Using Function Notation to Describe Rules (Part 2)

5 min

Narrative

This Warm-up refreshes the idea of evaluating and solving equations, preparing students for the main work of the lesson. It reminds students that to solve a variable equation is to find one or more values for the variable that would make the equation true. In subsequent activities, students will work with equations in function notation to find unknown input or output values.

Student Task

Consider the equation q=4+0.8pq = 4 + 0.8p.

  1. What value of qq would make the equation true when:

    1. pp is 7?
    2. pp is 100?

  2. What value of pp would make the equation true when:

    1. qq is 12?
    2. qq is 60?

Be prepared to explain or show your reasoning.

Sample Response

    1. q=9.6q=9.6
    2. q=84q=84
    1. p=10p=10
    2. p=70p=70
Activity Synthesis (Teacher Notes)

Invite students to share their response and strategy for answering the questions.

To find the values of pp in the second set of questions, some students may have guessed and checked, but many students should have recognized that they could solve the equations for pp (either before or after substituting the value of qq). If no students mentioned solving the equations, bring it to their attention.

Remind students that to solve 12=4+0.8p12=4+0.8p is to find the value of pp that makes the equation true.

Standards
Addressing
  • A-REI.1·Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
  • A-REI.1·Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
  • A-REI.1·Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
  • HSA-REI.A.1·Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

25 min