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<h4>Lesson Narrative</h4>
<p>This lesson has two key aims. The first aim is to familiarize students with the structure of perfect-square
  expressions. Students analyze various examples of perfect squares. They apply the distributive property repeatedly to
  expand perfect-square expressions given in factored form. The repeated reasoning allows them to generalize expressions
  of the form \((x+n)^2\) as equivalent to \(x^2+2nx+n^2\). (Note, students were first introduced to perfect square
  trinomials in Unit 6.)</p>
<p>The second aim is to help students see that perfect squares can be handy for solving equations because we can find
  their square roots.</p>
<p>Achieving these aims prepares students to solve quadratic equations by completing the square in upcoming lessons.
  Knowing that quadratic equations can be much more easily solved when one side is a perfect square and the other side
  is a number motivates students to transform expressions into that form. Recognizing the structure of a perfect square
  equips students to look for features that are necessary to complete a square.</p>
<h4>Learning Goals (Teacher Facing)</h4>
<p>Students will be able to:</p>
<ul class="os-raise-noindent">
  <li> Comprehend that equations containing a perfect-square expression on both sides of the equal sign can be solved by
    finding square roots. </li>
  <li> Comprehend that perfect squares of the form \((x+n)^2\) are equivalent to \(x^2+2nx+n^2\). </li>
  <li> Use the structure of expressions to identify them as perfect squares. </li>
</ul>
<h4>Learning Targets (Student Facing)</h4>
<ul class="os-raise-noindent">
  <li> Recognize perfect-square expressions written in different forms. </li>
  <li> Recognize quadratic equations that have a perfect-square expression and solve the 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(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>A11(A) simplify numerical radical expressions involving square roots</td>
      <td>Full coverage: Lesson provides content that covers all parts of this TEKS.</td>
    </tr>
    <tr>
      <td>A8(A) <u>solve quadratic equations having real solutions by</u> factoring, <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> 9.1.1: Equations with Quadratic Expressions on Both Sides of the Equal Sign </li>
  <li> 9.1.2: Recognizing Structure in Perfect-Square Expressions </li>
  <ul class="os-raise-noindent">
    <li> 9.1.2: Self Check </li>
    <li> 9.1.2: Additional Resources </li>
  </ul>
  <li> 9.1.3: Solving Multi Step Quadratic Equations Using Perfect Squares </li>
  <ul class="os-raise-noindent">
    <li> 9.1.3: Self Check </li>
    <li> 9.1.3: Additional Resources </li>
  </ul>
  <li> 9.1.4: Explain Why an Expression Is a Perfect Square </li>
</ul>
<p>Students will also complete a series of problems in the 9.1.5: Practice.</p>
<h4>Required Materials</h4>
<ul class="os-raise-noindent">
  <li>None</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
        </td>
      <th scope="col">
        New Vocabulary
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>
        <ul>
          <li> distributive property </li>
          <li> perfect square </li>
          <li> quadratic equation </li>
          <li> square root property </li>
          <li> perfect square trinomial </li>
        </ul>
      </td>
      <td>
        <ul>
        </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(C) learn new language structures, expressions, and basic and academic vocabulary heard during classroom
    instruction and interactions
  </li>
  <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>
  <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(C) develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and
    language structures used routinely in written classroom materials
  </li>
  <li>ELPS 4(D) use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary
    and other prereading activities to enhance comprehension of written text
  </li>
  <li>ELPS 4(E) read linguistically accommodated content area material with a decreasing need for linguistic accommodations
    as more English is learned
  </li>
  <li>ELPS 4(F) use visual and contextual support and support from peers and teachers to read grade-appropriate content area
    text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background
    knowledge needed to comprehend increasingly challenging language
  </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>
  <li>ELPS 4(H) read silently with increasing ease and comprehension for longer periods
  </li>
  <li>ELPS 4(I) demonstrate English comprehension and expand reading skills by employing basic reading skills such as
    demonstrating understanding of supporting ideas and details in text and graphic sources, summarizing text, and
    distinguishing main ideas from details commensurate with content area needs
  </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 supporting text evidence commensurate with content area needs
  </li>
  <li>ELPS 4(K) demonstrate English comprehension and expand reading skills by employing analytical skills such as
    evaluating written information and performing critical analyses 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>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/judge-not/" target="_blank">Judge Not</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>