Organization: Pearson Education
Product Name: Envision Algebra 1 Common Core
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Curriculum Standards:

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. - CCSS.Math.Practice.MP2.a
Identify the effect on the graph of replacing ??(????) by ??????(????????) + ??????????, ???????????? ??????????????(????????????????), ??????????????????(??????????????????????????????????????????), and ????????????????????????(?????????????????????????? + ????????????????????????????) for specific values of ?????????????????????????????? (both positive and negative); find the value of ???????????????????????????????? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. - CCSS.Math.Content.HSF-BF.B.3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. - CCSS.Math.Content.HSA-REI.B.3
Fit a linear function for a scatter plot that suggests a linear association. - CCSS.Math.Content.HSS-ID.B.6c
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?????????????????????????????????? – 2)/(???????????????????????????????????? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?????????????????????????????????????? – 1)(???????????????????????????????????????? + 1), (?????????????????????????????????????????? – 1)(????????????????????????????????????????????² + ?????????????????????????????????????????????? + 1), and (???????????????????????????????????????????????? – 1)(??????????????????????????????????????????????????³ + ????????????????????????????????????????????????????² + ?????????????????????????????????????????????????????? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. - CCSS.Math.Practice.MP8.a
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. - CCSS.Math.Content.HSS-ID.B.6a
Informally assess the fit of a function by plotting and analyzing residuals. - CCSS.Math.Content.HSS-ID.B.6b
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. - CCSS.Math.Practice.MP4.a
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. - CCSS.Math.Content.HSF-LE.A.3
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. - CCSS.Math.Practice.MP6.a
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). - CCSS.Math.Content.HSF-LE.A.2
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. - CCSS.Math.Content.HSS-CP.A.4
Interpret complicated expressions by viewing one or more of their parts as a single entity. Example: For example, interpret ????????????????????????????????????????????????????????(1+??????????????????????????????????????????????????????????)n as the product of ???????????????????????????????????????????????????????????? and a factor not depending on ??????????????????????????????????????????????????????????????. - CCSS.Math.Content.HSA-SSE.A.1b
Interpret parts of an expression, such as terms, factors, and coefficients. - CCSS.Math.Content.HSA-SSE.A.1a
Understand that two events ???????????????????????????????????????????????????????????????? and ?????????????????????????????????????????????????????????????????? are independent if the probability of ???????????????????????????????????????????????????????????????????? and ?????????????????????????????????????????????????????????????????????? occurring together is the product of their probabilities, and use this characterization to determine if they are independent. - CCSS.Math.Content.HSS-CP.A.2
Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. - CCSS.Math.Content.HSF-TF.B.7
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. - CCSS.Math.Content.HSF-IF.C.8a
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. - CCSS.Math.Content.HSA-REI.D.12
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. - CCSS.Math.Content.HSS-ID.B.5
Rewrite expressions involving radicals and rational exponents using the properties of exponents. - CCSS.Math.Content.HSN-RN.A.2
Explain why the ????????????????????????????????????????????????????????????????????????-coordinates of the points where the graphs of the equations ?????????????????????????????????????????????????????????????????????????? = ????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????) and ???????????????????????????????????????????????????????????????????????????????? = ??????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????) intersect are the solutions of the equation ??????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????) = ??????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????) and/or ??????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. - CCSS.Math.Content.HSA-REI.D.11
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). - CCSS.Math.Content.HSA-REI.D.10
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. - CCSS.Math.Content.HSN-RN.A.1
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. - CCSS.Math.Content.HSF-IF.C.9
Solve an equation of the form ??????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????) = ?????????????????????????????????????????????????????????????????????????????????????????????????????????? for a simple function ???????????????????????????????????????????????????????????????????????????????????????????????????????????? that has an inverse and write an expression for the inverse. Example: For example, ??????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????) =2 ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????³ or ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) = (????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????+1)/(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????–1) for ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? ? 1. - CCSS.Math.Content.HSF-BF.B.4a
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. - CCSS.Math.Content.HSF-LE.A.1a
Use the relation ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. - CCSS.Math.Content.HSN-CN.A.2
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. - CCSS.Math.Content.HSF-LE.A.1b
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: For example, the Fibonacci sequence is defined recursively by ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(0) = ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(1) = 1, ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????+1) = ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????((?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) + ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????-1) for ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? greater than or equal to 1. - CCSS.Math.Content.HSF-IF.A.3
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. - CCSS.Math.Content.HSF-IF.A.2
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? is a function and ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? is an element of its domain, then ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) denotes the output of ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? corresponding to the input ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. The graph of ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? is the graph of the equation ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? = ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????). - CCSS.Math.Content.HSF-IF.A.1
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. - CCSS.Math.Content.HSF-BF.A.2
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. - CCSS.Math.Practice.MP1.a
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. - CCSS.Math.Content.HSF-TF.C.9
Graph linear and quadratic functions and show intercepts, maxima, and minima. - CCSS.Math.Content.HSF-IF.C.7a
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. - CCSS.Math.Content.HSF-IF.C.7e
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: For example, rearrange Ohm’s law ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? = ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? to highlight resistance ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. - CCSS.Math.Content.HSA-CED.A.4
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. - CCSS.Math.Content.HSF-IF.C.7d
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² + 9???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? – ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. - CCSS.Math.Practice.MP7.a
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. - CCSS.Math.Content.HSA-CED.A.3
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. - CCSS.Math.Content.HSA-CED.A.2
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. - CCSS.Math.Content.HSF-IF.C.7c
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. - CCSS.Math.Content.HSA-REI.A.2
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. - CCSS.Math.Content.HSF-IF.C.7b
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. - CCSS.Math.Content.HSA-CED.A.1
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. - CCSS.Math.Content.HSA-REI.A.1
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. - CCSS.Math.Content.HSA-REI.C.6
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. - CCSS.Math.Content.HSA-REI.C.5
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. - CCSS.Math.Practice.MP3.a
Interpret the parameters in a linear or exponential function in terms of a context. - CCSS.Math.Content.HSF-LE.B.5
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. - CCSS.Math.Practice.MP5.a
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. - CCSS.Math.Content.HSG-CO.A.3
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: For example, find the points of intersection between the line ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? = –3???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and the circle ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² + ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² = 3. - CCSS.Math.Content.HSA-REI.C.7
Evaluate and compare strategies on the basis of expected values. Example: For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. - CCSS.Math.Content.HSS-MD.B.5b
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. - CCSS.Math.Content.HSF-TF.A.2
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. - CCSS.Math.Content.HSG-CO.C.9
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). - CCSS.Math.Content.HSG-GPE.B.5
Represent data with plots on the real number line (dot plots, histograms, and box plots). - CCSS.Math.Content.HSS-ID.A.1
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. - CCSS.Math.Content.HSS-ID.A.2
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). - CCSS.Math.Content.HSS-ID.A.3
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. - CCSS.Math.Content.HSA-APR.A.1
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. - CCSS.Math.Content.HSS-ID.C.7
Compute (using technology) and interpret the correlation coefficient of a linear fit. - CCSS.Math.Content.HSS-ID.C.8
Use the structure of an expression to identify ways to rewrite it. Example: For example, see ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????4 – ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????4 as (??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????²)² – (????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????²)², thus recognizing it as a difference of squares that can be factored as (??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² – ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????²)(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² + ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????²). - CCSS.Math.Content.HSA-SSE.A.2
Distinguish between correlation and causation. - CCSS.Math.Content.HSS-ID.C.9
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. - CCSS.Math.Content.HSN-RN.B.3
Factor a quadratic expression to reveal the zeros of the function it defines. - CCSS.Math.Content.HSA-SSE.B.3a
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. - CCSS.Math.Content.HSF-IF.B.6
Solve quadratic equations by inspection (e.g., for ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? ± ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? for real numbers ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. - CCSS.Math.Content.HSA-REI.B.4b
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: For example, if the function ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) gives the number of person-hours it takes to assemble ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? engines in a factory, then the positive integers would be an appropriate domain for the function. - CCSS.Math.Content.HSF-IF.B.5
Use the properties of exponents to transform expressions for exponential functions. Example: For example the expression 1.15 to the ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? power can be rewritten as ((1.15 to the 1/12 power) to the 12?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? power) is approximately equal to (1.012 to the 12???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? power) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. - CCSS.Math.Content.HSA-SSE.B.3c
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. - CCSS.Math.Content.HSF-IF.B.4
Use the method of completing the square to transform any quadratic equation in ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? into an equation of the form (???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? – ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)² = ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? that has the same solutions. Derive the quadratic formula from this form. - CCSS.Math.Content.HSA-REI.B.4a
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. - CCSS.Math.Content.HSA-SSE.B.3b
Compose functions. Example: For example, if ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) is the temperature in the atmosphere as a function of height, and ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) is the height of a weather balloon as a function of time, then ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????((?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)) is the temperature at the location of the weather balloon as a function of time. - CCSS.Math.Content.HSF-BF.A.1c
Define appropriate quantities for the purpose of descriptive modeling. - CCSS.Math.Content.HSN-Q.A.2
Combine standard function types using arithmetic operations. Example: For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. - CCSS.Math.Content.HSF-BF.A.1b
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. - CCSS.Math.Content.HSN-Q.A.1


