cabe0fb4-9672-456e-97fd-e1157f9c9da9.html

<h3>Warm Up (10 minutes)</h3>
<p>This warm up activity prompts students to recall strategies for multiplying mentally.</p>
<p>Each expression can be evaluated in different ways. For example, \(19 \cdot 21\) can be viewed as \(19 \cdot (20 + 1)\), as \(21 \cdot (20 &minus; 1)\), or as \((20 &minus; 1) \cdot (20 + 1)\), among other ways. Reasoning flexibly about the structure of numerical expressions encourages students to do the same when rewriting quadratic expressions in this lesson and beyond.</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 a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.</p>
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  <div class="os-raise-extrasupport-header">
    <p class="os-raise-extrasupport-title">Support for English Language Learners</p>
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    <p class="os-raise-extrasupport-name">MLR 8 Discussion Supports: Speaking</p>
    <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>
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  <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>
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  <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>
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<h4>Student Activity</h4>
<p>Finding a product mentally can be done by changing the way you look at a multiplication problem.</p>
<p>For example, \(9 \cdot 39\) can be thought of as \(9 \cdot (40 &minus; 1)\). For some people, this might be easier to calculate mentally since you can imagine the solution as \(360 &minus; 9\), or 351. This method leverages the distributive property of multiplication over addition.</p>
<p>For the following questions, find each product mentally. Then, explain how you changed the way you looked at each multiplication problem to use the distributive property.</p>
<ol class="os-raise-noindent">
  <li>(\(9 \cdot 11\))</li>
</ol>
<p><strong>Answer:</strong> 99<br>
  For example, \(9 \cdot 11\) can be thought of as \(9 \cdot (10 + 1)\). This simplifies to \(90 + 9\), or 99.</p>
<ol class="os-raise-noindent" start="2">
  <li>(\(19 \cdot 21\))</li>
</ol>
<p><strong>Answer:</strong> 399<br>
  For example, \(19 \cdot 21\) can be thought of as \(19 \cdot (20 + 1)\). This simplifies to \(380 + 19\), or 399.</p>
<ol class="os-raise-noindent" start="3">
  <li>(\(99 \cdot 101\))</li>
</ol>
<p><strong>Answer:</strong> 9999<br>
  For example, \(99 \cdot 101\) can be thought of as \(99 \cdot (100 + 1)\). This simplifies to \(9900 + 99\), or 9999.</p>
<ol class="os-raise-noindent" start="4">
  <li>(\(109 \cdot 101\))</li>
</ol>
<p><strong>Answer:</strong> 11,009<br>
  For example, \(109 \cdot 101\) can be thought of as \(109 \cdot (100 + 1)\). This simplifies to \(10,900 + 109\), or 11,009.</p>
<h4>Activity Synthesis</h4>
<p>Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:</p>
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  <li>"Who can restate _______&rsquo;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 _______&rsquo;s strategy?"</li>
  <li>"Do you agree or disagree? Why?"</li>
</ul>