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<p>In this unit, students will:</p>
<ul>
<li>Add, subtract, multiply, and divide polynomials of degree one and degree two.</li>
<li>Rewrite polynomial expressions using the distributive property.</li>
<li>Factor trinomials in the form \(ax^2 + bx + c\), including perfect square trinomials of degree two, and factor binomials that are the difference of two squares.</li>
</ul>
<p>To accomplish these unit-level learning goals, students will complete the following lessons and activities.</p>
<h3>Student Readiness for Unit 6</h3>
<p>To be ready for this unit, students will need to be able to:</p>
<ul>
<li>Simplify expressions with exponents.</li>
<li>Simplify expressions using the Distributive Property.</li>
<li>Find the greatest common factor (GCF) of two or more numbers.</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" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/ESsxc_tpg64;&rel=0" title="YouTube video player"></iframe></div>
</div>
<br>
<br>
<div class="os-raise-accordion">
<h3>Section A: Operations with Polynomials</h3>
<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/KAMV4bFSPys;&rel=0" title="YouTube video player"></iframe></div>
</div>
</div>
</div>
<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>Add and Subtract Polynomials</p>
</td>
<td>
<p>A1(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication</p><br>
<p>A10(A) add and subtract polynomials of degree one and degree two</p><br>
<p>A12(B) evaluate functions, expressed in function notation, given one or more elements in their domains</p>
</td>
</tr>
<tr>
<td>
<p>Multiplying Polynomials</p>
</td>
<td>
<p>A1(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication</p><br>
<p>A10(B) multiply polynomials of degree one and degree two</p><br>
<p>A12(B) evaluate functions, expressed in function notation, given one or more elements in their domains</p>
</td>
</tr>
<tr>
<td>
<p>Dividing Polynomials</p>
</td>
<td>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p><br>
<p>A10(C) determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend</p>
</td>
</tr>
<tr>
<td>
<p>Unit 6, Section A Quiz</p>
</td>
<td>*This quiz focuses on material from this section. Access the Unit Quiz to assess all sections.</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="os-raise-accordion">
<h3>Section B: Factoring Polynomials</h3>
<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/mEapxjLR6XA;&rel=0" title="YouTube video player"></iframe></div>
</div>
</div>
</div>
<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>Greatest Common Factor and Factor by Grouping</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</p><br>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p><br>
<p>A10(D) rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property</p><br>
<p>A10(E) factor, if possible, trinomials with real factors in the form \(ax^2+bx+c\), including perfect square trinomials of degree two</p><br>
<p>A10(F) decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial</p>
</td>
</tr>
<tr>
<td>
<p>Factor Trinomials</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><br>
<p>A1(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate</p><br>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p><br>
<p>A10(E) factor, if possible, trinomials with real factors in the form \(ax^2 + bx + c\), including perfect square trinomials of degree two</p>
</td>
</tr>
<tr>
<td>
<p>Factor Special Products</p>
</td>
<td>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p><br>
<p>A10(E) factor, if possible, trinomials with real factors in the form \(ax^2+bx+c\), including perfect square trinomials of degree two</p><br>
<p>A10(F) decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial</p>
</td>
</tr>
<tr>
<td>
<p>General Strategy for Factoring Polynomials</p>
</td>
<td>
<p>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</p><br>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p><br>
<p>A1(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication</p><br>
<p>A10(D) rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property</p><br>
<p>A10(E) factor, if possible, trinomials with real factors in the form \(ax^2+bx+c\), including perfect square trinomials of degree two</p><br>
<p>A10(F) decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial</p>
</td>
</tr>
<tr>
<td>
<p>Unit 6, Section B Quiz</p>
</td>
<td>*This quiz focuses on material from this section. Access the Unit Quiz to assess all sections.</td>
<td></td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="os-raise-accordion">
<h3>Unit Resources</h3>
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Vertical Alignment for Unit 6</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;&rel=0" 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; web-share" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/ESsxc_tpg64;&rel=0" title="YouTube video player"></iframe></div>
</div>
</div>
</div>
<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> 2.1 Use the Language of Algebra </li>
<li> 2.2 Evaluate, Simplify, and Translate Expressions </li>
<li> 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality </li>
<li> 3.5 Solve Equations Using Integers; The Division Property of Equality </li>
<li> 4.7 Solve Equations with Fractions </li>
<li> 5.4 Solve Equations with Decimals </li>
<li> 6.5 Solve Proportions and their Applications </li>
<li> 7.3 Distributive Property </li>
<li> 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality </li>
<li> 8.2 Solve Equations Using the Division and Multiplication Properties of Equality </li>
<li> 8.3 Solve Equations with Variables and Constants on Both Sides </li>
<li> 8.4 Solve Equations with Fraction or Decimal Coefficients </li>
<li> 9.7 Solve a Formula for a Specific Variable </li>
</ul>
</div>
</div>
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Assessments</button>
<div class="os-raise-accordion-content">
<table class="os-raise-textheavytable">
<thead>
<tr>
<th scope="col">Unit Level Resources</th>
</tr>
</thead>
<tbody>
<tr>
<td>Unit 6 Inquiry Project</td>
</tr>
<tr>
<td>Unit 6 Project</td>
</tr>
<tr>
<td>Unit 6 STAAR Review
<p><a href="https://k12.openstax.org/contents/raise/resources/2009bd33e1a6acddca680adb4c9e1ea6606cce97" target="_blank">Access the answer and alignment guide</a></p>
</td>
</tr>
<tr>
<td>Unit 6 Quiz</td>
</tr>
<tr>
<td>Unit 6 Wrap Up</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>