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Title: enVision Algebra 1 Common Core 2018


         Interactive Student Edition: Realize Reader: Algebra 1

         Beginning-of-Year Assessment
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

         Solving Equations and Inequalities

            Interactive Student Edition: Realize Reader: Topic 1

            1-4: Ex 1: Rewrite Literal Equations & Try It!
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-2: Ex 1: Solve Linear Equations & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-1: Ex 3: Operations With Rational Numbers & Try It!
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            1-4: Virtual Nerd™: How Do You Solve a Formula for a Variable?
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-2: Virtual Nerd™: How Do You Solve a Two-Step Equation with Fractions by Multiplying Away the Fraction?
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-4: MathXL for School: Enrichment
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            Topic 1: Readiness Assessment
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            Topic 1: enVision STEM Project

               Topic 1: enVision STEM Video

            Operations on Real Numbers

               Interactive Student Edition: Realize Reader: Lesson 1-1
                 Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

               Explore

                  1-1: Critique & Explain
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

               Understand and Apply

                  1-1: Ex 1: Understand Sets and Subsets & Try It!
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Additional Example 1
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Ex 2: Compare and Order Real Numbers & Try It!
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Ex 3: Operations With Rational Numbers & Try It!
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Ex 4: Operations With Rational and Irrational Numbers & Try It!
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Additional Example 4 with Try Another One
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Concept Summary
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Do You Understand?
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Do You Know How?
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

               Practice and Problem-Solving

                  1-1: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: MathXL for School: Mixed Review
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

               Assess & Differentiate

                  1-1: Ex 2: Compare and Order Real Numbers & Try It!
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Ex 4: Operations With Rational and Irrational Numbers & Try It!
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Ex 1: Understand Sets and Subsets & Try It!
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Virtual Nerd™: What's an Irrational Number?
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: MathXL for School: Enrichment
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Lesson Quiz
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: MathXL for School: Additional Practice
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: MathXL for School: Enrichment
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-1: Virtual Nerd™: What's an Irrational Number?
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            Solving Linear Equations

               Interactive Student Edition: Realize Reader: Lesson 1-2
                 Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Explore

                  1-2: Model & Discuss
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

               Understand and Apply

                  1-2: Ex 1: Solve Linear Equations & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-2: Ex 2: Solve Consecutive Integer Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Ex 3: Use Linear Equations to Solve Mixture Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Additional Example 3 with Try Another One
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Ex 4: Use Linear Equations to Solve Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Ex 5: Solve Work and Time Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Additional Example 5
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Concept Summary
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Do You Understand?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Do You Know How?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Practice and Problem-Solving

                  1-2: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: MathXL for School: Mixed Review
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

               Assess & Differentiate

                  1-2: Ex 1: Solve Linear Equations & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-2: Ex 4: Use Linear Equations to Solve Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Ex 2: Solve Consecutive Integer Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Virtual Nerd™: How Do You Solve a Two-Step Equation with Fractions by Multiplying Away the Fraction?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-2: Ex 5: Solve Work and Time Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Virtual Nerd™: How Do You Solve a Word Problem Using an Equation With Variables on Both Sides?
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-3: Ex 4: Use Equations to Solve Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: MathXL for School: Enrichment
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: MathXL for School: Enrichment
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Lesson Quiz
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-2: MathXL for School: Additional Practice
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: MathXL for School: Enrichment
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-2: Virtual Nerd™: How Do You Solve a Two-Step Equation with Fractions by Multiplying Away the Fraction?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-2: Virtual Nerd™: How Do You Solve a Two-Step Equation?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            Solving Equations with Variables on Both Sides

               Interactive Student Edition: Realize Reader: Lesson 1-3
                 Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Explore

