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<p>In this unit, students will:</p>
<ul>
<li> Simplify numeric and algebraic expressions using the laws of exponents and simplify numerical radical expressions involving square roots. </li>
<li> Interpret the meaning of the values of \(a\) and \(b\) in exponential functions of the form \(f(x)=ab^x\) in real-world problems and write exponential functions to describe problems arising from mathematical and real-world situations, including growth and decay. </li>
<li> Graph exponential functions that model growth and decay and identify key features. </li>
<li> Compare linear and exponential functions. </li>
</ul>
<p>To accomplish these unit-level learning goals, students will complete the following lessons and activities.</p>
<h3>Student Readiness for Unit 5</h3>
<p>To be ready for this unit, students will need to be able to:</p>
<ul>
<li> Write linear functions from a graph. </li>
<li> Interpret linear functions. </li>
<li> Evaluate exponential expressions. </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><br>
<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/wfvD0ro9qGM" title="YouTube video player"></iframe></div>
</div>
<br><br>
<div class="os-raise-accordion">
<h3>Section A: Looking at Growth and Decay</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/AdY2QKxeW_w" title="YouTube video player"></iframe></div>
</div>
</div>
</div>
<!-- Accordion 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">
<p>Lesson</p>
</th>
<th scope="col">
<p>Associated TEKS</p>
</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>Properties of Exponents</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>A11(B) simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents</p>
</td>
</tr>
<tr>
<td>
<p>Rational Exponents</p>
</td>
<td>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p><br>
<p>A11(B) simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents</p>
</td>
</tr>
<tr>
<td>
<p>Patterns of Growth</p>
</td>
<td>
<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>A9(C) write exponential functions in the form \(f(x)=ab^x\) (where \(b\) is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay</p>
</td>
</tr>
<tr>
<td>
<p>Representing Exponential Growth</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</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>A9(A) determine the domain and range of exponential functions of the form \(f(x)=ab^x\) and represent the domain and range using inequalities</p><br>
<p>A9(B) interpret the meaning of the values of \(a\) and \(b\) in exponential functions of the form \(f(x)=ab^x\) in real-world problems</p><br>
<p>A9(C) write exponential functions in the form \(f(x)=ab^x\) (where \(b\) is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay</p><br>
<p>A9(D) graph exponential functions that model growth and decay and identify key features, including \(y\)-intercept and asymptote, in mathematical and real-world problem</p>
</td>
</tr>
<tr>
<td>
<p>Representing Exponential Decay</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>A1(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication</p><br>
<p>A9(B) interpret the meaning of the values of \(a\) and \(b\) in exponential functions of the form \(f(x)=ab^x\) in real-world problems</p><br>
<p>A9(C) write exponential functions in the form \(f(x)=ab^x\) (where \(b\) is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay</p><br>
<p>A9(D) graph exponential functions that model growth and decay and identify key features, including \(y\)-intercept and asymptote, in mathematical and real-world problems</p>
</td>
</tr>
<tr>
<td>
<p>Negative Exponents and Scientific Notation</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</p>
<br>
<p>A1(E) create and use representations to organize, record, and communicate mathematical ideas</p>
<br>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p><br>
<p>A9(C) write exponential functions in the form \(f(x)=ab^x\) (where \(b\) is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay</p>
</td>
</tr>
<tr>
<td>
<p>Analyzing Graphs</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</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>A9(C) write exponential functions in the form \(f(x)=ab^x\) (where \(b\) is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay</p><br>
<p>A9(D) graph exponential functions that model growth and decay and identify key features, including \(y\)-intercept and asymptote, in mathematical and real-world problems</p>
</td>
</tr>
<tr>
<td>
<p>Unit 5, 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: Exponential Functions Overview</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/5O09qhN30_I" title="YouTube video player"></iframe></div>
</div>
</div>
</div>
<!-- Accordion 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">
<p>Lesson</p>
</th>
<th scope="col">
<p>Associated TEKS</p>
</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>Exponential Situations as Functions</p>
</td>
<td>
<p>A1(E) create and use representations to organize, record, and communicate mathematical ideas</p><br>
<p>A9(B) interpret the meaning of the values of \(a\) and \(b\) in exponential functions of the form \(f(x)=ab^x\) in real-world problems</p><br>
<p>A9(C) write exponential functions in the form \(f(x)=ab^x\) (where \(b\) is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay</p>
</td>
</tr>
<tr>
<td>
<p>Interpreting Exponential Functions</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>A9(A) determine the domain and range of exponential functions of the form \(f(x)=ab^x\) and represent the domain and range using inequalities</p><br>
<p>A9(B) interpret the meaning of the values of \(a\) and \(b\) in exponential functions of the form \(f(x)=ab^x\) in real-world problems</p><br>
