00bd57a9-c35b-4f9d-91e1-7a913abeabe6.html

<h3>Lesson Narrative</h3>
<p>So far in the unit, students have primarily used descriptions, expressions, and equations to represent relationships
  and constraints. In this lesson, they revisit the idea that graphs can be a useful way to represent relationships.
  Students are reminded that each point on a graph is a solution to an equation the graph represents. They analyze
  points on and off a graph and interpret them in context. In explaining correspondences between equations, verbal
  descriptions, and graphs, students hone their skill at making sense of problems.</p>
<p>In this lesson, students are also introduced to the use of graphing technology to graph equations. This introduction
  could happen independently as long as it precedes the second activity in the lesson.</p>
  <br>
  <table class="os-raise-textheavytable">
    <caption>Learning Objectives</caption>
    <thead>
      <tr>
        <th scope="col">Learning Goals (Teacher Facing)</th>
        <th scope="col">Learning Targets (Student Facing)</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td>
<ul>
  <li><span>Comprehend that the graph of a linear equation in two variables represents all pairs of values that are
      solutions to the equation.</span><br></li>
  <li>Interpret points on a graph of a linear equation to answer questions about the quantities in context.</li>
  <li>Use graphing technology to graph linear equations and identify solutions to the equations.</li>
</ul>

        </td>
        <td>
<ul>
  <li>Use graphing technology to graph linear equations and identify solutions to the equations.</li>
  <li>Explain how the coordinates of the points on the graph of a linear equation are related to the equation.</li>
  <li>Explain the meaning of points on a graph in terms of the situation it represents when given the graph of a linear
    equation.</li>
</ul>

        </td>
      </tr>
    </tbody>
  </table>
<br>
<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>A1(D) communicate mathematical ideas, reasoning, and their implications using multiple representations,
        including symbols, diagrams, graphs, and language as appropriate
      </td>
      <td>Math process coverage: Lesson provides content that supports this TEKS.
      </td>
    </tr>
    <tr>
      <td>A2(C) <u>write linear equations in two variables given</u> a table of values, <u>a graph, and a verbal
          description</u>
      </td>
      <td>Partial coverage: Lesson provides content that covers part of this TEKS. The parts that are covered have been
        underlined.
      </td>
    </tr>
    <tr>
      <td>A3(C) <u>graph linear functions on the coordinate plane and identify key features, including
          \(x\)-intercept</u>, \(y\)-intercept, zeros, and slope, in mathematical and real-world problem
      </td>
      <td>Partial coverage: Lesson provides content that covers part of this TEKS. The parts that are covered have been
        underlined.
      </td>
    </tr>
  </tbody>
</table>
<br>
<h4>Lesson Activities<br></h4>
<ul>
  <li>1.5.1: Analyzing Graphs of Linear Equations</li>
  <li>1.5.2: Graphing Linear Functions in Two Variables
    <ul>
      <li>1.5.2: Self Check <br>
      </li>
      <li>1.5.2: Additional Resources </li>
    </ul>
  </li>
  <li>1.5.3: Examining an Equation in Two Variables and Its Graph, Part 1
    <ul>
      <li>1.5.3: Self Check <br></li>
      <li>1.5.3: Additional Resources <br></li>
    </ul>
  </li>
  <li>1.5.4: Writing, Graphing, and Solving a Linear Equation
    <ul>
      <li>1.5.4: Self Check <br></li>
      <li>1.5.4: Additional Resources</li>
    </ul>
  </li>
  <li>1.5.5: Examining an Equation in Two Variables and Its Graph, Part 2</li>
</ul>
<p>Students will also complete a series of problems in the 1.5.5: Practice.</p>
<h4>Required Materials</h4>
<ul>
  <li>Graphing technology</li>
</ul>
<h4>Required Preparation</h4>
<p>Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their
  own device.</p>
<div>
  <h4>Lesson Vocabulary</h4>
  <div>
    <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 include:</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>constraint&nbsp;</li>
              <li>equation</li>
              <li>expression</li>
              <li>model</li>
              <li>variable&nbsp;</li>
            </ul>
          </td>
          <td>
            <ul>
              <li>origin</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/879158409/raise-unit-1-spn-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 1 Spanish Vocabulary</a></li>
      <li><a href="https://quizlet.com/879586040/raise-unit-1-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 1 Vocabulary</a></li>
    </ul>
      <br>
    <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(F) listen to and derive meaning from a variety of media such as audiotape, video, DVD, and CD-ROM to build and reinforce concept and language attainment
      </li>
      <li>ELPS 3(E) share information in cooperative learning interactions
      </li>
      <li>ELPS 4(G) demonstrate comprehension of increasingly complex English by participating in shared reading, retelling, or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs
      </li>
    </ul>
      <br>
    <h4>Support for Building Character</h4>
    <div class="body">Throughout this unit, find ways to encourage and support students to work on cultivating their
      <strong>social intelligence</strong>. <br>&nbsp;<br>Here are some tips to try during this lesson:<br>
      <ul>
        <li><a href="https://characterlab.org/tips-of-the-week/more-than-meets-the-eye/" target="_blank">More Than Meets
            the Eye</a></li>
        <li><a href="https://characterlab.org/tips-of-the-week/heart/" target="_blank">Heart</a></li>
      </ul>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.<br>