Merge pull request #1776 from openstax/octoberpush3

october3push

html/01604439-3ddf-4454-8113-ea3a6f9119b7.html

@@ -9,7 +9,6 @@ <h4>Lesson Narrative</h4>
 <p>Rearranging parts of an equation strategically so that it can be solved requires students to make use of structure.
   Maintaining the equality of an equation while transforming it prompts students to attend to precision.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul class="os-raise-noindent">
   <li> Comprehend that to "complete the square" is to determine the value of \(c\) that will make the expression
     \(x^2+bx+c\) a perfect square. </li>

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@@ -3,7 +3,6 @@ <h4>Lesson Narrative</h4>
 <p>Students will write equations of lines given certain information. Students are familiar with identifying the slope and \(y\)-intercept from the equation of a line. In this lesson, they will write the equation of a line given the slope and \(y\)-intercept. It can be helpful to use graphs of the lines so students can see how the values of the slope and \(y\)-intercept affect the graph.</p>
 <p>Students will learn to use the point-slope form to write the equation of a line when given the slope and a point and when given two points. Students will use skills of manipulating equations as they substitute and solve. Encourage students to write out their steps and find ways to verify their answers, such as sharing with a partner or using a graphing utility or Desmos. </p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li>Choose a method to write the equation of a line based on the information given.<br>
   </li>

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@@ -4,7 +4,6 @@ <h3>Solutions to Inequalities in One Variable<br></h3>
 <p>Two optional activities are included in this lesson. The first is to give students an additional opportunity to make sense of the solutions to an inequality in terms of a situation. The second extension activity introduces them to graphing two-variable equations as a way to find solutions to one-variable inequalities.</p>
 <p>Later, students will use the understanding they build here to solve more sophisticated problems and to find solutions to linear inequalities in two variables.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li>Find the solution to a one-variable inequality by reasoning and by solving a related equation and testing values greater than and less than that solution.</li>
   <li>Graph the solution to an inequality as a ray on a number line and interpret the solution in context.</li>

html/02810ef2-2564-4a68-9d7c-38e3b9bd9c00/anilocam-a.html

@@ -4,7 +4,6 @@ <h3>Solutions to Inequalities in One Variable<br></h3>
 <p>Two optional activities are included in this lesson. The first is to give students an additional opportunity to make sense of the solutions to an inequality in terms of a situation. The second extension activity introduces them to graphing two-variable equations as a way to find solutions to one-variable inequalities.</p>
 <p>Later, students will use the understanding they build here to solve more sophisticated problems and to find solutions to linear inequalities in two variables.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li>Find the solution to a one-variable inequality by reasoning and by solving a related equation and testing values greater than and less than that solution.</li>
   <li>Graph the solution to an inequality as a ray on a number line and interpret the solution in context.</li>

html/02810ef2-2564-4a68-9d7c-38e3b9bd9c00/anilocam-b.html

@@ -4,7 +4,6 @@ <h3>Solutions to Inequalities in One Variable<br></h3>
 <p>Two optional activities are included in this lesson. The first is to give students an additional opportunity to make sense of the solutions to an inequality in terms of a situation. The second extension activity introduces them to graphing two-variable equations as a way to find solutions to one-variable inequalities.</p>
 <p>Later, students will use the understanding they build here to solve more sophisticated problems and to find solutions to linear inequalities in two variables.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li>Find the solution to a one-variable inequality by reasoning and by solving a related equation and testing values greater than and less than that solution.</li>
   <li>Graph the solution to an inequality as a ray on a number line and interpret the solution in context.</li>

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@@ -2,7 +2,6 @@ <h4>Lesson Narrative</h4>
 <p>This lesson introduces students to function notation. Students encounter situations in which referencing certain functions and their input-output pairs gets complicated, wordy, or unclear. This motivates a way to talk about functions that is more concise and precise.</p>
 <p>Students learn that function notation is a succinct way to name a function and to specify its input and output. They interpret function notation in terms of the quantities in a situation and use function notation to represent simple statements about a function. The work in this lesson prompts students to reason quantitatively and abstractly and communicate precisely.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li>Interpret statements that use function notation and explain (orally and in writing) their meaning in terms of a situation.</li>
   <li>Understand that function notation is a succinct way to name a function and specify its input and output.</li>

