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<h3>Warm Up (5 minutes)</h3>
<p>This Math Talk invites students to use what they know about fractions, decimals, and the meaning of percent to
mentally solve problems. The strategies elicited here will be helpful later in the lesson when students calculate
prices that involve a percent increase and write an equation to generalize the calculation.</p>
<p>Finding different percents of the same value (200) is also an opportunity to reason repeatedly and look for and make
use of structure. </p>
<p>Students are likely to approach the problems in different ways. They may:</p>
<ul>
<li>Convert each percentage into a fraction and multiply the fraction by 200. For example, they may think of 25% as \(
\frac14 \), 12% as \( \frac{12}{100} \) or \( \frac{3}{25} \), and 8% as \( \frac{8}{100} \) or \( \frac{2}{25} \).
</li>
<li>Convert each percentage into a decimal and multiply it by 200.</li>
<li>Notice that 1% of 200 is 2 and that any percentage of 200 can be found by multiplying the percentage by 2. For
example, 25% of 200 is \( 25 \cdot 2 \), and \( p \)% of 200 is \( p \cdot 2 \) or \( 2p \).</li>
</ul>
<p>This activity invites students to use what they know about fractions, decimals, and the meaning of percent to
mentally solve problems. </p>
<ol class="os-raise-noindent">
<li>
What is 25% of 200?
</li>
</ol>
<p><strong>Answer:</strong> 50</p>
<ol class="os-raise-noindent" start="2">
<li>
What is 12% of 200?
</li>
</ol>
<p><strong>Answer:</strong> 24</p>
<ol class="os-raise-noindent" start="3">
<li>
What is 8% of 200?
</li>
</ol>
<p><strong>Answer:</strong> 16</p>
<ol class="os-raise-noindent" start="4">
<li>
How would you determine \(p\)% of 200?
</li>
</ol>
<p><strong>Answer:</strong></p>
<ul>
<li>
\(2p\)
</li>
<li>
\(\(\frac{p}{100} \cdot 200\)\)
</li>
<li>
Change the percentage to a decimal and multiply it by 200.
</li>
<li>
Since percent means “per hundred” and there are two hundreds, the percentage is multiplied by two.
</li>
</ul>
<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>
<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>
<br>
<h4>Student Activity</h4>
<p>You will be asked to evaluate the percentage of a number mentally. Sometimes, a visual is helpful to do this. If
needed, use the GeoGebra activity to help you determine the requested values. Then, look for a pattern that can be
used to describe how to find the percentage of any number. </p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/XSFd8GkK/width/1035/height/468/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" title="Copy of Percentage of an Amount (1%)"> </iframe></div>
</div>
<ol class="os-raise-noindent" start="1">
<li> What is 25% of 200? </li>
</ol>
<p> <strong>Answer:</strong> 50</p>
<ol class="os-raise-noindent" start="2">
<li> What is 12% of 200? </li>
</ol>
<p> <strong>Answer:</strong> 24</p>
<ol class="os-raise-noindent" start="3">
<li> What is 8% of 200? </li>
</ol>
<p> <strong>Answer:</strong> 16</p>
<ol class="os-raise-noindent" start="4">
<li>How would you determine \( p \)% of \( 200 \)?</li>
</ol>
<p class="os-raise-text-bold">Answer:</p>
<p>Your answers may vary, here are some examples:</p>
<ul>
<li>\(2p\)</li>
<li>\(\frac{p}{100} \cdot 200\)</li>
<li>Change the percentage to a decimal and multiply it by 200.</li>
<li>Since percent means “per hundred” and there are two hundreds, the percentage is multiplied by two.</li>
</ul>
<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>
<ul>
<li>“Who can restate \( \underline{\hspace{.5in}} \)’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 \( \underline{\hspace{.5in}} \)’s strategy?”</li>
<li>“Do you agree or disagree? Why?”</li>
</ul>
<p>If one of the strategies shown in the Narrative is not mentioned, consider sharing it with students. </p>
<br>
<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>Use this routine to support whole-class discussion as
students explain how they matched the description to the graph. Display the following sentence frames for all to see:
“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.<br>
</p>
<p class="os-raise-text-italicize">Design Principle(s): Optimize output (for explanation)</p>
<p>
</p>
</div>
</div>