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<p>In this unit, students will:</p>
<ul>
<li>Decide whether relations define a function and evaluate functions expressed in function notation.</li>
<li>Graph linear functions on the coordinate plane and identify key features, identify transformations of the parent function \(f(x)=x\), and represent domain and range using inequalities for real-world situations.</li>
<li>Identify terms of arithmetic and geometric sequences and write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms.</li>
</ul>
<p>To accomplish these unit-level learning goals, students will complete the following lessons and activities.</p>
<h3>Student Readiness for Unit 4</h3>
<p>To be ready for this unit, students will need to be able to:</p>
<ul>
<li>Find the slope of the line that goes through two points on a graph.</li>
<li>Interpret the meaning of a situation from a graph.</li>
<li>Use a pattern to find the next term in a sequence.</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/mk5ZcsyyzYw;&rel=0" title="YouTube video player"></iframe></div>
</div>
<br>
<br>
<div class="os-raise-accordion">
<h3>Section A: Functions and Their Representations</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/RlXNDJfsnXs;&rel=0" 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) for Section A</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>Introduction to Functions</td>
<td>A1.1(A) Define, describe, and identify functions as linear or nonlinear.</td>
</tr>
<tr>
<td>Understanding Function Notation</td>
<td>A1.2(B) Interpret statements that use function notation in terms of a context.</td>
</tr>
<tr>
<td>Graphing Functions</td>
<td>A1.2(C) Analyze graphs of functions and determine the domain and range, intercepts, zeros, relative maxima and minima, and other characteristics.</td>
</tr>
<tr>
<td>Linear Functions and Their Graphs</td>
<td>A1.3(D) Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.</td>
</tr>
<tr>
<td>Evaluating Functions</td>
<td>A1.4(A) Evaluate functions for specific inputs given the formula of the function.</td>
</tr>
<tr>
<td>Application of Functions</td>
<td>A1.5(B) Apply the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.</td>
</tr>
<tr>
<td>Unit 4, Section A Quiz</td>
<td>*This quiz assesses the material covered in Section A. Prepare for comprehensive assessments in Unit 4 or the STAAR with additional review and practice.</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="os-raise-accordion">
<!-- Accordion for Section B -->
<h3>Section B: Analyzing and Creating Graphs of Functions</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/jRuvprQ0xC0;&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>Features of 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>A1(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication</p><br>
<p>A3(A) determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including \(y = mx + b, Ax + By = C\), and \(y -y_1= m (x -x_1 )\)</p><br>
<p>A3(C) graph linear functions on the coordinate plane and identify key features, including \(x\)-intercept, \(y\)-intercept, zeros, and slope, in mathematical and real-world problem</p><br>
<p>A7(A) graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including \(x\)-intercept, \(y\)-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry</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>Finding Slope</p>
</td>
<td>
<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> 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>
</td>
</tr>
<tr>
<td>
<p>Using Graphs to Find Average Rate of Change</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>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>
</td>
</tr>
<tr>
<td>
<p>Interpreting and Creating 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(E) create and use representations to organize, record, and communicate mathematical ideas</p><br>
<p>A3(C) graph linear functions on the coordinate plane and identify key features, including \(x\)-intercept, \(y\)-intercept, zeros, and slope, in mathematical and real-world problems</p><br>
<p>A7(A) graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including \(x\)-intercept, \(y\)-intercept, zeros, maximum, and minimum values</p>
</td>
</tr>
<tr>
<td>
<p>Comparing Graphs</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>A12(B) evaluate functions, expressed in function notation, given one or more elements in their domains</p>
</td>
</tr>
<tr>
<td>
<p>Graphing a Function Using Transformations</p>
</td>
<td>
<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>A2(C) write linear equations in two variables given a table of values, a graph, and a verbal description</p><br>
<p>A3(E) determine the effects on the graph of the parent function \(f(x) = x\) when \(f(x)\) is replaced by \(af(x)\), \(f(x) + d\), \(f(x - c)\), \(f(bx)\) for specific values of \(a\), \(b\),\(c\), and \(d\)</p>
</td>
</tr>
<tr>
<td>
<p>Unit 4, 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">
<!-- Accordion for Section C -->
<h3>Section C: A Closer Look at Inputs and Outputs</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/EH-tpD20Q3M;&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>Domain and Range (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(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>A1(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication</p><br>
<p>A2(A) determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities</p>
</td>
</tr>
<tr>
<td>
<p>Domain and Range (Part 2)</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(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication</p><br>
<p>A2(A) determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities</p>
</td>
</tr>
<tr>
<td>
<p>Unit 4, 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>Section D: Sequences</h3>
<!-- Accordion for Section D 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/Hw56wHm3oGo;&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>Sequences</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(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate</p><br>
<p>A12(C) identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes</p>
</td>
</tr>
<tr>
<td>
<p>Introducing Geometric Sequences</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>A12(C) identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes</p>
</td>
</tr>
<tr>
<td>
<p>Different Types of Sequences</p>
</td>
<td>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p><br>
<p>A12(C) identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes</p>
</td>
</tr>
<tr>
<td>
<p>Sequences Are Functions</p>
</td>
<td>
<p>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</p><br>
<p>A12(C) identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes;</p>
</td>
</tr>
<tr>
<td>
<p>The nth Term of an Arithmetic Sequence</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>A12(D) write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms</p>
</td>
</tr>
<tr>
<td>
<p>Unit 4, Section D 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 4 -->
<div class="os-raise-accordion-item">
<button class="os-raise-accordion-header">Vertical Alignment for Unit 4</button>
<div class="os-raise-accordion-content">
<h3>Vertical Alignment for Unit 4</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;&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/KOsF647uobs;&rel=0" title="YouTube video player"></iframe></div>
</div>
</div>
</div>
<!-- Accordion for Pre-Algebra Unit 4 -->
<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> 9.1 Use a Problem Solving Strategy </li>
</ul>
</div>
</div>
<!-- Accordion 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-textheavytable">
<thead>
<tr>
<th scope="col">
<p>Unit Level Resources</p>
</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>Unit 4 Inquiry Project</p>
</td>
</tr>
<tr>
<tr>
<td>
<p>Unit 4 Project</p>
</td>
</tr>
<tr>
<td>
<p>Unit 4 STAAR Review</p>
<p><a href="https://k12.openstax.org/contents/raise/resources/490105819df4c5c34ea21e7d1654d280dbbbe051" target="_blank">Access the answer and alignment guide</a></p>
</td>
</tr>
<tr>
<td>
<p>Unit 4 Quiz</p>
</td>
</tr>
<tr>
<td>
<p>Unit 4 Wrap Up</p>
</td>
</tr>
</tr>
</tbody>
</table>
</div>
</div>
</div>