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@@ -6,7 +6,6 @@ <h4>Lesson Narrative</h4>
   see&mdash;without graphing and without necessarily completing the solving process&mdash;the number of solutions that
   the equations have.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul class="os-raise-noindent">
   <li> Recognize that the number of solutions to a quadratic equation can be revealed when the equation is written as
     <em>expression in factored form </em>\(=0\).</li>

html/0e01d382-c0c0-4cd8-bc4e-23acf7cf58dc.html

@@ -10,7 +10,6 @@ <h4>Lesson Narrative</h4>
 <p>One of the activities in this lesson works best when each student has access to devices that can run Desmos because
   students benefit from estimating the line of best fit in a dynamic way.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li>Fit a linear model to a scatter plot of data and informally judge its goodness of fit.</li>
   <li>Interpret (orally and in writing) the rate of change and vertical intercept for a linear model in everyday

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@@ -8,7 +8,6 @@ <h4> Lesson Narrative</h4>
   use a graph of the sequence to justify why it could be arithmetic. Throughout the lesson, students will work with and
   create different representations of functions.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li>
     Compare and contrast (orally and in writing) arithmetic and geometric sequences.

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@@ -1,7 +1,7 @@
 <h4>Activity (20 minutes)</h4>
 <p>Previously, students compared functions by analyzing their graphs on the same coordinate plane. Each
   graph was a continuous graph.</p>
-<p>The activities in this lesson are an extension of the TEKS expectations.</p>
+<p>This activity is an extension of the expectations in the TEKS.</p>
 <p>In this activity, students compare functions represented in separate graphs. Each graph is a
   discrete graph, showing the viewership of three TV shows as functions of the episode number. Students
   interpret features of the graphs and relate them to descriptions about the shows and to statements in

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@@ -9,7 +9,6 @@ <h4>Lesson Narrative</h4>
 <p>Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate
   technology to solve problems. Consider making technology available.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul class="os-raise-noindent">
   <li> Analyze and critique (orally and in writing) solutions to quadratic equations that are found using the quadratic
     formula. </li>

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@@ -1,6 +1,6 @@
 <h4>Activity</h4>
 
-<p>The activities in this lesson are an extension of the TEKS expectations.</p>
+<p>This activity is an extension of the expectations in the TEKS.</p>
 <p>Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.</p>
 <p>If your teacher gives you the data card:</p>
 <ol class="os-raise-noindent">

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@@ -11,7 +11,6 @@ <h4>Lesson Narrative</h4>
 <p>This lesson represents an extension from the TEKS listed and can be used as an enrichment to enhance the students’
   understanding of "linear functions that provide a reasonable fit to data" (A4.C).</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li>Calculate and plot the residuals for a given data set and use the information to determine the goodness of fit for
     a linear model.</li>

html/2a0a7e9e-7222-48ae-beab-48fc3fa2b86a.html

@@ -3,7 +3,6 @@ <h4>Lesson Narrative</h4>
 <p>In this and following lessons, students will often work with properties of exponents, a topic developed in grade 8. There is also an activity to emphasize the convention that \(a^0=1\) for a non-zero number \(a\).</p>
 <p>Technology isn&rsquo;t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li> Explain (in writing) how to see \(a\) and \(b\) on the graph of an equation of the form \(y=a\cdot b^x\). </li>
   <li> Interpret \(a\) and \(b\) given equations of the form \(y=a\cdot b^x\) and a context of exponential growth. </li>

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@@ -5,7 +5,6 @@ <h4>Lesson Narrative</h4>
 <p>There are different ways to derive the quadratic formula. The path chosen here involves temporarily replacing the \(kx\) in \((kx)^2+2(kx)m\) with a single letter, say \(Q\), so the expression for which we are completing the square is a monic quadratic expression: \(Q^2+2Qm\). An extension activity in the last lesson on completing the square includes this strategy. If desired, consider using it to familiarize students with the idea of using a temporary placeholder to reason with complicated expressions.</p>
 <p>In this lesson, students analyze and complete partially worked-out derivations of the quadratic formula, explaining each step along the way. As they do so, students practice constructing logical arguments.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul class="os-raise-noindent">
   <li> Explain (in writing) the steps used to derive the quadratic formula. </li>
   <li> Explain (orally and in writing) how the solutions obtained by completing the square are expressed by the quadratic formula. </li>

