90504638-698e-4cf3-b39b-d4cd9f99c237.html

<h3>Lesson Narrative</h3>
<p>This is the first of three lessons that develop the idea of solving systems of linear equations in two variables by elimination.</p>
<p>Students warm up to the idea of adding equations visually. They examine a diagram of three hangers where the third hanger contains the combined contents of the first two hangers and all three hangers are balanced. Then, they analyze the result of adding two linear equations in standard form and notice that doing so eliminates one of the variables, enabling them to solve for the other variable and, consequently, to solve the system. In studying and testing a new strategy of adding equations and then offering their analyses, students construct viable arguments and critique the reasoning of others.</p>
<p>Next, students connect the solution they found using this method to the graphs of the equations in a system and the graph of the third equation (that results from adding or subtracting the original equations). They observe that the solution they found is the solution to the system and that the graph of the third equation intersects the other two graphs at the identical point: the intersection of the first two.</p>
<p>The foundational idea is that adding or subtracting equations in a system creates a new equation whose solutions coincide with those of the original system. Students begin using this insight to solve systems, but they are not yet expected to construct an argument as to why this approach works.</p>
<h4>Learning Goals (Teacher Facing)</h4>
<ul>
  <li>Recognize that adding or subtracting equations in a system creates a new equation with a solution that coincides with that of the original system, so the new equation can be used to solve the original system.</li>
  <li>Solve systems of equations by adding or subtracting the equations strategically to eliminate a variable.</li>
  <li>Use graphing technology to graph the sums and differences of the equations in a system and analyze and describe (orally and in writing) the behaviors of the graphs.</li>
</ul>
<h4>Learning Targets (Student Facing)</h4>
<ul>
  <li>Solve systems of equations by adding or subtracting them to eliminate a variable.</li>
  <li>Demonstrate that adding or subtracting equations in a system creates a new equation, where one of the solutions to this equation is the solution to the system.</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(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication </td>
      <td>Math process coverage: Lesson provides content that supports this TEKS. </td>
    </tr>
    <tr>
      <td>A5(C) solve systems of two linear equations with two variables for mathematical and 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>2.4.1: Combining Two True Equations</li>
  <li>2.4.2: Adding Equations
    <ul>
      <li>2.4.2: Self Check</li>
    </ul>
    <ul>
      <li>2.4.2: Additional Resources</li>
    </ul>
  </li>
  <li>2.4.3: Adding and Subtracting Systems of Equations and Using Their Graphs
    <ul>
      <li>2.4.3: Self Check</li>
    </ul>
    <ul>
      <li>2.4.3: Additional Resources</li>
    </ul>
  </li>
  <li>2.4.4: Determining the Best Method for Solving a System of Equations</li>
</ul>
<p>Students will also complete a series of problems in the 2.4.5: Practice.</p>
<h4>Required Materials</h4>
<ul>
  <li>Graphing technology</li>
</ul>
<h4>Required Preparation</h4>
<p>None</p>
<p>Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device.</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>
  <li>Vocabulary words that are emphasized in this lesson include:</li>
</ul>
<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>systems of equations</li>
          <li>solutions to a system of equations</li>
          <li>substitution</li>
        </ul></td>
      <td><ul>
          <li>elimination</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>
<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(D) speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency </li>
  <li>ELPS 3(E) share information in cooperative learning interactions </li>
  <li>ELPS 3(F) ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments </li>
  <li>ELPS 5(B) write using newly acquired basic vocabulary and content-based grade-level vocabulary </li>
</ul>
<br>
<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/we-can-do-it/" target="_blank">We Can Do It</a></li>
  <li><a href="https://characterlab.org/tips-of-the-week/the-stories-we-tell/" target="_blank">The Stories We Tell</a></li>
</ul>
<p>You can find other tips located here in the <a href="https://characterlab.org/playbooks/growth-mindset/" target="_blank">Playbook on Growth Mindset</a> from Character Lab.</p>