Equations for Functions

5 min

Teacher Prep
Setup
Groups of 2. 1–2 minutes quiet work time then partner discussion followed by whole-class discussion.

Narrative

The purpose of this Warm-up is for students to use repeated reasoning to write an algebraic expression to represent a rule of a function (MP8).

Launch

Arrange students in groups of 2. Give students 1–2 minutes of quiet work time and then time to share their algebraic expression with their partner. Follow with a whole-class discussion.

Student Task

Fill in the table of input-output pairs for the given rule. Write an algebraic expression for the rule in the box in the diagram.

Input-output rule diagram. Input, s, the side length of a square, right arrow, box for the rule is left blank, right arrow, output, A, the area of the square.

input output
8
2.2
121412\frac14
ss

 

Sample Response

Input-output rule diagram. Input, s, the side length of a square, right arrow, s squared, right arrow, output, A, the area of the square.

input output
8 64
2.2 4.84
121412\frac14 150116150\frac{1}{16}
ss s2s^2 or AA
Activity Synthesis (Teacher Notes)

The purpose of this discussion is for students to connect a rule to a table of input-output pairs and an algebraic expression. Students are also reintroduced to the terms “independent variables” and “dependent variables” in the context of the inputs and outputs of functions.

Select students to share how they found each of the outputs. After each response, ask the class if they agree or disagree. Record and display responses for all to see. If both responses are not mentioned by students for the last row, tell students that we can either put s2s^2 or AA there. Tell students we can write the equation A=s2A = s^2 to represent the rule of this function.

End the discussion by telling students that while we’ve used the terms “input” and “output” so far to talk about specific values, when a letter is used to represent any possible input we call it the independent variable, and the letter used to represent all the possible outputs is the dependent variable. Students may recall these terms from earlier grades. In this case, ss is the independent variable and AA the dependent variable, and we say “AA depends on ss.”

Standards
Addressing
  • 8.F.1·Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
  • 8.F.A.1·<p>Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. <span>Function notation is not required in Grade 8.</span></p>

15 min

15 min