b62ed6a8-5f62-46c2-b7e5-00a810b4de27.html

<h3>Cool Down (5 minutes)</h3>
<h4>Student Activity</h4>
<p>Tyler completes the table comparing values of the expressions \(5x^2\) and \(2^x\).</p>
<table class="os-raise-skinnytable">
  <thead>
    <tr>
      <th scope="col">\(x\)</th>
      <th scope="col">\(5x^2\)</th>
      <th scope="col">\(2^x\)</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>\(1\)</td>
      <td>\(5\)</td>
      <td>\(2\)</td>
    </tr>
    <tr>
      <td>\(2\)</td>
      <td>\(20\)</td>
      <td>\(4\)</td>
    </tr>
    <tr>
      <td>\(3\)</td>
      <td>\(45\)</td>
      <td>\(8\)</td>
    </tr>
    <tr>
      <td>\(4\)</td>
      <td>\(80\)</td>
      <td>\(16\)</td>
    </tr>
  </tbody>
</table>
<br>
<p>Tyler concludes that \(5x^2\) will always result in greater values than \(2^x\) for the same value of \(x\). Do you
  agree? Explain or show your reasoning.</p>
<p><strong>Answer:</strong> Tyler is not correct. For lesser values of \(x\), \(5x^2\) results in greater values than
  \(2^x\), but \(2^x\) eventually results in greater values because it always doubles when \(x\) increases by \(1\).
  When \(x=9\), \(5(9)^2=405\) and \(2^9=512\), so \(2^9\) is greater.</p>
<h4>Response to Student Thinking</h4>
<h5>More Chances</h5>
<p>Students will have more opportunities to understand the mathematical ideas in this cool down, so there is no need to
  slow down or add additional work to the next lessons. Instead, use the results of this cool down to provide guidance
  for what to look for and emphasize over the next several lessons to support students in advancing their current
  understanding.</p>