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<h4> Lesson Narrative</h4>
<p>This lesson introduces a method for factoring trinomials of the form \(x^2 + bx + c\). By undoing FOIL, students can
reverse the process used to multiply binomials and find the factored form of the trinomials.</p>
<p>This lesson also introduces multiple ways to factor trinomials of the form \(ax^2 + bx + c\). The simplest way is to
factor out the GCF and determine what simplifies the form of the trinomial. If the form is still \(ax^2 + bx + c\),
then students may choose from trial and error and the “\(ac\)” method. The “\(ac\)” method
will work for any trinomial of the form \(ax^2 + bx + c\).</p>
<p>If a polynomial does not seem to fit the known forms for factoring, it may be possible to substitute the variable
\(u\) for an expression, thus simplifying the trinomial into a more recognizable form. The trinomial can then be
factored, and the original expression is then substituted back in for \(u\).</p>
<h4>Learning Goals (Teacher Facing)</h4>
<ul>
<li> Factor trinomials of the form \(x^2 + bx + c\) by undoing FOIL. </li>
<li> Factor trinomials of the form \(ax^2 + bx + c\) using trial and error to guess the binomial factors of the
factored form. </li>
<li> Factor trinomials of the form \(ax^2 + bx + c\) using the “\(ac\)” method to factor any trinomial.
</li>
<li> Factor trinomials that do not readily appear to be of the form \(ax^2 + bx + c\) by substituting \(u\)<em>
f</em>or a value before factoring. </li>
<li> Analyze a trinomial and determine their own way of factoring. </li>
</ul>
<h4>Learning Targets (Student Facing)</h4>
<ul>
<li> Factor trinomials of the form \(x^2 + bx + c\). </li>
<li> Factor trinomials of the form \(ax^2 + bx + c\) using trial and error. </li>
<li> Factor trinomials of the form \(ax^2 + bx + c\) using the “\(ac\)” method. </li>
<li> Factor trinomials using substitution. </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(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</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>A10(E) <u>factor, if possible, trinomials with real factors in the form \(\underline{ax^2 + bx + c}\)</u>, including
perfect square trinomials of degree two</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>
<li> 6.5.1: Undoing FOIL </li>
<li> 6.5.2: Factoring Trinomials with Leading Coefficients of 1</li>
<ul>
<li> 6.5.2: Self Check </li>
<li> 6.5.2: Additional Resources </li>
</ul>
<li> 6.5.3: Factoring Trinomials Using Trial and Error </li>
<ul>
<li> 6.5.3: Self Check </li>
<li> 6.5.3: Additional Resources </li>
</ul>
<li> 6.5.4: Factoring Trinomials Using the “\(ac\)” Method and Substitution </li>
<ul>
<li> 6.5.4: Self Check </li>
<li> 6.5.4: Additional Resources </li>
</ul>
<li> 6.5.5: Choosing Your Own Method to Factor Trinomials </li>
</ul>
<p>Students will also complete a series of problems in the 6.5.6: Practice.</p>
<h4>Required Materials</h4>
<ul>
<li>Paper and pencil </li>
</ul>
<h4> Required Preparation</h4>
<ul>
<li>None </li>
</ul>
<h4>Lesson Vocabulary</h4>
<p>During this lesson, it is important to:</p>
<ul>
<li> Familiarize students with the vocabulary words they will see throughout the lesson. 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 include:</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> binomial </li>
<li> trinomial </li>
<li> polynomial </li>
<li> factoring </li>
<li> greatest common factor (GCF) </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/881785388/raise-unit-6-spn-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 6 Spanish Vocabulary</a></li>
<li><a href="https://quizlet.com/881535297/raise-unit-6-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 6 Vocabulary</a></li>
</ul>
<h4>Support for English Language Learners</h4>
<br />
<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(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>
<h4>Support for Building Character</h4>
<p>Throughout this unit, find ways to encourage and support students to work on cultivating their
<strong>judgment</strong>.</p>
<p>Here are some tips to try during this lesson:</p>
<ul>
<li> <a href="https://characterlab.org/tips-of-the-week/fundamental-beliefs/" target="_blank">Fundamental Beliefs</a>
</li>
<li> <a href="https://characterlab.org/tips-of-the-week/reserve-judgment/" target="_blank">Reserve Judgment</a> </li>
</ul>
<p>You can find other tips located here in the <a href="https://characterlab.org/playbooks/judgment/"
target="_blank">Playbook on Judgment</a> from Character Lab.</p>