2fa9a9f9-fe1a-4344-bc6b-cca308334ba8.html

<h3>Cool Down (5 minutes)</h3>
<h4>Student Activity</h4>
<ol class="os-raise-noindent">
  <li>The equation \( 4(x-2) = 100 \) is a true equation for a particular value of \( x \). Explain why \( 2(x-2) = 50 \) is also true for the same value of \( x \). </li>
</ol>
<p><strong>Answer:</strong> </p>
<p>If \( 4(x-2) \) and 100 are equal, then multiplying \( 4(x-2) \) by \( \frac12 \) and multiplying 100 by \( \frac12 \) will give two results that are also equal, so \( 2(x-2)=50 \) must be true.</p>
<p>For questions 2—4, use the following situation:</p>
<blockquote>
  <p>To solve the equation 7.5d=2.5d, Lin divides each side by 2.5d, and Elena subtracts 2.5d from each side. </p>
</blockquote>

<ol class="os-raise-noindent" start="2">
  <li>Will Lin&rsquo;s move lead to a solution? Explain your reasoning.</li>
</ol>
<p><strong>Answer:</strong> Lin's move will not work. Dividing by 2.5d gives 3=1, which is not true. Dividing by the variable we are trying to solve makes us think there is no solution. </p>
<ol class="os-raise-noindent" start="3">
  <li>Will Elena’s move lead to a solution? Explain your reasoning.</li>
</ol>
<p><strong>Answer:</strong> Compare your answer: Elena’s move will work. Subtracting 2.5d from both sides gives 5d=0. </p>
<ol class="os-raise-noindent" start="4">
  <li>What is the solution to the equation?</li>
</ol>
<p><strong>Answer:</strong> 0</p>
<h4>Response to Student Thinking</h4>
<p><strong>Points to Emphasize</strong></p>
<p>Address student misconceptions about dividing by a variable at the beginning of the next lesson. If students struggle with division in the first part of the cool-down, look for moments to emphasize the procedure of doing the same thing to both sides in Lessons 1.1.8 and 1.1.9.</p>