663ad983-58f0-48fe-a79e-04121edef332.html

<h4> Warm Up (5 minutes)</h4>
<p>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. </p>
<h4> Student Activity </h4>
<p>Consider the equation \(q = 4 + 0.8p\).</p>

    <ol class="os-raise-noindent">
      <li>What value of \(q\) would make the equation true when \(p\) is 7? </li>
    </ol>
    <p> <strong>Answer: </strong> </p>
    <p>\(q = 4 + 0.8(7)\)</p>
    <p>\(q = 4 + 5.6\)</p>
    <p>\(q=9.6\)</p>

    <ol class="os-raise-noindent" start="2">
      <li>What value of \(q\) would make the equation true when \(p\) is 100?</li>
    </ol>
    <p> <strong>Answer: </strong></p>
    <p>\(q = 4 + 0.8(100)\)</p>
    <p>\(q = 4 + 80\)</p>  
    <p>\(q=84\)</p>

    <ol class="os-raise-noindent" start="3" type="1">
      <li>What value of \(p\) would make the equation true when \(q\) is 12?</li>

    </ol>
    <p> <strong>Answer: </strong></p>
    <p>\(12 = 4 + 0.8p\)</p>
    <p>\(12 - 4 = 4 + 0.8p - 4\)</p>
    <p>\(8 = 0.8p\)</p>
   <p>\( 8  0.8 = 0.8p 0.8\)</p>
    <p>\(p=10\)</p>

    <ol class="os-raise-noindent" start="4" type="1"><li> What value of \(p\) would make the equation true when \(q\) is 60?</li></ol>
    <p> <strong>Answer: </strong></p>
    <p>\(60 = 4 + 0.8p\)</p>
    <p>\(60 - 4 = 4 + 0.8p - 4\)</p>
    <p>\(56 = 0.8p\)</p>
    <p>\(56  0.8 = 0.8p 0.8\)</p>
    <p>\(p=70\)</p>



<h4>Activity Synthesis </h4>
<ul>
  <li>Invite students to share their response and strategy for answering the questions.</li>
  <li>To find the values of \(p\) 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 \(p\) (either before or after substituting the value of \(q\)). If no students mentioned solving the equations, bring it to their attention. </li>
  <li>Remind students that to solve \(12 = 4 + 0.8p \) is to find the value of \(p\) that makes the equation true. </li>
</ul>