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<h4>Lesson Narrative</h4>
<p>By now, students have seen how the parameters of a quadratic expression in standard form and in factored form relate to the graph representing the function. In the past few lessons, students worked with decontextualized quadratic functions. In this lesson, they transfer what they learned about the graphs to make sense of quadratic functions that model concrete contexts.</p>
<p>Students interpret equations and graphs of quadratic functions in terms of the situations they represent. They use their analyses to solve problems and to compare quadratic functions given in different representations. Along the way, they practice reasoning quantitatively and abstractly.</p>
<br>
<table class="os-raise-textheavytable">
<caption>Learning Objectives</caption>
<thead>
<tr>
<th scope="col">Learning Goals (Teacher Facing)</th>
<th scope="col">Learning Targets (Student Facing)</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<ul>
<li> Interpret (orally and in writing) the graph and equation representing a function in terms of the context. </li>
</ul>
</td>
<td>
<ul>
<li> Explain how a quadratic equation and its graph relate to a situation. </li>
</ul>
</tr>
</tbody>
</table>
<br>
<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(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>
A7(A) graph quadratic functions on the coordinate plane and <u>use the graph to identify key attributes, if possible, including \(x\)-intercept, \(y\)-intercept, zeros, maximum value, minimum values, vertex</u>, and the equation of the axis of symmetry
</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> 7.14.1: Evaluating Quadratic Functions in the Real World </li>
<li> 7.14.2: Interpreting a Functional Relationship Between Two Quantities </li>
<ul>
<li> 7.14.2: Self Check </li>
<li> 7.14.2: Additional Resources </li>
</ul>
<li> 7.14.3: Analyzing Functions Using Different Representations </li>
<ul>
<li> 7.14.3: Self Check </li>
<li> 7.14.3: Additional Resources </li>
</ul>
<li> 7.14.4: Using Quadratic Functions to Solve Problems </li>
<li> 7.14.5: Identifying Key Features of Graphed Functions </li>
</ul>
<p>Students will also complete a series of problems in 7.14.6: Practice.</p>
<h4>Required Materials</h4>
<ul>
<li> Graphing technology </li>
<li> Pre-printed cards, cut from copies of the <a href="https://k12.openstax.org/contents/raise/resources/96538e4d9bb2da16d08e86549f7a651b60ca3a91" target="_blank">blackline master</a> </li>
<li> Scientific calculators </li>
</ul>
<h4>Required Preparation</h4>
<p>Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device.</p>
<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:</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>\(y\)-intercept </li>
<li> vertex </li>
<li> quadratic function </li>
<li> maximum </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/881785225/raise-unit-7-spn-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 7 Spanish Vocabulary</a></li>
<li><a href="https://quizlet.com/881562770/raise-unit-7-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 7 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 1(F) use accessible language and learn new and essential language in the process</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 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(D) speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency</li>
<li>ELPS 3(E) share information in cooperative learning interactions
</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(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 5(B) write using newly acquired basic vocabulary and content-based grade-level vocabulary
</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>proactivity</strong>.</p>
<p>Here are some tips to try during this lesson:</p>
<ul>
<li> <a href="https://characterlab.org/tips-of-the-week/all-together-now/" target="_blank">All Together Now</a> </li>
<li> <a href="https://characterlab.org/tips-of-the-week/guided-mastery/" target="_blank">Guided Mastery</a> </li>
</ul>
<p>You can find other tips located here in the <a href="https://characterlab.org/playbooks/proactivity/" target="_blank">Playbook on Proactivity</a> from Character Lab.</p>