The purpose of this lesson is to introduce students to the term “function.” A function is a rule that produces a single output for a given input.

A key aspect of functions is that for each input, there is one and only one output. The Warm-up primes students for this idea by inviting them to consider a list of positive and negative numbers, including 3 and -3, and to consider what happens to the list after each number is squared.

In the next activities, students first consider if a given statement is enough to uniquely answer the question that follows, and if it is, they draw an input-output diagram. Then they use the statements and diagrams to describe the inputs and outputs more precisely by using function language, such as “The output is a function of the input” and “The output depends on the input” (MP6).

In the optional activity, students see how the same function can be described in different ways but still have the same input-output pairs. This helps solidify the notion of a function as something different from the method of calculating its values.