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6023a5a0-8a56-4475-8b28-689cfcd423aa.html
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<h4>Activity</h4>
<p>For numbers 1 - 4, use the situation below:</p>
<blockquote>
<p>
After a parade, a group of volunteers is helping to pick up the trash along a 2-mile stretch of a road. The group
decides to divide the length of the road so that each volunteer is responsible for cleaning up equal-length
sections.
</p>
<p>Find the length of a road section for each volunteer if there are the following numbers of volunteers. Be prepared to show your reasoning.
</p>
</blockquote>
<img alt="Mummers' Parade in Philly." class="img-fluid atto_image_button_text-bottom" height="430" src="https://k12.openstax.org/contents/raise/resources/dfb7838fc9d86de04e46523624735a8692051722" width="600">
<br>
<br>
<!--Q1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="5f27c081-5795-4f2c-8a1f-1ee4e2a6a1c0" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>8 volunteers</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\( \frac14 \) mile</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="22bc94f1-cb73-4629-a9dd-36c9ec386ee8" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>10 volunteers</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\( \frac15 \) mile</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="8250420e-ef8e-4437-8964-4a9f21951cda" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>25 volunteers</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\( \frac {2}{25} \) mile or 0.08 mile</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q4-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d52966f7-7a7c-4696-ba23-eae8096880b9" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>36 volunteers</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\( \frac{2}{36} \) or \( \frac{1}{18} \) mile</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q5-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="a35a88c8-3c40-4bd3-afcd-44c0803a5b15" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li>Write an equation that would make it easy to find \( l \), the length of a road section in miles for each
volunteer, if there are \( n \) volunteers.
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\( l = \frac{2}{n} \)</p>
</div>
</div>
<!--Interaction End -->
<br>
<p>For numbers 6 - 9, find the number of volunteers in the group if each volunteer cleans up a section of the following
lengths. Be prepared to show your reasoning.
</p>
<!--Q6-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d1dae426-1a46-4f16-b636-7e7f6d9af9e8" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="6">
<li>0.4 mile</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(n=\frac{2}{0.4}=\) 5 volunteers</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q7-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="144bc1d6-f810-4860-b0db-f9f156c59dcd" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="7">
<li>
\( \frac {2}{7} \) mile
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(n=\frac2{\displaystyle\frac27}=\frac{2}{1}\times\frac{7}{2}=\) 7 volunteers</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q8-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b1d490af-48ee-4381-aed0-adc1675df5fb" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="8">
<li>0.125 mile</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(n=\frac{2}{0.125}=\) 16 volunteers</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q9-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d894767b-f703-4ec5-85c6-99e7e5c4c5c6" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="9">
<li>
\( \frac {6}{45} \) mile
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(n=\frac2{\displaystyle\frac{6}{45}}=\frac{2}{1} \times \frac{45}{6}=\) 15 volunteers</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q10-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="7698b556-a809-45d7-86fa-491141778456" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="10">
<li>Write an equation that would make it easy to find the number of volunteers, \( n \), if each volunteer cleans up a
section that is \( l \) miles. </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\( n = \frac{2}{ l} \)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!-- "Start "Are you Ready for More? click to reveal. If you have more than one on a page, you will need to change the Data-fire/data-wait-for-events for each set.-->
<div class="os-raise-ib-cta" data-button-text="Are you ready for more?" data-fire-event="RFM1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-cta-prompt">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<!--Q1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="aa3e6472-de87-4ac0-9df6-ce5265af0166" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<p>Let's think about the graph of the equation \( y=\frac{2}{x} \).</p>
<ol class="os-raie-noindent">
<li>
Create a list
\((x,y)\) pairs that will help you graph the equation. Make sure to include some negative numbers for \(x\) and some numbers that are not integers.
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here is an example:</p>
<ul>
<li>\((-2.5,-0.8)\)</li>
<li>\((-1,-2)\)</li>
<li>\((0.5,4)\)</li>
<li>\((1.25,1.6)\)</li>
</ul>
</div>
</div>
<!--End interaction-->
<br>
<!--Q2-->
<div class="os-raise-ib-desmos-gc" data-schema-version="1.0" data-wait-for-event="RFM1"></div>
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="427a1b87-8092-43d2-9cd6-c680835a02f4" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raie-noindent" start="2">
<li>
Use the graphing tool or technology outside the course. Graph the equation that represents this scenario using the
Desmos tool above.
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<div class="os-raise-d-flex os-raise-justify-content-between">
<div class="os-raise-mx-auto">
<img alt="Image of Demos screen of the plots of coordiantes for the equation of the fraction two over x." src="https://k12.openstax.org/contents/raise/resources/164b3020a1663ad321ecc53c4cbf4ab40f1d3d7f">
</div>
<div class="os-raise-mx-auto">
<img alt="Graph of the equation of the fraction two over x." src="https://k12.openstax.org/contents/raise/resources/e1680e9f8278894aa656e8b20857a78c1dca29aa" width="400">
</div>
</div>
<br>
</div>
</div>
<!--End interaction-->
<br>
<!--Q3-->
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="dc7c644d-1ce0-4ac8-8a85-f73378059d03" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raie-noindent" start="3">
<li>
What do you think the graph looks like when \(x\) is between 0 and \(\frac12\)? Continue to use the graphing tool or
technology outside the course to graph the function
\(y=\frac{2}{x}\) with your points. Try some values of \(x\) to test your idea. (Students were provided access to Desmos.)
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here is an example:</p>
<p>The graph gets steeper and steeper as \(x\) gets closer to 0.</p>
<p><img src="https://k12.openstax.org/contents/raise/resources/bba34b4119919710e25d5a614d6d772cf523e636" width="300"></p>
</div>
</div>
<!--End interaction-->
<br>
<!--Q4-->
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="c2171d3e-1598-4da1-9146-9c03362f1f8e" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raie-noindent" start="4">
<li>
What is the largest value \(y\) can ever be?
</li>
</ol>
<p>\(y=\frac{2}{x}\) with your points. Try some values of \(x\) to test your idea. In Desmos, zoom in on your graph.</p>
<p>When you have finished graphing, select the <strong>solution</strong> button to compare your work. </p>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here is an example:</p>
<p>There is no limit to the value of <span data-mathml="<math xmlns='http://www.w3.org/1998/Math/MathML'><mi>y</mi></math>" id="MathJax-Element-45-Frame" role="presentation" tabindex="0"><span id="MathJax-Span-261"><span id="MathJax-Span-262"><span id="MathJax-Span-263">𝑦</span></span></span></span>.</p>
</div>
</div>
<!--End interaction-->