567f2b30-4427-43d7-90b8-1fe1d5937efe.html

<h3>Warm Up (5 minutes)</h3>
<p>The purpose of this warm up is to elicit the idea that looking at two graphs simultaneously can yield information about solutions that satisfy both constraints in a situation simultaneously, which will be useful when students solve systems of equations graphically in their Algebra 1 class. While students may notice and wonder many things about these images, intersection points and solutions are the important discussion points.</p>
<p>Through articulating things they notice and things they wonder about the point of intersection and what it means in the situation, students have an opportunity to attend to precision in the language they use to describe what they see. They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.</p>
<h4>Launch</h4>
<p>Display the graph for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students quiet thinking time, and then time to discuss the things they notice and wonder with their partner. Students can then work together to answer questions 3–6. Follow with a whole class discussion.</p>
<h4>Student Activity</h4>
<blockquote>
  <p>For questions 1–6, use the given graph and scenario:</p>
  <p><img src="https://k12.openstax.org/contents/raise/resources/035b6f8b53155d20a84c2a6e62831f0db3bac6bb" width="300"/></p>
  <p>A club is selling snacks at a track meet. Oranges cost $1 each and protein bars cost $4 each. They sell a total of 100 items, and collect $304.</p>
</blockquote>
<ol class="os-raise-noindent">
  <li>What do you notice?&nbsp;</li>
</ol>
<p><strong>Answer:</strong></p>
<p>Things students may notice:</p>
<ul>
  <li> There are two lines. </li>
  <li> It&rsquo;s about snacks. </li>
  <li> The lines intersect. </li>
  <li> The point of intersection is labeled \((32, 68)\). </li>
  <li> The sum of 32 and 68 is 100. </li>
</ul>
<ol class="os-raise-noindent" start="2">
<li>What do you wonder?</li>
</ol>
<p><strong>Answer:</strong></p>
<p>Things students may wonder:</p>
<ul>
  <li> What does each line mean? </li>
  <li> What does the point of intersection mean? </li>
  <li> Where can you see the information from the problem on the graph? </li>
</ul>
<ol class="os-raise-noindent" start="3">
<li>What is the approximate \(y\)–intercept of the green dashed line?</li>
</ol>
<p><strong>Answer:</strong> Answers may vary: 76</p>
<ol class="os-raise-noindent" start="4">
<li>What is the approximate slope of the green dashed line?</li>
</ol>
<p><strong>Answer:</strong> Answers may vary: \(-\frac14\)</p>
<ol class="os-raise-noindent" start="5">
<li>What is the approximate \(y\)-intercept of the orange solid line?
 </li>
</ol>
<p><strong>Answer:</strong> Answers may vary: 100</p>
<ol class="os-raise-noindent" start="6">
<li>What is the approximate slope of the orange solid line?</li>
</ol>
<p><strong>Answer:</strong> Answers may vary:  -1</p>
<h4>Activity Synthesis</h4>
<p>Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After all responses have been recorded without commentary or editing, ask students, &ldquo;Is there anything on this list that you are wondering about?&rdquo; Encourage students to respectfully disagree, ask for clarification, or point out contradicting information. If the meaning of the point of intersection does not come up during the conversation, ask students to discuss this idea.</p>
<p>Solicit a discussion asking students what the point of intersection means in the context of the problem. Consider the labels of the \(x\)- and \(y\)-axes. What do the lines mean in the context of the problem? Connect the lines and intersection to the possible ways that oranges and protein bars can be sold to make $304.</p>