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@@ -3,7 +3,6 @@ <h4>Lesson Narrative</h4>
 <p>In earlier lessons, students have determined the \(x\)-coordinate of the vertex of a graph by determining the value exactly between the two \(x\)-intercepts. They have seen that the vertex of a graph that represents a quadratic function tells us the maximum or minimum value of the function. Because of this, we are often interested in identifying the vertex of a graph. In this lesson, students are introduced to quadratic expressions in vertex form and learn that this form allows us to easily see where the vertex of a graph is located.</p>
 <p>Students use technology to experiment with the parameters of expressions in vertex form, examine how they are visible on the graphs, and articulate their observations, all of which require attending to precision. They also consider how the connections between expressions and graphs here are like or unlike other connections they studied in earlier lessons.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul class="os-raise-noindent">
   <li> Comprehend quadratic expressions in "vertex form" by seeing the form as a constant plus a coefficient times a squared term. </li>
   <li> Coordinate (using words and other representations) the parameters of a quadratic expression in vertex form and the graph that represents it. </li>

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@@ -6,7 +6,6 @@ <h4>Lesson Narrative</h4>
   &minus; b)(a + b)\).</p>
 <p>Recognizing the patterns of these special products will allow for the easy factoring of these particular cases.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li> Recognize the patterns of perfect square trinomials and factor them into the form \((a + b)^2\) or \((a &minus;
     b)^2\). </li>

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@@ -3,7 +3,6 @@ <h4>Lesson Narrative</h4>
 <p>Students recall that the radical symbol \((\sqrt{\;\;})\) can be used to denote the positive square root of a number. Many quadratic equations have a positive and a negative solution, and up until this point, students have been writing them separately. For example, the solutions of \(x^2=49\) are \(x=7\) and \(x=-7\). Here, students are introduced to the plus-minus symbol \((\pm)\) as a way to express both solutions (for example, \(x= \pm 7\)).</p>
 <p>Students also briefly recall the meanings of rational and irrational numbers. (They will have a more thorough review later in the unit.) They see that sometimes the solutions are expressions that involve a rational number and an irrational number&mdash;for example, \(x=\pm \sqrt{8}+3\). While this is a compact, exact, and efficient way to express irrational solutions, it is not always easy to intuit the size of the solutions just by looking at the expressions. Students make sense of these solutions by finding their decimal approximations and by solving the equations by graphing. The work here gives students opportunities to reason quantitatively and abstractly.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul class="os-raise-noindent">
   <li> Coordinate and compare (orally and in writing) solutions to quadratic equations obtained by completing the square and those obtained by graphing. </li>
   <li> Explain that the "plus-minus" symbol is used to represent both square roots of a number and that the square root notation expresses only the positive square root. </li>

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@@ -15,7 +15,6 @@ <h4>Lesson Narrative</h4>
 <p>The terms "standard form" and "factored form" are not yet used and will be introduced in an upcoming lesson, after
   students have had some experience working with the expressions.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li> Use area diagrams to reason about the product of two sums and to write equivalent expressions. </li>
   <li> Use the distributive property to write equivalent quadratic expressions. </li>

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@@ -10,7 +10,6 @@ <h4>Lesson Narrative</h4>
   appropriate tools to solve problems. Consider making technology available, in case it is requested.</p>
   <p>Activity 7.2.4 provides an opportunity for students to explain their work algebraically and written in complete sentences. Encourage all learners, especially EL students to use apostrophe s correctly, use contractions correctly, as well as other grammer rules. Provide feedback to students to extend their details in their writing and use appropriate sentence lengths, combining phrases as they acquire more English. </p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li> Comprehend that a &ldquo;quadratic relationship&rdquo; can be expressed with a squared term. </li>
   <li> Describe (orally and in writing) a pattern of change associated with a quadratic relationship. </li>

