5f7b5898-364f-4e8d-be69-367de678ca25.html

<h3>Activity (25 minutes)</h3>
<p>This activity will help students use the strategies learned in the unit and in the previous activity to create their own missing measures problems. It will require thinking through the entire problem and presenting the relevant information to a partner, who will then solve for the missing measures. </p>
<h4>Launch</h4>
<ol><li>Give students a copy of the table to complete or have students create their own table on paper.</li> 
<li>Tell students they will create 3 problems for a partner to solve. Give students time to create their rectangles. Then partners trade tables to solve the missing measures in their partner&rsquo;s rectangles. 
<li>Give students time to work out the problems their partner created. Then have students share their responses with their partner.</li> <li>Follow with a brief whole-class discussion.</li></ol>
<h4>Student Activity</h4>
<p>You will use the table to create an activity for your partner to find missing dimensions, similar to the previous activity you completed.</p>
<p><strong>Step 1 - 
  </strong>On a separate piece of paper, create 3 different rectangles with length and width formed by degree one binomials. Find the area of each rectangle.</p>
<p><strong>Step 2 - 
  </strong></p>
<p><strong>For rectangle A:</strong></p>
<ul>
  <li> Fill in the table with the binomials that form the length and width of one of the rectangles you created. Leave the area column blank for rectangle A. </li>
</ul>
<p><strong>For rectangle B:</strong></p>
<ul>
  <li> Fill in the table with the binomial that represents the length of the second rectangle you created and with the binomial or trinomial that represents the area of the rectangle. Leave the width column blank for rectangle B. </li>
</ul>
<p><strong>For rectangle C:</strong></p>
<ul>
  <li> Fill in the table with the binomial or trinomial that represents the area of the third rectangle you created. Leave the length and width columns blank for rectangle C. </li>
</ul>
<table class="os-raise-wideadjustedtable">
  <thead>
    <tr>
      <th scope="col"> Rectangle </th>
      <th scope="col"> Length (units) </th>
      <th scope="col"> Width (units) </th>
      <th scope="col"> Area (square units) </th>
    </tr> 
    </thead>
  <tbody>
    <tr>
      <td>
        A
      </td>
      <td></td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <td>
        B
      </td>
      <td></td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <td>
        C
      </td>
      <td></td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
</table>
<strong><br>
</strong>
<p><strong>Step 3 - 
  </strong>Trade tables with your partner.</p>
<p><strong>Step 4 - 
  </strong>Each partner works to find the missing information for each of the rectangles their partner created.</p>
<p><strong>Step 5 - 
  </strong>Partners compare answers to see if they match. Discuss discrepancies.</p>
<h4>Student Response</h4>
<p><strong>Answer: </strong>Your answer may vary, but here is a sample.</p>
<table class="os-raise-wideadjustedtable">
  <thead>
    <tr>
      <th scope="col"> Rectangle </th>
      <th scope="col"> Length (units) </th>
      <th scope="col"> Width (units) </th>
      <th scope="col"> Area (square units) </th>
    </tr> 
    </thead>
  <tbody>
    <tr>
      <td>
        A
      </td>
      <td>
        \(x+3\)
      </td>
      <td>
        \(x-3\)
      </td>
      <td>
        \(x^2-9\) (Solution)
      </td>
    </tr>
    <tr>
      <td>
        B
      </td>
      <td>
        \(x+2\)
      </td>
      <td>
        \(x-3\) (Solution)
      </td>
      <td>
        \(x^2-x-6\)
      </td>
    </tr>
    <tr>
      <td>
        C
      </td>
      <td>
        \(x+3\) (Solution)
      </td>
      <td>
        \(x+3\) (Solution)
      </td>
      <td>
        \(x^2+6x+9\)
      </td>
    </tr>
  </tbody>
</table>
<br>
<h4>Anticipated Misconceptions</h4>
<p>Students may think they can just write any polynomial and be able to factor it. Students may find it easier to choose two binomials and multiply them to find the area to be sure the polynomial representing the area is factorable.</p>
<h4>Project Synthesis</h4>
<p>Select students or groups to share the results of their rectangles. Have students explain their methods and reasoning. If none of the students mentions it, ask if anyone created the binomial or trinomial for the area first and then factored.</p>
<p>Discuss any issues students had in either creating the rectangles or solving their partner&rsquo;s rectangles.</p>