1e12d41d-3db3-457c-866f-347eea031fc1.html

<h3>Warm Up (10 minutes)</h3>
<p>This warm up reminds students of two facts: that to use the zero product property, the product of the factors must be 0, and that there is no number that can be squared to get a negative number. At this point, students don't yet know about complex numbers or that squaring a complex number produces a negative number. Consequently, for now we can just say that there is no number (with a silent "that you know about yet") that can be squared to get a negative number.</p>
<h4>Launch</h4>
<p>Display one problem at a time. Give students quiet time to think individually for each problem and ask them to give a signal when they have an answer and an explanation. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.</p>
<div class="os-raise-extrasupport">
  <div class="os-raise-extrasupport-header">
    <p class="os-raise-extrasupport-title">Support for English Language Learners</p>
  <p class="os-raise-extrasupport-name">MLR 8 Discussion Supports: Speaking</p>
  </div>
  <div class="os-raise-extrasupport-body">
    <p>Display sentence frames to support students when they explain their strategy. For example, “First, I _____ because . . .” or “I noticed _____ so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.</p>
    <p class="os-raise-text-italicize">Design Principle(s): Optimize output (for explanation)</p>
    <p>
     </div>
</div>  
    <br>
    <div class="os-raise-extrasupport">
      <div class="os-raise-extrasupport-header">
        <p class="os-raise-extrasupport-title">Support for Students with Disabilities</p>
      <p class="os-raise-extrasupport-name"> Representation: Internalize Comprehension</p>
   </div>
  <div class="os-raise-extrasupport-body">
        <p>
          To support working memory, provide students with sticky notes or mini whiteboards. </p>
          <p class="os-raise-text-italicize">Supports accessibility for: Memory; Organization</p>
</div>
      </div>

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<h4>Student Activity</h4>
<p>Decide whether each statement is true or false.</p>
<ol class="os-raise-noindent">
  <li>3 is the only solution to \(x^2&minus;9=0\).</li>
</ol>
<ul class="os-raise-noindent">
  <li> True </li>
  <li> False </li>
</ul>
<p><strong>Answer:</strong> False. There are two solutions because there are two numbers that can be squared to get 9. Both 3 and &ndash;3 are possible solutions.</p>
<ol class="os-raise-noindent" start="2">
  <li>A solution to \(x^2+25=0\) is &ndash;5.&nbsp;</li>
</ol>
<ul class="os-raise-noindent">
  <li> True </li>
  <li> False </li>
</ul>
<p><strong>Answer:</strong> False. There is no solution to \(x^2+25=0\) because no real number can be squared to get &ndash;25.</p>
<ol class="os-raise-noindent" start="3">
  <li>\(x(x&minus;7)=0\) has two solutions.</li>
</ol>
<ul class="os-raise-noindent">
  <li> True </li>
  <li> False </li>
</ul>
<p><strong>Answer:</strong> True. There are two factors, 0 and 7, that could make the product of the expression 0.</p>
<ol class="os-raise-noindent" start="4">
  <li>5 and &ndash;7 are the solutions to \((x&minus;5)(x+7)=12\).</li>
</ol>
<ul class="os-raise-noindent">
  <li> True </li>
  <li> False </li>
</ul>
<p><strong>Answer:</strong> False. The product of the two factors is not 0, so we cannot solve it using the zero product property (which gives 5 and &ndash;7 as solutions). If we evaluate the expression \((x&minus;5)(x+7)\) at those two values, the result will be 0, not 12.</p>
<h4>Activity Synthesis</h4>
<p>Ask students to share their response and explanation for each problem. Record and display their responses for all to see. After each explanation, give the class a chance to agree or disagree. To involve more students in the conversation, consider asking:</p>
<ul class="os-raise-noindent">
  <li>"Who can restate _______'s reasoning in a different way?"</li>
  <li>"Did anyone have the same strategy but would explain it differently?"</li>
  <li>"Did anyone solve the problem in a different way?"</li>
  <li>"Does anyone want to add on to _______'s strategy?"</li>
  <li>"Do you agree or disagree? Why?"</li>
</ul>
<p>Make sure students understand the rationale that makes each statement true or false, as shown in the student response.</p>