1d6860c9-6536-4d6c-bb40-4034a218ec07.html

<h4>Lesson Narrative</h4>
<p>In earlier lessons, students saw that the quadratic formula can be used to solve any quadratic equation, but also
  that it might not be the most practical approach for all equations. Here, students deepen their understanding about
  the merits and potential drawbacks of using the quadratic formula. They pay close attention to each step in the
  solving process and analyze errors commonly made when applying the formula. Students also consider how to verify that
  the solutions they obtained with the quadratic formula are correct.</p>
<p>In analyzing the solution process and checking their work and the work of others, students practice attending to
  precision and critiquing the reasoning of others.</p>
<p>Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate
  technology to solve problems. Consider making technology available.</p>
<h4>Learning Goals (Teacher Facing)</h4>
<ul class="os-raise-noindent">
  <li> Analyze and critique (orally and in writing) solutions to quadratic equations that are found using the quadratic
    formula. </li>
  <li> Determine whether a given value is a solution to a quadratic equation. </li>
</ul>
<h4>Learning Targets (Student Facing)</h4>
<ul class="os-raise-noindent">
  <li> Identify common errors when using the quadratic formula. </li>
  <li> Describe some ways to tell if a number is a solution to a quadratic equation. </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(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or
        strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the
        reasonableness of the solution
      </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>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas
      </td>
      <td>Math process coverage: Lesson provides content that supports this TEKS.
      </td>
    </tr>
    <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>A8(A) <u>solve quadratic equations having real solutions by</u> factoring, taking square roots, completing the
        square, and <u>applying the quadratic formula</u>
      </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</h4>
<p>Here are the instructional activities for the lesson:</p>
<ul class="os-raise-noindent">
  <li> 9.7.1: Evaluating Variable Expressions </li>
  <li> 9.7.2: Common Calculation Errors When Using the Quadratic Formula </li>
  <ul class="os-raise-noindent">
    <li> 9.7.2: Self Check </li>
    <li> 9.7.2: Additional Resources </li>
  </ul>
  <li> 9.7.3: Different Methods of Checking Solutions of Quadratic Equations </li>
  <ul class="os-raise-noindent">
    <li> 9.7.3: Self Check </li>
    <li> 9.7.3: Additional Resources </li>
  </ul>
  <li> 9.7.4: Practice Spotting Calculation Errors </li>
</ul>
<p>Students will also complete a series of problems in the 9.7.5: Practice.</p>
<h4>Required Materials</h4>
<ul class="os-raise-noindent">
  <li> Scientific calculators </li>
</ul>
<h4>Required Preparation</h4>
<p>Be prepared to display a graph for all to see in the activity synthesis of "Different Methods of Checking Solutions
  of Quadratic Equations" There is an image to display if graphing technology is not available.</p>
<h4>Lesson Vocabulary</h4>
<p>During this lesson, it is important to:</p>
<ul class="os-raise-noindent">
  <li> Familiarize students with the vocabulary words they will see throughout the lesson. </li>
  <li> Encourage students to look for these words and notice their use and meanings. </li>
  <li> Encourage students to use key vocabulary words in "math talk" 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> maximum </li>
          <li> quadratic equation </li>
          <li> quadratic formula </li>
          <li> zero (of a function) </li>
        </ul>
      </td>
      <td>
        <ul>
          <li> none </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/881784766/raise-unit-9-spn-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 9 Spanish Vocabulary</a></li>
  <li><a href="https://quizlet.com/881567564/raise-unit-9-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 9 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(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 2(I) demonstrate listening comprehension of increasingly complex spoken English by following directions,
    retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking
    notes commensurate with content and grade-level needs
  </li>
  <li>ELPS 3(E) share information in cooperative learning interactions
  </li>
  <li>ELPS 3(G) express opinions, ideas, and feelings ranging from communicating single words and short phrases to
    participating in extended discussions on a variety of social and grade-appropriate academic topics
  </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>intellectual
    humility</strong>.</p>
<p>Here are some tips to try during this lesson:</p>
<ul class="os-raise-noindent">
  <li> <a href="https://characterlab.org/tips-of-the-week/see-whats-possible/" target="_blank">See What's Possible</a>
  </li>
  <li> <a href="https://characterlab.org/tips-of-the-week/career-paths/" target="_blank">Career Paths</a> </li>
</ul>
<p>You can find other tips located here in the<a href="https://characterlab.org/playbooks/intellectual-humility/"
    target="_blank"> Playbook on Intellectual Humility</a> from Character Lab.</p>