                  1-3: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Define appropriate quantities for the purpose of descriptive modeling. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

               Understand and Apply

                  1-3: Ex 1: Solving Equations With a Variable on Both Sides & Try It!
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-3: Additional Example 1B with Try Another One
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-3: Ex 2: Understand Equations With Infinitely Many and No Solutions & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Ex 3: Solve Mixture Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Ex 4: Use Equations to Solve Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Additional Example 4
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Concept Summary
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Do You Understand?
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Do You Know How?
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Practice and Problem-Solving

                  1-3: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: MathXL for School: Mixed Review
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Assess & Differentiate

                  1-3: Ex 1: Solving Equations With a Variable on Both Sides & Try It!
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

                  1-2: Ex 2: Solve Consecutive Integer Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-3: Virtual Nerd™: How Do You Solve a Word Problem Using an Equation With Variables on Both Sides?
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Ex 4: Use Equations to Solve Problems & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: MathXL for School: Enrichment
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Lesson Quiz
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-3: MathXL for School: Additional Practice
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: MathXL for School: Enrichment
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Virtual Nerd™: How Do You Solve an Equation with Variables on Both Sides and Grouping Symbols?
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Virtual Nerd™: How Do You Solve a Word Problem Using an Equation With Variables on Both Sides?
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            Literal Equations and Formulas

               Interactive Student Edition: Realize Reader: Lesson 1-4
                 Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

               Explore

                  1-4: Model & Discuss
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

               Understand and Apply

                  1-4: Ex 1: Rewrite Literal Equations & Try It!
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance  t. 

                  1-4: Additional Example 1
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: Ex 2: Use Literal Equations to Solve Problems & Try It!
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: Ex 3: Rewrite a Formula & Try It!
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: Additional Example 3A with Try Another One
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: Ex 4: Apply Formulas & Try It!
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: Concept Summary
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: Do You Understand?
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: Do You Know How?
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

               Practice and Problem-Solving

                  1-4: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: MathXL for School: Mixed Review
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Assess & Differentiate

                  1-4: Ex 1: Rewrite Literal Equations & Try It!
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: Virtual Nerd™: How Do You Solve a Formula for a Variable?
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: MathXL for School: Enrichment
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: Lesson Quiz
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: MathXL for School: Additional Practice
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: MathXL for School: Enrichment
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: Virtual Nerd™: What is a Literal Equation?
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

                  1-4: Virtual Nerd™: How Do You Solve a Formula for a Variable?
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            Solving Inequalities in One Variable

               Interactive Student Edition: Realize Reader: Lesson 1-5
                 Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

               Explore

                  1-5: Model & Discuss
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

               Understand and Apply

                  1-5: Ex 1: Solve Inequalities & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-5: Additional Example 1B
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-5: Ex 2: Solve an Inequality With Variables on Both Sides & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-5: Ex 3: Understand Inequalities With Infinitely Many or No Solutions & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-5: Ex 4: Use Inequalities to Solve Problems & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-5: Additional Example 4 with Try Another One
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-5: Concept Summary
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-5: Do You Understand?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-5: Do You Know How?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

               Practice and Problem-Solving

                  1-5: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-5: MathXL for School: Mixed Review
                    Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Assess & Differentiate

                  1-5: Ex 1: Solve Inequalities & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-5: Virtual Nerd™: How Do You Solve and Graph a Two-Step Inequality?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-5: MathXL for School: Enrichment
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-5: Lesson Quiz
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-5: MathXL for School: Additional Practice
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-5: MathXL for School: Enrichment
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-5: Virtual Nerd™: How Do You Solve and Graph a Two-Step Inequality?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-5: Virtual Nerd™: How Do You Solve a Word Problem By Writing an Inequality?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            Mathematical Modeling in 3 Acts: Collecting Cans

               Topic 1: Collecting Cans - Act 1 Video with Questions

               Topic 1: Collecting Cans - Act 2 Content

               Topic 1: Collecting Cans - Act 2 Questions

               Topic 1: Collecting Cans - Act 3 Video

               Topic 1: Collecting Cans - Act 3 Questions

            Compound Inequalities

               Interactive Student Edition: Realize Reader: Lesson 1-6
                 Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

               Explore

                  1-6: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Understand and Apply

                  1-6: Ex 1: Understand Compound Inequalities & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Ex 2: Solve a Compound Inequality Involving Or & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Additional Example 2
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Ex 3: Solve a Compound Inequality Involving And & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Ex 4: Solve Problems Involving Compound Inequalities & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Additional Example 4 with Try Another One
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Concept Summary
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Do You Understand?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Do You Know How?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

               Practice and Problem-Solving

                  1-6: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-6: MathXL for School: Mixed Review
                    Curriculum Standards: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Assess & Differentiate

                  1-6: Ex 1: Understand Compound Inequalities & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Virtual Nerd™: How Do You Solve an AND Compound Inequality and Graph It On a Number Line?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: MathXL for School: Enrichment
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Lesson Quiz
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: MathXL for School: Additional Practice
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-6: MathXL for School: Enrichment
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Virtual Nerd™: How Do You Solve an AND Compound Inequality and Graph It On a Number Line?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

                  1-6: Virtual Nerd™: How Do You Solve an OR Compound Inequality and Graph it on a Number Line?
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            Absolute Value Equations and Inequalities

               Interactive Student Edition: Realize Reader: Lesson 1-7
                 Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Explore

                  1-7: Model & Discuss
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

               Understand and Apply

                  1-7: Ex 1: Understand Absolute Value Equations & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Ex 2: Apply an Absolute Value Equation & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Ex 3: Understand Absolute Value Inequalities & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Additional Example 3A
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Ex 4: Write an Absolute Value Inequality & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

                  1-7: Additional Example 4 with Try Another One
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Concept Summary
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Do You Understand?
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Do You Know How?
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Practice and Problem-Solving

                  1-7: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: MathXL for School: Mixed Review
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

               Assess & Differentiate

                  1-7: Ex 3: Understand Absolute Value Inequalities & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Ex 1: Understand Absolute Value Equations & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Virtual Nerd™: How do you Figure Out if an Absolute Value Inequality is an AND or OR Compound Inequality?
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Ex 2: Apply an Absolute Value Equation & Try It!
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: MathXL for School: Enrichment
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Lesson Quiz
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: MathXL for School: Additional Practice
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: MathXL for School: Enrichment
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Virtual Nerd™: How do you Figure Out if an Absolute Value Inequality is an AND or OR Compound Inequality?
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-7: Virtual Nerd™: How Do You Solve a Word Problem Using an Absolute Value Inequality?
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            Topic 1: MathXL for School: Topic Review
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

