0927af67-5caa-4fcd-b571-dd93f9d10d22.html

<h4>Activity (20 minutes)</h4>
<p>This activity is designed to give students opportunities to use their understandings from this unit to perform mathematical modeling.</p>
<p>The trail mix context is familiar from the previous activity, but students are challenged to choose quantities, determine how to represent them, interpret and reason about them, and use the model they create to make choices. It also enables students to reflect on their model and revise it as needed.</p>
<p>Students are likely to want to use graphing technology, as the nutritional information involves decimals and the inequalities written would be inconvenient to graph by hand. This is an opportunity for students to choose tools strategically.</p>
<p>No time estimate is given here because the time would depend on decisions about the research students do and on the expectations for collaboration and presentation.</p>
<h4>Launch</h4>
<ol>
  <li>Arrange students in groups of 2-4. Provide access to Desmos or other graphing technology.</li>
  <li>Explain the expectations for researching nutritional values, for collaboration with group members, and for presentation of student work. (If each group is presenting one response, provide each group with tools for creating a visual display. If each student is presenting a response, give each student tools for creating a visual display.)</li>
</ol>
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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">Engagement: Develop Effort and Persistence</p>
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  <div class="os-raise-extrasupport-body">
      <p>Provide prompts, reminders, guides, rubrics, or checklists that focus on increasing the length of on-task orientation in the face of distractions. For each question, allot a specific amount of work time and display expectations. Display a countdown timer, along with a bulleted list of what teams or individuals are to produce to complete a given step. For instance, during question 1, display a 5 minute countdown timer and the list: "You're finished if you. . . (1) Have your two ingredients (2) Have the nutrition information ready."</p>
      <p class="os-raise-text-italicize">Supports accessibility for: Attention; Social-emotional skills</p>
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<h4>Student Activity</h4>
<p>It's time to design your own trail mix!</p>
<ol class="os-raise-noindent">
  <li>Choose two ingredients that you like to eat. (You can choose from the ingredients in the previous activity, or you can look up nutrition information for other ingredients.)</li>
  <li>Think about the constraints for your trail mix. What do you want to be true about its calories, protein, sugar, fat, or fiber?</li>
  <li>Write inequalities to represent your constraints. Then, graph the inequalities.<br>
    <br>
    <img alt="Blank coordinate plane with grid, origin O." class="img-fluid atto_image_button_text-bottom" height="270" src="https://k12.openstax.org/contents/raise/resources/04008b8056fd0131e83e7d1f4598ab1d60b92222" width="271"><br>
    <br>
  </li>
  <li>Is it possible to make a trail mix that meets all your constraints using your ingredients? If not, make changes to your constraints or your ingredients and record them here.<br>
  </li>
  <li>Write a possible combination of ingredients for your trail mix.</li>
</ol>
<div class="os-raise-usermessage-lightbulb">
  <p>Pause here so your teacher can review your work and give further instructions for displaying your work.</p>
</div>
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<p><strong>Answer:</strong></p>
<p>Answers may vary, but here is a sample of some equations that could be true for this situation.</p>
<ol class="os-raise-noindent">
  <li>Sunflower seeds and raisins</li>
  <li>The trail mix should have less than 300 calories and more than 5 grams of protein.</li>
  <li>Let x represent the amount of sunflower seeds in grams and y represent the amount of raisins in grams.
    <ul>
      <li>\(5.5x + 3y &lt; 300\)</li>
      <li>\(0.2x + 0.03y &gt; 5\)</li>
      <li><img alt="Two inequalities on a grid. Raisins in grams. Sunflower seeds in grams. &nbsp;" class="img-fluid atto_image_button_text-bottom" height="310" src="https://k12.openstax.org/contents/raise/resources/05774aaffad2159354ba04058bf404424cd36d0b" width="329"></li>
    </ul>
  </li>
  <li>Yes<br>
  </li>
  <li> 30 grams of sunflower seeds and 40 grams of raisins </li>
</ol>
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<h4>Activity Synthesis</h4>
<p>Allow enough time for students to present their trail mix recipes. Consider a gallery walk as a way for students to share their display and to ask and answer questions.</p>

<h4>Project Synthesis</h4>
<p>Select groups to share their visual displays. Encourage students to ask questions about the mathematical thinking or design approach that went into creating the display.</p>
<p><strong>Use the following questions to lead a class discussion.</strong></p>


<ul>
  <li>What constraints did every group use?</li>
  <li>How do the graphs of the various mixes compare?</li>
  <li>Did anyone have to revise or change their model in order to come up with a solution they could use?</li>
  <li>How did you use the graph to choose a recipe for your mix?</li>
</ul>
<ul>
</ul>
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<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"><!--Extra Support Name-->MLR7 Compare and Connect: Representing, Conversing</p>
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  <div class="os-raise-extrasupport-body"> 
    <!--Support Content--><p>Use this routine to prepare students for the whole-class discussion. At the appropriate time, invite groups to create a visual display of their work. Students should consider what types of details (annotations, notes, diagrams, arrows, etc.) to include on their displays that will help communicate their reasoning. Begin the whole-class discussion by selecting and arranging 2–4 displays for all to see. Give students 2–3 minutes of quiet think time to interpret the displays before inviting the authors to present their work.
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    <p class="os-raise-text-italicize"><!--Support Italics-->Design Principle(s): Optimize output; Cultivate conversation</p>
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