288630e1-538b-4433-b67b-216d1b9be95a.html

<h3>Lesson Narrative</h3>
<p>This lesson reinforces the concept of the solution of a system of two linear equations. Students are also asked to write systems of equations from a table of values and connect that to a graph of a system of equations using technology.</p>
<p>Students then write the systems of equations from a graph and solve the system using the graph. In the cool down, students will explore how a system of equations represents a real world problem.</p>
<p>Making internet-enabled devices available gives students an opportunity to choose appropriate tools strategically.</p>
<h4>Learning Goals (Teacher Facing)</h4>
<p>Students will be able to:&nbsp;</p>
<ul>
  <li> Write a system of equations from a table of values, a graph, and a verbal description. </li>
  <li> Graph systems of equations by hand and determine solutions. </li>
  <li> Estimate solutions to real-world problems by graphing systems of equations. </li>
</ul>
<h4>Learning Targets (Student Facing)</h4>
<ul>
  <li> Write a system of equations. </li>
  <li> Graph systems of equations by hand. </li>
  <li> Estimate real-world solutions by graphing systems of equations. </li>
</ul>
<table class="os-raise-textheavytable">
  <caption>
  Texas Essential Knowledge and Skills (TEKS)
  </caption>
  <thead>
    <tr>
      <th scope="col">TEKS</th>
      <th scope="col">Explanation of Coverage</th>
    </tr>
  </thead>
  <tbody>
                  <tr>
          <td>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</td>
          <td>Math process coverage: Lesson provides content that supports this TEKS.</td>
      </tr>
            <tr>
          <td>A1(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques including mental math, estimation, and number sense as appropriate, to solve problems</td>
          <td>Math process coverage: Lesson provides content that supports this TEKS.</td>
      </tr>
      <tr>
          <td>A2(I) write systems of two linear equations given a table of values, a graph, and a verbal description</td>
          <td>Full coverage: Lesson provides content that covers all parts of this TEKS.</td>
      </tr>
    <tr>
      <td>A3(F) graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist
      </td>
      <td> Full coverage: Lesson provides content that covers all parts of this TEKS.</td>
    </tr>
      <tr>
      <td>A3(G) estimate graphically the solutions to systems of two linear equations with two variables in real-world problems</td>
          <td>Full coverage: Lesson provides content that covers all parts of this TEKS.
</td>
      </tr>
  </tbody>
</table>
<br>
<h4>Lesson Activities</h4>
<p>Here are the instructional activities for the lesson:</p>
<ul>
  <li> 2.2.1: Interpreting Graphs of Systems of Equations </li>
  <li> 2.2.2: Writing Systems of Equations from Tables </li>
  <ul>
    <li> 2.2.2: Self Check </li>
    <li> 2.2.2: Additional Resources </li>
  </ul>
  <li> 2.2.3: Graphs of Systems of Equations </li>
  <ul>
    <li> 2.2.3: Self Check </li>
    <li> 2.2.3: Additional Resources </li>
  </ul>
  <li> 2.2.4: Systems of Equations in the Real-World </li>
</ul>
<p>Students will also complete a series of problems in the 2.2.5: Practice.</p>
<h4>Required Materials</h4>
<p>Graph paper</p>
<h4>Required Preparation</h4>
<p>None</p>
<h4>Lesson Vocabulary</h4>
<p>During this lesson, it is important to:</p>
<ul>
  <li> Familiarize students with the vocabulary words they will see throughout the lesson. Encourage students to look for these words and notice their use and meanings. </li>
  <li> Encourage students to use key vocabulary words in &ldquo;math talk&rdquo; and their written and oral explanations. </li>
  <li> Utilize a word wall. Sample cards are located here: <a href="https://k12.openstax.org/contents/raise/resources/8ed3aa68763498713b44d3c2e537ffe61b4755f0" target="_blank">Mathematics Vocabulary Word Wall Cards</a>. </li>
</ul>
<p>Vocabulary words that are emphasized in this lesson:</p>
<table class="os-raise-textheavytable">
  <thead>
    <tr>
      <th scope="col">Previous Vocabulary</th>
      <th scope="col">New Vocabulary</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><ul>
          <li> slope </li>
          <li>\( y\)-intercept </li>
          <li> slope-intercept formula </li>
        </ul></td>
      <td><ul>
          <li> identities </li>
          <li> contradictions </li>
        </ul></td>
    </tr>
  </tbody>
</table>
<br>
<p>To support newcomers or students identified at the beginning level of language proficiency, share the following Quizlet links to help students gain an understanding of the academic vocabulary. Use the Spanish versions to anchor student understanding before bridging to the English versions. </p>
<ul>
  <li><a href="https://quizlet.com/881194743/raise-unit-2-spn-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 2 Spanish Vocabulary</a></li>
  <li><a href="https://quizlet.com/881145916/raise-unit-2-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 2 Vocabulary</a></li>
</ul>
  <h4>Support for English Language Learners</h4>
      <p>Throughout this lesson, activities are incorporated that align to the following ELPS. The suggested activities are only a sampling of the types of support and scaffolding that can extend the learning for English language learners. Continue to find additional opportunities as you build your own set of ELL learning routines.</p>
  <ul>
    <li> ELPS 2(A) distinguish sounds and intonation patterns of English with increasing ease </li>
    <li> ELPS 2(B) recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters </li>
    <li> ELPS 3(A) practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce English words in a manner that is increasingly comprehensible </li>
    <li> ELPS 4(A) learn relationships between sounds and letters of the English language and decode (sound out) words using a combination of skills such as recognizing sound-letter relationships and identifying cognates, affixes, roots, and base words </li>
    <li> ELPS 4(B) recognize directionality of English reading such as left to right and top to bottom </li>
    <li> ELPS 4(H) read silently with increasing ease and comprehension for longer periods </li>
    <li> ELPS 4(J) demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between ideas, drawing inferences and conclusions from text and graphic sources, and finding evidence supporting text evidence commensurate with content area needs </li>
    <li> ELPS 5(C) spell familiar English words with increasing accuracy, and employ English spelling patterns and rules with increasing accuracy as more English is acquired </li>
    <li> ELPS 5(D) edit writing for standard grammar and usage, including subject-verb agreement, pronoun agreement, and appropriate verb tenses commensurate with grade-level expectations as more English is acquired </li>
    <li> ELPS 5(E) employ increasingly complex grammatical structures in content area writing commensurate with grade-level expectations </li>
    <ul>
      <li> ELPS 5(Ei) using correct verbs, tenses, and pronouns/antecedents </li>
    </ul>
<br>
</ul>
<h4>Support for Building Character</h4>
<p>Throughout this unit, find ways to encourage and support students to work on cultivating their <strong>growth mindset.</strong></p>
<p>Here are some tips to try during this lesson:</p>
<ul>
  <li> <a href="https://characterlab.org/tips-of-the-week/cultivating-confidence/" target="_blank">Cultivating Confidence</a> </li>
  <li> <a href="https://characterlab.org/tips-of-the-week/can-i-or-cant-i/" target="_blank">Can I, or Can&rsquo;t I?</a> </li>
</ul>
<p>You can find other tips located here in the <a href="https://characterlab.org/playbooks/social-intelligence/" target="_blank">Playbook on Social Intelligence</a> from Character Lab.</p>