            Topic 1: Performance Assessment Form A
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

            1-7: Ex 3: Understand Absolute Value Inequalities & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-2: Ex 2: Solve Consecutive Integer Problems & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-1: Ex 2: Compare and Order Real Numbers & Try It!
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            1-6: Ex 1: Understand Compound Inequalities & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-1: Ex 1: Understand Sets and Subsets & Try It!
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            1-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

            1-7: Ex 1: Understand Absolute Value Equations & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-5: Ex 1: Solve Inequalities & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-1: Ex 3: Operations With Rational Numbers & Try It!
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            1-2: Ex 1: Solve Linear Equations & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-4: Ex 1: Rewrite Literal Equations & Try It!
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-2: Ex 4: Use Linear Equations to Solve Problems & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-7: Virtual Nerd™: How do you Figure Out if an Absolute Value Inequality is an AND or OR Compound Inequality?
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-3: Virtual Nerd™: How Do You Solve a Word Problem Using an Equation With Variables on Both Sides?
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-6: Virtual Nerd™: How Do You Solve an AND Compound Inequality and Graph It On a Number Line?
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-7: Ex 2: Apply an Absolute Value Equation & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-5: Virtual Nerd™: How Do You Solve and Graph a Two-Step Inequality?
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-2: Virtual Nerd™: How Do You Solve a Two-Step Equation with Fractions by Multiplying Away the Fraction?
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-4: Virtual Nerd™: How Do You Solve a Formula for a Variable?
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-2: Ex 5: Solve Work and Time Problems & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-7: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-3: Ex 4: Use Equations to Solve Problems & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-6: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-7: MathXL for School: Enrichment
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-3: MathXL for School: Enrichment
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-6: MathXL for School: Enrichment
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-5: MathXL for School: Enrichment
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-4: MathXL for School: Enrichment
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-2: MathXL for School: Enrichment
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            Topic 1: Assessment Form A
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            1-7: Ex 3: Understand Absolute Value Inequalities & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-2: Ex 2: Solve Consecutive Integer Problems & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-1: Ex 2: Compare and Order Real Numbers & Try It!
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            1-6: Ex 1: Understand Compound Inequalities & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-1: Ex 1: Understand Sets and Subsets & Try It!
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            1-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

            1-7: Ex 1: Understand Absolute Value Equations & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-5: Ex 1: Solve Inequalities & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-1: Ex 3: Operations With Rational Numbers & Try It!
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            1-2: Ex 1: Solve Linear Equations & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-4: Ex 1: Rewrite Literal Equations & Try It!
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-2: Ex 4: Use Linear Equations to Solve Problems & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-7: Virtual Nerd™: How do you Figure Out if an Absolute Value Inequality is an AND or OR Compound Inequality?
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-3: Virtual Nerd™: How Do You Solve a Word Problem Using an Equation With Variables on Both Sides?
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-6: Virtual Nerd™: How Do You Solve an AND Compound Inequality and Graph It On a Number Line?
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-7: Ex 2: Apply an Absolute Value Equation & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-5: Virtual Nerd™: How Do You Solve and Graph a Two-Step Inequality?
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-2: Virtual Nerd™: How Do You Solve a Two-Step Equation with Fractions by Multiplying Away the Fraction?
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-4: Virtual Nerd™: How Do You Solve a Formula for a Variable?
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-2: Ex 5: Solve Work and Time Problems & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-7: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-3: Ex 4: Use Equations to Solve Problems & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-6: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-7: MathXL for School: Enrichment
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-3: MathXL for School: Enrichment
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            1-6: MathXL for School: Enrichment
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-5: MathXL for School: Enrichment
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-4: MathXL for School: Enrichment
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-2: MathXL for School: Enrichment
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            Topic 1: Assessment Form C
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

         Linear Equations

            Interactive Student Edition: Realize Reader: Topic 2

            1-4: Ex 1: Rewrite Literal Equations & Try It!
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-4: Virtual Nerd™: How Do You Solve a Formula for a Variable?
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-4: MathXL for School: Enrichment
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            2-4: Ex 1: Write an Equation of a Line Parallel to a Given Line & Try It!
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: Virtual Nerd™: How Do You Know if Two Lines Are Parallel?
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: MathXL for School: Enrichment
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            3-2: Ex 3: Analyze a Linear Function & Try It!
              Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-2: Virtual Nerd™: What is a Linear Function?
              Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            2-1: Ex 4: Interpret Slope and y-Intercept & Try It!
              Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-3: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-4: Ex 2: Understand the Slopes of Perpendicular Lines & Try It!
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: Virtual Nerd™: How Do You Know if Two Lines Are Perpendicular?
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            3-1: Ex 3: Classify Relations and Functions & Try It!
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: MathXL for School: Enrichment
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            Topic 2: Readiness Assessment
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Graph linear and quadratic functions and show intercepts, maxima, and minima. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            Topic 2: enVision STEM Project

               Topic 2: enVision STEM Video

            Slope-Intercept Form

               Interactive Student Edition: Realize Reader: Lesson 2-1
                 Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

               Explore

                  2-1: Model & Discuss
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Interpret parts of an expression, such as terms, factors, and coefficients. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 

               Understand and Apply

                  2-1: Ex 1: Graph a Linear Equation & Try It!
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-1: Ex 2: Write an Equation from a Graph & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: Additional Example 2A
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: Ex 3: Understand Slope-Intercept Form & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: Additional Example 3A with Try Another One
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: Ex 4: Interpret Slope and y-Intercept & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-1: Concept Summary
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-1: Do You Understand?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-1: Do You Know How?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

               Practice and Problem-Solving

                  2-1: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-1: MathXL for School: Mixed Review
                    Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

               Assess & Differentiate

                  2-1: Ex 3: Understand Slope-Intercept Form & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: Ex 1: Graph a Linear Equation & Try It!
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-3: Virtual Nerd™: How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  3-2: MathXL for School: Enrichment
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-1: Ex 4: Interpret Slope and y-Intercept & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-3: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-1: Ex 2: Write an Equation from a Graph & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: Virtual Nerd™: How Do You Write an Equation of a Line in Slope-Intercept Form if You Have a Graph?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: Lesson Quiz
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: MathXL for School: Additional Practice
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-1: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: Virtual Nerd™: How Do You Write an Equation of a Line in Slope-Intercept Form if You Have a Graph?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: Virtual Nerd™: How Do You Write the Equation of a Line in Slope-Intercept Form If You Have the Slope and the Y-Intercept?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            Point-Slope Form