<p>A9(D) graph exponential functions that model growth and decay and identify key features, including \(y\)-intercept and asymptote, in mathematical and real-world problems</p><br>
<p>A9(E) write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems</p>
</td>
</tr>
<tr>
<td>
<p>Looking at Rates of Change</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</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(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication</p><br>
<p>A3(B) calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems</p><br>
<p>A9(C) write exponential functions in the form \(f(x)=ab^x\) (where \(b\) is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay</p><br>
<p>A9(E) write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems</p>
</td>
</tr>
<tr>
<td>
<p>Modeling Exponential Behavior</p>
</td>
<td>
<p>A2(B) write linear equations in two variables in various forms,including \(y = mx + b, Ax + By = C\), and \(y -y_1= m (x -x_1 )\), given one point and the slope and given two points</p><br>
<p>A2(D) write and solve equations involving direct variation</p><br>
<p>A2(E) write the equation of a line that contains a given point and is parallel to a given line</p><br>
<p>A2(F) write the equation of a line that contains a given point and is perpendicular to a given line</p><br>
<p>A9(C) write exponential functions in the form \(f(x)=ab^x\) (where \(b\) is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay</p><br>
<p>A9(E) write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems</p>
</td>
</tr>
<tr>
<td>
<p>Reasoning about Exponential Graphs (Part 1)</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(E) create and use representations to organize, record, and communicate mathematical ideas</p><br>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p><br>
<p>A3(E) determine the effects on the graph of the parent function \(f(x) = x\) when \(f(x)\) is replaced by \(af(x)\), \(f(x) + df(x - c)\),\( f(bx)\) for specific values of \(a\), \(b\),\(c\), and \(d\)</p><br>
<p>A9(C) write exponential functions in the form \(f(x)=ab^x\) (where \(b\) is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay</p><br>
<p>A9(D) graph exponential functions that model growth and decay and identify key features, including \(y\)-intercept and asymptote, in mathematical and real-world problems</p>
</td>
</tr>
<tr>
<td>
<p>Reasoning about Exponential Graphs (Part 2)</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</p><br>
<p>A9(B) interpret the meaning of the values of \(a\) and \(b\) in exponential functions of the form \(f(x)=ab^x\) in real-world problems</p><br>
<p>A9(C) write exponential functions in the form \(f(x)=ab^x\) (where \(b\) is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay</p><br>
<p>A9(D) graph exponential functions that model growth and decay and identify key features, including \(y\)-intercept and asymptote, in mathematical and real-world problems</p>
</td>
</tr>
<tr>
<td>
<p>Unit 5, Section B 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">
<h3>Section C: Comparing Linear and Exponential Functions</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/Aw292c1JT20" title="YouTube video player"></iframe></div>
</div>
</div>
</div>
<!-- Accordion 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">
<p>Lesson</p>
</th>
<th scope="col">
<p>Associated TEKS</p>
</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>Which One Changes Faster?</p>
</td>
<td>
<p>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</p><br>
<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(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(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>A3(B) calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems</p><br>
<p>A9(B) interpret the meaning of the values of \(a\) and \(b\) in exponential functions of the form \(f(x)=ab^x\) in real-world problems</p><br>
<p>A9(D) graph exponential functions that model growth and decay and identify key features, including \(y\)-intercept and asymptote, in mathematical and real-world problems</p>
</td>
</tr>
<tr>
<td>
<p>Changes over Equal Intervals</p>
</td>
<td>
<p>A1(E) create and use representations to organize, record, 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>A3(B) calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems</p><br>
<p>A9(B) interpret the meaning of the values of \(a\) and \(b\) in exponential functions of the form \(f(x)=ab^x\) in real-world problems</p>
</td>
</tr>
<tr>
<td>
<p>Unit 5, 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">
<h3>Unit Resources</h3>
<!-- Accordion for Vertical Alignment for Unit 5 -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Vertical Alignment for Unit 5</button>
<div class="os-raise-accordion-content">
<h3>Vertical Alignment for Unit 5</h3>
<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; web-share" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/KZ3h8Q8Es0k" title="YouTube video player"></iframe></div>
</div>
</div>
</div>
<!-- Accordion for Pre-Algebra Resources from OpenStax -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Pre-Algebra Resources from OpenStax</button>
<div class="os-raise-accordion-content">
<h3>Pre-Algebra Resources from OpenStax</h3>
<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>10.2 Use Multiplication Properties of Exponents</li>
<li>10.5 Integer Exponents and Scientific Notation</li>
</ul>
</div>
</div>
<!-- Accordion for Assessments -->
<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">
<p>Unit Level Resources</p>
</th>
</tr>
</thead>
<tbody>
<tr>
<td>Unit 5 Project</td>
</tr>
<tr>
<td>
<p>Unit 5 STAAR Review</p>
<p><a href="https://k12.openstax.org/contents/raise/resources/ae12d25d088dc91f1a6e129c4af58f982c3d23b8" target="_blank">Access the answer and alignment guide</a></p>
</td>
</tr>
<tr>
<td>
<p>Unit 5 Quiz</p>
</td>
</tr>
<tr>
<td>
<p>Unit 5 Wrap Up</p>
</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>