find this activity easy, and some will find it very hard.  How can you make it challenging for all students?  Should you have certain students challenge other students?  Should you make teams?  Help students to introduce harder formulas into the game, like x2 or 3x?  Make sure you help students learn more about equations as you go.



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