               Interactive Student Edition: Realize Reader: Lesson 2-2
                 Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

               Explore

                  2-2: Critique & Explain
                    Curriculum Standards: Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Interpret parts of an expression, such as terms, factors, and coefficients. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 

               Understand and Apply

                  2-2: Ex 1: Understand Point-Slope Form of a Linear Equation & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Ex 2: Write an Equation in Point-Slope Form & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Additional Example 2A with Try Another One
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Ex 3: Sketch the Graph of a Linear Equation in Point-Slope Form & Try It!
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-2: Ex 4: Apply Linear Equations & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Additional Example 4A
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Concept Summary
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Do You Understand?
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Do You Know How?
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

               Practice and Problem-Solving

                  2-2: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: MathXL for School: Mixed Review
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Assess & Differentiate

                  2-1: Ex 1: Graph a Linear Equation & Try It!
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-3: Virtual Nerd™: How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  3-2: MathXL for School: Enrichment
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-2: Ex 2: Write an Equation in Point-Slope Form & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Virtual Nerd™: How do you write an equation of a line in point-slope form if you have the slope and one point?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Ex 1: Understand Point-Slope Form of a Linear Equation & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Lesson Quiz
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: MathXL for School: Additional Practice
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Virtual Nerd™: How do you write an equation of a line in point-slope form if you have the slope and one point?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-2: Virtual Nerd™: How do you write an equation of a line in point-slope form if you have two points?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            Standard Form

               Interactive Student Edition: Realize Reader: Lesson 2-3
                 Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

               Explore

                  2-3: Explore & Reason
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Interpret parts of an expression, such as terms, factors, and coefficients. 

               Understand and Apply

                  2-3: Ex 1: Understand Standard Form of a Linear Equation & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-3: Ex 2: Sketch the Graph of a Linear Equation in Standard Form & Try It!
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-3: Ex 3: Relate Standard Form to Horizontal and Vertical Lines & Try It!
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-3: Additional Example 3A with Try Another One
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-3: Ex 4: Use the Standard Form of a Linear Equation & Try It!
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-3: Additional Example 4A
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-3: Concept Summary
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-3: Do You Understand?
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-3: Do You Know How?
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

               Practice and Problem-Solving

                  2-3: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-3: MathXL for School: Mixed Review
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

               Assess & Differentiate

                  2-3: Ex 1: Understand Standard Form of a Linear Equation & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-3: Virtual Nerd™: How Do You Write an Equation of a Line in Standard Form from a Word Problem?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-1: Ex 1: Graph a Linear Equation & Try It!
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-3: Virtual Nerd™: How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  3-2: MathXL for School: Enrichment
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-3: Lesson Quiz
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-3: MathXL for School: Additional Practice
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-3: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

                  2-3: Virtual Nerd™: How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  2-3: Virtual Nerd™: How Do You Write an Equation of a Line in Standard Form from a Word Problem?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            Mathematical Modeling in 3 Acts: How Tall is Tall?

               Topic 2: How Tall is Tall? - Act 1 Video with Questions

               Topic 2: How Tall is Tall? - Act 2 Content

               Topic 2: How Tall is Tall? - Act 2 Questions

               Topic 2: How Tall is Tall? - Act 3 Video

               Topic 2: How Tall is Tall? - Act 3 Questions

            Parallel and Perpendicular Lines

               Interactive Student Edition: Realize Reader: Lesson 2-4
                 Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

               Explore

                  2-4: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 

               Understand and Apply

                  2-4: Ex 1: Write an Equation of a Line Parallel to a Given Line & Try It!
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Ex 2: Understand the Slopes of Perpendicular Lines & Try It!
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Ex 3: Write an Equation of a Line Perpendicular to a Given Line & Try It!
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Ex 4: Classify Lines & Try It!
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Additional Example 4A with Try Another One
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Ex 5: Solve a Real-World Problem & Try It!
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Additional Example 5A
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Concept Summary
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Do You Understand?
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Do You Know How?
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

               Practice and Problem-Solving

                  2-4: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-4: MathXL for School: Mixed Review
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

               Assess & Differentiate

                  2-4: Ex 1: Write an Equation of a Line Parallel to a Given Line & Try It!
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Virtual Nerd™: How Do You Know if Two Lines Are Parallel?
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: MathXL for School: Enrichment
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Ex 2: Understand the Slopes of Perpendicular Lines & Try It!
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Virtual Nerd™: How Do You Know if Two Lines Are Perpendicular?
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-4: Lesson Quiz
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-4: MathXL for School: Additional Practice
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  2-4: MathXL for School: Enrichment
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Virtual Nerd™: How Do You Know if Two Lines Are Parallel?
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

                  2-4: Virtual Nerd™: How Do You Know if Two Lines Are Perpendicular?
                    Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            Topic 2: MathXL for School: Topic Review
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            Topic 2: Performance Assessment Form A
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Graph linear and quadratic functions and show intercepts, maxima, and minima. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            2-1: Ex 1: Graph a Linear Equation & Try It!
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            2-3: Virtual Nerd™: How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            2-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            3-2: MathXL for School: Enrichment
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            2-3: Ex 1: Understand Standard Form of a Linear Equation & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-3: Virtual Nerd™: How Do You Write an Equation of a Line in Standard Form from a Word Problem?
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: Ex 2: Write an Equation in Point-Slope Form & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: Virtual Nerd™: How do you write an equation of a line in point-slope form if you have the slope and one point?
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-4: Ex 2: Understand the Slopes of Perpendicular Lines & Try It!
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: Virtual Nerd™: How Do You Know if Two Lines Are Perpendicular?
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-4: MathXL for School: Enrichment
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-1: Ex 4: Interpret Slope and y-Intercept & Try It!
              Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-3: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-4: Ex 1: Write an Equation of a Line Parallel to a Given Line & Try It!
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: Virtual Nerd™: How Do You Know if Two Lines Are Parallel?
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-2: Ex 1: Understand Point-Slope Form of a Linear Equation & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: Ex 3: Understand Slope-Intercept Form & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            Topic 2: Assessment Form A
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-1: Ex 4: Interpret Slope and y-Intercept & Try It!
              Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-3: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-2: Ex 1: Understand Point-Slope Form of a Linear Equation & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-4: Ex 2: Understand the Slopes of Perpendicular Lines & Try It!
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: Virtual Nerd™: How Do You Know if Two Lines Are Perpendicular?
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-4: MathXL for School: Enrichment
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-2: Ex 2: Write an Equation in Point-Slope Form & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: Virtual Nerd™: How do you write an equation of a line in point-slope form if you have the slope and one point?
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: Ex 1: Graph a Linear Equation & Try It!
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            2-3: Virtual Nerd™: How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            2-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            3-2: MathXL for School: Enrichment
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            2-3: Ex 1: Understand Standard Form of a Linear Equation & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-3: Virtual Nerd™: How Do You Write an Equation of a Line in Standard Form from a Word Problem?
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-4: Ex 1: Write an Equation of a Line Parallel to a Given Line & Try It!
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: Virtual Nerd™: How Do You Know if Two Lines Are Parallel?
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-1: Ex 3: Understand Slope-Intercept Form & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            Topic 2: Assessment Form C
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