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@@ -2,7 +2,6 @@ <h4>Lesson Narrative</h4>
 <p>In this lesson, students continue to examine the ties between quadratic expressions in standard form and the graphs that represent them. The focus this time is on the coefficient of the linear term, the \(b\) in \(ax^2+bx+c\), and how changes to it affect the graph. Students are not expected to know how to modify given expressions to transform the graphs in certain ways, but they will notice that adding a linear term to the squared term translates the graph in both horizontal and vertical directions. This understanding will help students to conclude that writing an expression such as \(x^2+bx\) in factored form can help us reason about the graph.</p>
 <p>Students also practice writing expressions that produce particular graphs. To do so, students make use of the structure in quadratic expressions and what they learned about the connections between expressions and graphs.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li> Describe (orally and in writing) how the \(b\) in \(ax^2+bx+c\) affects the graph. </li>
   <li> Write quadratic expressions in standard and factored forms that match given graphs. </li>

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@@ -1,5 +1,5 @@
 <h3>Activity (15 minutes)</h3>
-<p>The activities in this lesson are an extension of the TEKS expectations.</p>
+<p>This activity is an extension of the expectations in the TEKS.</p>
 <p>This activity gives students another opportunity to represent the quantities in a situation with a table and a graph, identify key features of the graph, and interpret those features in terms of the situation.</p>
 <h4>Launch</h4>
 <p>The following are some videos that show the same clip of a ball being dropped, but played back at different speeds. Show one or more of the videos for all to see. Before showing the videos, ask students to think about what information or quantities to look for while watching the videos. You may choose to provide students with a <a href="https://k12.openstax.org/contents/raise/resources/7e35fe918911187fa5873fba0c9a4b85b9fd234e" target="_blank">hard copy</a> of the task. </p>

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@@ -2,7 +2,6 @@ <h4>Lesson Narrative</h4>
 <p>This lesson serves two goals. The first is to relate the work in the past couple of lessons on quadratic expressions back to the quadratic functions that represent situations. Now students have additional insights that enable them to show (algebraically) that two different expressions can define the same function.</p>
 <p>The second goal is to prompt students to notice connections between different forms of quadratic expressions and features of the graphs that represent the expressions. Students are asked to identify the \(x\)- and \(y\)-intercepts of graphs representing expressions in standard and factored form. They observe that some numbers in the expressions are related to the intercepts and hypothesize about the patterns they observe. This work sets the foundation for upcoming lessons, in which students look more closely at how the parameters of quadratic expressions are related to their graphs.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li> Coordinate (orally and in writing) a quadratic expression given in factored form and the intercepts of its graph. </li>
   <li> Interpret (orally and in writing) the meaning of \(x\)-intercepts and \(y\)-intercepts on a graph of a quadratic function that represents a context. </li>

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@@ -3,7 +3,6 @@ <h4>Lesson Narrative</h4>
 <p>Students also begin to connect statements in function notation to graphs of functions. They see each input-output pair of a function \(f\) as a point with coordinates \((x,f(x))\) when \(x\) is the input, and they use information in function notation to sketch a possible graph of a function.</p>
 <p>Students&rsquo; work with graphs is expected to be informal here. In a later lesson, students will focus on identifying features of graphs more formally.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li>Describe connections between statements that use function notation and a graph of the function.</li>
   <li>Practice interpreting statements that use function notation and explaining (orally and in writing) their meaning in terms of a situation.</li>

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@@ -10,7 +10,6 @@ <h3>Lesson Narrative</h3>
 <p>In the next lesson, students will revisit the idea that coordinate pairs that are on a graph of an equation in two
   variables are solutions to the equation.</p>
 <h4>Learning Goals (Teacher Facing)</h4>
-<p>Students will be able to:</p>
 <ul>
   <li>Explain (orally and in writing) the meaning of solutions to equations in one variable and two variables.</li>
   <li>Find solutions to equations in one variable and in two variables by reasoning about the relationships in context.