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<p>In this unit, students will:</p>
<ul>
<li>Solve quadratic equations by factoring and using the zero product property.</li>
<li>Write quadratic functions when given real solutions and graphs of their related equations.</li>
<li>Write quadratic functions using technology to find a reasonable fit to data.</li>
</ul>
<p>To accomplish these unit-level learning goals, students will complete the following lessons and activities.</p>
<h3>Student Readiness for Unit 8</h3>
<p>To be ready for this unit, students will need to be able to:</p>
<ul>
<li>Write equivalent expressions using the distributive property.</li>
<li>Find the \(x\)-intercepts of the graph of a quadratic equation given in factored form.</li>
<li>Match quadratic graphs and their functions.</li>
</ul>
<p>This Unit Overview Video will provide a big picture look at the content found in this unit as well as the prerequisite skills that students need for accessing the content in the unit.</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/kYvnFYB_TSk?si=LD6nN4GfwjlGwSIE" title="YouTube video player"></iframe></div>
</div>
<br><br>
<!-- Accordion structure for different sections -->
<div class="os-raise-accordion">
<h3>Section A: Finding Unknown Inputs</h3>
<!-- Accordion for Section A Video Overview -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Overview Video</button>
<div class="os-raise-accordion-content">
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/-W3ZHHjVAYg" title="YouTube video player"></iframe></div>
</div>
</div>
</div>
<!-- Placeholder for Section A Standards Alignment Table -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Texas Essential Knowledge and Skills (TEKS)</button>
<div class="os-raise-accordion-content">
<table class="os-raise-textheavyadjustedtable">
<thead>
<tr>
<th scope="col">Lesson</th>
<th scope="col">Associated TEKS</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>Finding Unknown Inputs</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</p>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p>
<p>A8(A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.</p>
</td>
</tr>
<tr>
<td>
<p>When and Why Do We Write Quadratic Equations</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</p>
<p>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</p>
<p>A8(A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula</p>
</td>
</tr>
<tr>
<td>
<p>Unit 8, Section A Quiz </p>
</td>
<td>*This quiz focuses on material from this section. Access the Unit Quiz to assess all sections or the STAAR Review for a cumulative assessment.</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="os-raise-accordion">
<h3>Section B: Solving Quadratic Equations</h3>
<!-- Accordion for Section B Video Overview -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Overview Video</button>
<div class="os-raise-accordion-content">
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/oeXSaJ6WJOg" title="YouTube video player"></iframe></div>
</div>
</div>
</div>
<!-- Placeholder for Section B Standards Alignment Table -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Texas Essential Knowledge and Skills (TEKS)</button>
<div class="os-raise-accordion-content">
<table class="os-raise-textheavyadjustedtable">
<thead>
<tr>
<th scope="col">Lesson</th>
<th scope="col">Associated TEKS</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>Solving Quadratic Equations by Reasoning</p>
</td>
<td>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p>
<p>A8(A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula</p>
</td>
</tr>
<tr>
<td>
<p>Solving Quadratic Equations with the Zero Product Property</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</p>
<p>A8(A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula</p>
</td>
</tr>
<tr>
<td>
<p>How Many Solutions?</p>
</td>
<td>
<p>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</p>
<p>A1(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate</p>
<p>A8(A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula</p>
</td>
</tr>
<tr>
<td>
<p>Rewriting Quadratic Expressions in Factored Form, Part 1</p>
</td>
<td>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p>
<p>A8(A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula</p>
</td>
</tr>
<tr>
<td>
<p>Rewriting Quadratic Expressions in Factored Form, Part 2</p>
</td>
<td>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p>
<p>A8(A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula</p>
</td>
</tr>
<tr>
<td>
<p>Rewriting Quadratic Expressions in Factored Form, Part 3</p>
</td>
<td>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p>
<p>A8(A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula</p>
</td>
</tr>
<tr>
<td>
<p>Solving Quadratic Equations by Using Factored Form</p>
</td>
<td>
<p>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</p>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p>
<p>A1(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication</p>
<p>A8(A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula</p>
</td>
</tr>