         1-1: Ex 1: Understand Sets and Subsets & Try It!
           Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

         1-1: Ex 2: Compare and Order Real Numbers & Try It!
           Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

         2-2: Ex 2: Write an Equation in Point-Slope Form & Try It!
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         1-7: Virtual Nerd™: How do you Figure Out if an Absolute Value Inequality is an AND or OR Compound Inequality?
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         1-7: Ex 3: Understand Absolute Value Inequalities & Try It!
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         1-5: MathXL for School: Enrichment
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         1-5: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

         1-5: Virtual Nerd™: How Do You Solve and Graph a Two-Step Inequality?
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         2-2: Virtual Nerd™: How do you write an equation of a line in point-slope form if you have the slope and one point?
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         2-3: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

         2-1: Ex 4: Interpret Slope and y-Intercept & Try It!
           Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

         1-1: Ex 3: Operations With Rational Numbers & Try It!
           Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

         2-4: Ex 2: Understand the Slopes of Perpendicular Lines & Try It!
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

         2-1: Ex 1: Graph a Linear Equation & Try It!
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

         2-3: Ex 1: Understand Standard Form of a Linear Equation & Try It!
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         2-1: Ex 3: Understand Slope-Intercept Form & Try It!
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         2-2: Ex 1: Understand Point-Slope Form of a Linear Equation & Try It!
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         1-4: Ex 1: Rewrite Literal Equations & Try It!
           Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

         2-3: Virtual Nerd™: How Do You Write an Equation of a Line in Standard Form from a Word Problem?
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         1-4: Virtual Nerd™: How Do You Solve a Formula for a Variable?
           Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

         1-5: Ex 1: Solve Inequalities & Try It!
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         2-2: MathXL for School: Enrichment
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         2-4: MathXL for School: Enrichment
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

         2-4: Ex 1: Write an Equation of a Line Parallel to a Given Line & Try It!
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

         2-2: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         9-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         1-2: Virtual Nerd™: How Do You Solve a Two-Step Equation with Fractions by Multiplying Away the Fraction?
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         1-7: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         1-4: MathXL for School: Enrichment
           Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

         2-4: Virtual Nerd™: How Do You Know if Two Lines Are Perpendicular?
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

         1-6: Ex 1: Understand Compound Inequalities & Try It!
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         1-3: Virtual Nerd™: How Do You Solve a Word Problem Using an Equation With Variables on Both Sides?
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         1-6: MathXL for School: Enrichment
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         2-4: Virtual Nerd™: How Do You Know if Two Lines Are Parallel?
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

         1-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

         2-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         2-3: Virtual Nerd™: How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

         3-2: MathXL for School: Enrichment
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

         1-6: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         1-6: Virtual Nerd™: How Do You Solve an AND Compound Inequality and Graph It On a Number Line?
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         9-6: Ex 3: Find Approximate Solutions & Try It!
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         1-7: Ex 1: Understand Absolute Value Equations & Try It!
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         9-4: Ex 4: Determine a Reasonable Solution & Try It!
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         1-2: Ex 1: Solve Linear Equations & Try It!
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         2-1: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         1-7: Ex 2: Apply an Absolute Value Equation & Try It!
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         1-7: MathXL for School: Enrichment
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         2-3: MathXL for School: Enrichment
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

         Benchmark Test 1
           Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

         Linear Functions

            Interactive Student Edition: Realize Reader: Topic 3

            3-4: Virtual Nerd™: How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
              Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-4: Example 3 & Try It!
              Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-2: Example 2
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 

            3-4: Example 2 & Try It!
              Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            2-9: Example 3 & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            Topic 3: Readiness Assessment
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            Topic 3: enVision STEM Project

               Topic 3: enVision STEM Video

            Relations and Functions

               Interactive Student Edition: Realize Reader: Lesson 3-1
                 Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

               Explore

                  3-1: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. 

               Understand and Apply

                  3-1: Ex 1: Recognize Domain and Range & Try It!
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

                  3-1: Ex 2: Analyze Reasonable Domains and Ranges & Try It!
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: Ex 3: Classify Relations and Functions & Try It!
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

                  3-1: Additional Example 3A with Try Another One
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble )  engines in a factory, then the positive integers would be an appropriate domain for the function. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

                  3-1: Ex 4: Identify Constraints on the Domain & Try It!
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: Additional Example 4
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: Concept Summary
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: Do You Understand?
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: Do You Know How?
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

               Practice and Problem-Solving

                  3-1: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: MathXL for School: Mixed Review
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

               Assess & Differentiate

                  3-1: Ex 3: Classify Relations and Functions & Try It!
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

                  3-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

                  3-1: MathXL for School: Enrichment
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

                  3-1: Ex 1: Recognize Domain and Range & Try It!
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

                  3-1: Additional Example 4
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??((?). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: Ex 2: Analyze Reasonable Domains and Ranges & Try It!
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: Virtual Nerd™: How Do You Make a Mapping Diagram for a Relation?
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: Ex 4: Identify Constraints on the Domain & Try It!
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: Lesson Quiz
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

                  3-1: MathXL for School: Additional Practice
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: MathXL for School: Enrichment
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

                  3-1: Virtual Nerd™: How Do You Make a Mapping Diagram for a Relation?
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-1: Virtual Nerd™: How Can You Tell if a Relation is Not a Function?
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            Linear Functions

               Interactive Student Edition: Realize Reader: Lesson 3-2
                 Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

               Explore

                  3-2: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 

               Understand and Apply

                  3-2: Ex 1: Evaluate Functions in Function Notation & Try It!
                    Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

