This lesson is the beginning of students’ introduction to functions. While students will not use the word “function” until later, the purpose of this lesson is to focus students on the idea of input and output pairs connected by a rule.

In a partner activity, students take turns guessing each other’s rules from input-output pairs. While some rules are straightforward, other rules require perseverance to identify a rule that depends on if the input is odd or even (MP1).

Next, students learn to make sense of rules represented by input-output diagrams to fill out a table with inputs and associated outputs. In each table, the first input-output pair is identical, illustrating that a single pair is insufficient for determining a rule. The last table returns to the topic of the Warm-up and introduces the idea that not all inputs are possible for a rule.

The Lesson Synthesis mentions how much of the work students do in grade 8 involves linear functions. This is also true of this course, and the idea that two input-output pairs is not always sufficient to determine a rule is still relevant.