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We often introduce students to functions with the concept of an "in-out" machine. We put a number "in" the hopper; the machine spits "out" a new number. The task is to predict what number will come out, no matter what number is put in.

In this activity, however, we put in two numbers—one on each side of the operator. This makes the task more challenging. Good strategies to use and discuss include being systematic, choosing easy numbers, and controlling variables. For example, we might start with two zeros as inputs and then change only one number at a time.

Any student who has been exposed to multiplication can do this activity. It never requires multiplying by a number greater than 5. That said, figuring out the operations can be complex. The problem may turn into one of organizing information rather than raw computation.

More experienced students can still benefit from this activity. The mystery operations are, after all, functions in two variables. You can challenge high school students by asking how they would represent one of these operations graphically.

NCTM Standard 1 (1998) sets the purpose of number and operations for grades 3–5.

Mathematics instructional programs should foster the development of number and operation sense so that all students...understand the meaning of operations and how they relate to each other?.

Many books have activities or whole chapters devoted to introducing functions, often with in-out machines. For example, United We Solve (EEPS Media, 1996) is a collection of cooperative math problems aimed at middle-grade programs. Mystery Operations was adapted from a set of cooperative problems in this book.

And if you search for "function machine" on the Web, you will find some other online activities. Here is a function machine activity from the Shodor Education Foundation.

Back to Mystery Operation

 

 
 

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