                  3-2: Additional Example 1B with Try Another One
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

                  3-2: Ex 2: Write a Linear Function Rule & Try It!
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-2: Additional Example 2
                    Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-2: Ex 3: Analyze a Linear Function & Try It!
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-2: Ex 4: Apply Linear Functions & Try It!
                    Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

                  3-2: Concept Summary
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

                  3-2: Do You Understand?
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

                  3-2: Do You Know How?
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

               Practice and Problem-Solving

                  3-2: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

                  3-2: MathXL for School: Mixed Review
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

               Assess & Differentiate

                  3-2: Ex 4: Apply Linear Functions & Try It!
                    Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

                  3-2: Additional Example 2
                    Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-2: Ex 3: Analyze a Linear Function & Try It!
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-2: Virtual Nerd™: What is a Linear Function?
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-2: Ex 2: Write a Linear Function Rule & Try It!
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-2: Lesson Quiz
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

                  3-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-2: MathXL for School: Additional Practice
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

                  3-2: MathXL for School: Enrichment
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  3-2: Virtual Nerd™: What is a Linear Function?
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-2: Virtual Nerd™: What is Function Notation?
                    Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

            Transforming Linear Functions

               Interactive Student Edition: Realize Reader: Lesson 3-3
                 Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Explore

                  3-3: Critique & Explain
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. 

               Understand and Apply

                  3-3: Ex 1: Vertical Translations of Linear Functions & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Concept

                  3-3: Ex 2: Horizontal Translations of Linear Functions & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Additional Example 2
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Ex 3: Stretches and Compressions of Linear Functions & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Additional Example 3 with Try Another One
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Concept Summary
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Do You Understand?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Do You Know How?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Practice and Problem-Solving

                  3-3: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: MathXL for School: Mixed Review
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

               Assess & Differentiate

                  3-3: Ex 3: Stretches and Compressions of Linear Functions & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Virtual Nerd™: What Does the Value of 'm' Do to the Graph of f(x)=mx?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??((? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Ex 2: Horizontal Translations of Linear Functions & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Virtual Nerd™: Transforming Linear Functions
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Lesson Quiz
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: MathXL for School: Additional Practice
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Virtual Nerd™: Transforming Linear Functions
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  3-3: Virtual Nerd™: What Does the Value of 'm' Do to the Graph of f(x)=mx?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            Mathematical Modeling in 3 Acts: The Express Lane

               Topic 3: The Express Lane - Act 1 Video with Questions

               Topic 3: The Express Lane - Act 2 Content

               Topic 3: The Express Lane - Act 2 Questions

               Topic 3: The Express Lane - Act 3 Video

               Topic 3: The Express Lane - Act 3 Questions

            Arithmetic Sequences

               Interactive Student Edition: Realize Reader: Lesson 3-4
                 Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

               Explore

                  3-4: Explore & Reason

               Understand and Apply

                  3-4: Ex 1: Connect Sequences and Functions & Try It!
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-4: Additional Example 1A with Try Another One
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-4: Concept: Recursive Definition

                  3-4: Ex 2: Apply the Recursive Formula & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Concept: Explicit Formula

                  3-4: Ex 3: Apply the Explicit Formula & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Additional Example 3A
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Ex 4: Write an Explicit Formula From a Recursive Formula & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Ex 5: Write a Recursive Formula From an Explicit Formula & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Concept Summary
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??((?+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Do You Understand?
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Do You Know How?
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

               Practice and Problem-Solving

                  3-4: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: MathXL for School: Mixed Review
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Assess & Differentiate

                  3-4: Ex 2: Apply the Recursive Formula & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Virtual Nerd™: How Do You Find the Nth Term in an Arithmetic Sequence?
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??((?) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Ex 3: Apply the Explicit Formula & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Virtual Nerd™: What is an Explicit Formula?
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Ex 1: Connect Sequences and Functions & Try It!
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??((?-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-4: Additional Example 3A
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: MathXL for School: Enrichment
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-4: Lesson Quiz
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: MathXL for School: Additional Practice
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: MathXL for School: Enrichment
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

                  3-4: Virtual Nerd™: How Do You Find the Nth Term in an Arithmetic Sequence?
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  3-4: Virtual Nerd™: What is an Explicit Formula?
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            Scatter Plots and Lines of Fit

               Interactive Student Edition: Realize Reader: Lesson 3-5
                 Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

               Explore

                  3-5: Model & Discuss
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Fit a linear function for a scatter plot that suggests a linear association. Interpret parts of an expression, such as terms, factors, and coefficients. 

               Understand and Apply

                  3-5: Ex 1: Understand Association & Try It!
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Ex 2: Understand Correlation & Try It!
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Additional Example 2 with Try Another One
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Ex 3: Write the Equation of a Trend Line & Try It!
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Ex 4: Interpret Trend Lines & Try It!
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Additional Example 4
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Concept Summary
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Do You Understand?
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Do You Know How?
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

               Practice and Problem-Solving

                  3-5: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  3-5: MathXL for School: Mixed Review
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??((? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Assess & Differentiate

                  3-5: Ex 4: Interpret Trend Lines & Try It!
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Ex 1: Understand Association & Try It!
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Virtual Nerd™: How Do You Use a Scatter Plot to Find a Positive Correlation?
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Ex 3: Write the Equation of a Trend Line & Try It!
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-6: Ex 1: Find the Line of Best Fit & Try It!
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: MathXL for School: Enrichment
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Lesson Quiz
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: MathXL for School: Additional Practice
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: MathXL for School: Enrichment
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Virtual Nerd™: How Do You Use a Scatter Plot to Find a Positive Correlation?
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: Virtual Nerd™: How Do You Use a Scatter Plot to Find a Negative Correlation?
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            Analyzing Lines of Fit

               Interactive Student Edition: Realize Reader: Lesson 3-6
                 Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. Distinguish between correlation and causation. Fit a linear function for a scatter plot that suggests a linear association. Informally assess the fit of a function by plotting and analyzing residuals. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

               Explore

                  3-6: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Compute (using technology) and interpret the correlation coefficient of a linear fit. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Distinguish between correlation and causation. Fit a linear function for a scatter plot that suggests a linear association. Informally assess the fit of a function by plotting and analyzing residuals. 