<tr>
<td>
<p>Rewriting Quadratic Expressions in Factored Form, Part 4</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</p>
<p>A8(A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula</p>
</td>
</tr>
<tr>
<td>
<p>Unit 8, Section B Quiz </p>
</td>
<td>*This quiz focuses on material from this section. Access the Unit Quiz to assess all sections or the STAAR Review for a cumulative assessment.</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="os-raise-accordion">
<h3>Section C: Working with Quadratic Equations and Graphs</h3>
<!-- Accordion for Section C Video Overview -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Overview Video</button>
<div class="os-raise-accordion-content">
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/9YtdJkqF_qs" title="YouTube video player"></iframe></div>
</div>
</div>
</div>
<!-- Placeholder for Section C Standards Alignment Table -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Texas Essential Knowledge and Skills (TEKS)</button>
<div class="os-raise-accordion-content">
<table class="os-raise-textheavyadjustedtable">
<thead>
<tr>
<th scope="col">Lesson</th>
<th scope="col">Associated TEKS</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>Writing Quadratic Equations Given Real Solutions</p>
</td>
<td>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p>
<p>A6(C) write quadratic functions when given real solutions and graphs of their related equations </p>
</td>
</tr>
<tr>
<td>
<p>Using Technology to Find the Quadratic Regression</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</p>
<p>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</p>
<p>A8(B) write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems</p>
</td>
</tr>
<tr>
<td>
<p>Unit 8, Section C Quiz</p>
</td>
<td>
<p>*This quiz focuses on material from this section. Access the Unit Quiz to assess all sections or the STAAR Review for a cumulative assessment.</p>
</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="os-raise-accordion">
<br>
<h3>Unit Resources</h3>
<!-- Accordion for Vertical Alignment for Unit 8 -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Vertical Alignment for Unit 8</button>
<div class="os-raise-accordion-content">
<p>What is vertical alignment? You may be familiar with aligning your math lesson to a set of standards. But what does TEA mean when they discuss the importance of vertical alignment? Vertical alignment documents the progression of learning from grade level to grade level.</p>
<p>Students learn many different sets of knowledge and skills related to mathematics that build upon each other. Understanding this progression of learning across the curriculum continuum provides teachers and administrators the ability to better support mathematical conceptual and skill-based development.</p>
<p>As a teacher, understanding the TEKS mathematical vertical alignment will help you better understand what your students have already mastered and how what you are teaching them will be critical for mastery in future learning opportunities.</p>
<p>For Algebra I teachers, we recommend using the Texas Education Agency’s <a href="https://k12.openstax.org/contents/raise/resources/c1d455b65dade9bf6cba34312c3742132cb76c48" target="_blank">TEKS Vertical Alignment Chart Grades 5 through Algebra 1 and Algebra 2</a>. To understand how to read and use the Vertical Alignment chart, watch this <a href="https://www.youtube.com/watch?v=I1xp5nd44Eg" target="_blank">introductory video</a>.</p>
<p>Watch this video walkthrough of using the vertical alignment to better understand your students’ readiness for learning new content in each unit of RAISE.</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/WYECWbO2_CU" title="YouTube video player" web-share></iframe></div>
</div>
</div>
</div>
<!-- Accordion for Pre-Algebra Resources from OpenStax for Unit 8 -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Pre-Algebra Resources from OpenStax</button>
<div class="os-raise-accordion-content">
<p>As you work with individual students and find gaps in their prior learning, one source that you can pull remedial or reinforcing content from is the <a href="https://openstax.org/details/books/prealgebra-2e" target="_blank">OpenStax Pre-Algebra</a> textbook. </p>
<ul>
<li>
5.7 Simplify and Use Square Roots
</li>
<li>
7.3 Distributive Property
</li>
<li>
10.3 Multiply Polynomials
</li>
</ul>
</div>
</div>
<!-- Placeholder for Unit Level Resources -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Assessments</button>
<div class="os-raise-accordion-content">
<table class="os-raise-textheavyadjustedtable">
<thead>
<tr>
<th scope="col">Unit Level Resources</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>Unit 8 Project</p>
</td>
</tr>
<tr>
<td>
<p>Unit 8 STAAR Review</p>
<p><a href="https://k12.openstax.org/contents/raise/resources/97b9eb6a38403427d0d89d299fd88a89880b378e" target="_blank">Access the answer and alignment guide</a></p>
</td>
</tr>
<tr>
<td>
<p>Unit 8 Quiz</p>
</td>
</tr>
<tr>
<td>
<p>Unit 8 Wrap Up</p>
</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>