83061887-e58c-4b56-bd53-196af10fb8a5.html

<h4>Lesson Narrative</h4>
<p>In this lesson, students learn about the zero product property. They use it to reason about the solutions to
  quadratic equations that each have a quadratic expression in factored form on one side and 0 on the other side. They
  see that when an expression is a product of two or more factors and that product is 0, one of the factors must be 0.
  This fact enables us to find unknown values in the factored expression.</p>
<p>Students also continue to make connections to their earlier work on quadratic functions. They have seen that
  sometimes we want to find the input values of a function when the output is zero. They also learned that the factored
  form can help us identify the zeros of a quadratic function and the \(x\)-intercepts of its graph. They have not
  investigated how or why this form enables us to do so, however. Here, students make use of the structure of a
  quadratic expression in factored form and the zero product property to understand the connections between the numbers
  in the form and the \(x\)-intercepts of its graph.</p>
<h4>Learning Goals (Teacher Facing)</h4>
<ul class="os-raise-noindent">
  <li> Given quadratic equations where one side is a product of factors and the other is zero, find the solution(s) and
    explain (orally and in writing) why the solutions make the equation true. </li>
  <li> Explain (in written and spoken language) that the "zero product property" means that if the product of two
    numbers is 0, then one of the factors must also be 0. </li>
</ul>
<h4>Learning Targets (Student Facing)</h4>
<ul class="os-raise-noindent">
  <li> Explain the meaning of the "zero product property."</li>
  <li> Find solutions to quadratic equations when one side is a product of factors and the other side is zero. </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>
        A8(A) <u>solve quadratic equations having real solutions by factoring</u>, <u>taking square roots</u>, completing the
        square, and applying the quadratic formula.
      </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> 8.4.1: Introducing the Zero Product Property </li>
  <li> 8.4.2: Solving Equations of Increasing Complexity Using Reasoning </li>
  <ul class="os-raise-noindent">
    <li> 8.4.2: Self Check </li>
    <li> 8.4.2: Additional Resources </li>
  </ul>
  <li> 8.4.3: Applying the Zero Product Property to Solve a Real-World Projectile Problem </li>
  <ul class="os-raise-noindent">
    <li> 8.4.3: Self Check </li>
    <li> 8.4.3: Additional Resources </li>
  </ul>
  <li> 8.4.4: Solving Equations Using the Zero Product Property and Reasoning </li>
</ul>
<p>Students will also complete a series of problems in the 8.4.5: Practice.</p>
<h4>Required Materials</h4>
<ul class="os-raise-noindent">
  <li> Paper and pencil </li>
</ul>
<h4>Required Preparation</h4>
<ul class="os-raise-noindent">
  <li> None </li>
</ul>
<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 class="os-raise-noindent">
          <li> quadratic equation </li>
          <li> quadratic function </li>
          <li> factored form (of a quadratic expression) </li>
          <li> standard form (of a quadratic expression) </li>
          <li> variable </li>
          <li> zero of the function </li>
          <li> root </li>
        </ul>
      </td>
      <td>
        <ul>
          <li> zero product property </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/881785079/raise-unit-8-spn-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 8 Spanish Vocabulary</a></li>
  <li><a href="https://quizlet.com/881565975/raise-unit-8-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 8 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 3(B) expand and internalize initial English vocabulary by learning and using high-frequency English words
    necessary for identifying and describing people, places, and objects, by retelling simple stories and basic
    information represented or supported by pictures, and by learning and using routine language needed for classroom
    communication</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 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>
<p>Throughout this unit, find ways to encourage and support students to work on cultivating their
  <strong>curiosity</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/compound-interest/" target="_blank">Compound Interest</a>
  </li>
  <li> <a href="https://characterlab.org/tips-of-the-week/finding-flow/" target="_blank">Finding Flow</a> </li>
</ul>
<p>You can find other tips located here in the <a href="https://characterlab.org/playbooks/curiosity/"
    target="_blank">Playbook on Curiosity</a> from Character Lab.</p>