               Understand and Apply

                  3-6: Ex 1: Find the Line of Best Fit & Try It!
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-6: Ex 2: Understand Correlation Coefficients & Try It!
                    Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

                  3-6: Concept: Residuals

                  3-6: Ex 3: Interpret Residual Plots & Try It!
                    Curriculum Standards: Informally assess the fit of a function by plotting and analyzing residuals. 

                  3-6: Additional Example 3
                    Curriculum Standards: Informally assess the fit of a function by plotting and analyzing residuals. 

                  3-6: Ex 4: Interpolate and Extrapolate Using Linear Models & Try It!
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  3-6: Additional Example 4A with Try Another One
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  3-6: Ex 5: Correlation and Causation & Try It!
                    Curriculum Standards: Distinguish between correlation and causation. 

                  3-6: Concept Summary
                    Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. Distinguish between correlation and causation. Fit a linear function for a scatter plot that suggests a linear association. Informally assess the fit of a function by plotting and analyzing residuals. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  3-6: Do You Understand?
                    Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. Distinguish between correlation and causation. Fit a linear function for a scatter plot that suggests a linear association. Informally assess the fit of a function by plotting and analyzing residuals. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  3-6: Do You Know How?
                    Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. Distinguish between correlation and causation. Fit a linear function for a scatter plot that suggests a linear association. Informally assess the fit of a function by plotting and analyzing residuals. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

               Practice and Problem-Solving

                  3-6: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. Distinguish between correlation and causation. Fit a linear function for a scatter plot that suggests a linear association. Informally assess the fit of a function by plotting and analyzing residuals. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  3-6: MathXL for School: Mixed Review
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Fit a linear function for a scatter plot that suggests a linear association. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Assess & Differentiate

                  3-6: Ex 4: Interpolate and Extrapolate Using Linear Models & Try It!
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  3-6: Ex 2: Understand Correlation Coefficients & Try It!
                    Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

                  3-6: Virtual Nerd™: What is the Correlation Coefficient?
                    Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

                  3-6: Ex 3: Interpret Residual Plots & Try It!
                    Curriculum Standards: Informally assess the fit of a function by plotting and analyzing residuals. 

                  3-6: Additional Example 3
                    Curriculum Standards: Informally assess the fit of a function by plotting and analyzing residuals. 

                  3-5: Ex 3: Write the Equation of a Trend Line & Try It!
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-6: Ex 1: Find the Line of Best Fit & Try It!
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-5: MathXL for School: Enrichment
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-6: Ex 5: Correlation and Causation & Try It!
                    Curriculum Standards: Distinguish between correlation and causation. 

                  3-6: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-6: MathXL for School: Enrichment
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-6: Lesson Quiz
                    Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. Distinguish between correlation and causation. Fit a linear function for a scatter plot that suggests a linear association. Informally assess the fit of a function by plotting and analyzing residuals. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  3-6: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-6: MathXL for School: Additional Practice
                    Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. Distinguish between correlation and causation. Fit a linear function for a scatter plot that suggests a linear association. Informally assess the fit of a function by plotting and analyzing residuals. 

                  3-6: MathXL for School: Enrichment
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-6: Virtual Nerd™: What is Linear Regression?
                    Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

                  3-6: Virtual Nerd™: What is the Correlation Coefficient?
                    Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

            Topic 3: MathXL for School: Topic Review
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Compute (using technology) and interpret the correlation coefficient of a linear fit. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Fit a linear function for a scatter plot that suggests a linear association. Informally assess the fit of a function by plotting and analyzing residuals. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            Topic 3: Performance Assessment Form A
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            3-3: Ex 3: Stretches and Compressions of Linear Functions & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: Virtual Nerd™: What Does the Value of 'm' Do to the Graph of f(x)=mx?
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-5: Ex 4: Interpret Trend Lines & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-6: Ex 5: Correlation and Causation & Try It!
              Curriculum Standards: Distinguish between correlation and causation. 

            3-2: Ex 2: Write a Linear Function Rule & Try It!
              Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-5: Ex 1: Understand Association & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: Virtual Nerd™: How Do You Use a Scatter Plot to Find a Positive Correlation?
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: Ex 2: Understand Correlation & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-4: Ex 1: Connect Sequences and Functions & Try It!
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-4: Additional Example 3A
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-4: MathXL for School: Enrichment
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-1: Ex 3: Classify Relations and Functions & Try It!
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: MathXL for School: Enrichment
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-6: Ex 2: Understand Correlation Coefficients & Try It!
              Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

            3-6: Virtual Nerd™: What is the Correlation Coefficient?
              Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

            3-2: Ex 4: Apply Linear Functions & Try It!
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

            3-2: Additional Example 2
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-1: Ex 1: Recognize Domain and Range & Try It!
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: Additional Example 4
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            3-4: Ex 3: Apply the Explicit Formula & Try It!
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-4: Virtual Nerd™: What is an Explicit Formula?
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-5: Ex 3: Write the Equation of a Trend Line & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-6: Ex 1: Find the Line of Best Fit & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: MathXL for School: Enrichment
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-3: Ex 2: Horizontal Translations of Linear Functions & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: Virtual Nerd™: Transforming Linear Functions
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: MathXL for School: Enrichment
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-1: Ex 2: Analyze Reasonable Domains and Ranges & Try It!
              Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            3-1: Virtual Nerd™: How Do You Make a Mapping Diagram for a Relation?
              Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            3-1: Ex 4: Identify Constraints on the Domain & Try It!
              Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            Topic 3: Assessment Form A
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Compute (using technology) and interpret the correlation coefficient of a linear fit. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Fit a linear function for a scatter plot that suggests a linear association. Distinguish between correlation and causation. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-1: Ex 3: Classify Relations and Functions & Try It!
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? =  =(??). 

            3-1: MathXL for School: Enrichment
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-5: Ex 4: Interpret Trend Lines & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-3: Ex 3: Stretches and Compressions of Linear Functions & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: Virtual Nerd™: What Does the Value of 'm' Do to the Graph of f(x)=mx?
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-5: Ex 2: Understand Correlation & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: Ex 3: Write the Equation of a Trend Line & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-6: Ex 1: Find the Line of Best Fit & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: MathXL for School: Enrichment
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-2: Ex 4: Apply Linear Functions & Try It!
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

            3-2: Additional Example 2
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-1: Ex 1: Recognize Domain and Range & Try It!
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: Additional Example 4
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            3-4: Ex 1: Connect Sequences and Functions & Try It!
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-4: Additional Example 3A
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-4: MathXL for School: Enrichment
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??((?) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-4: Ex 3: Apply the Explicit Formula & Try It!
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-4: Virtual Nerd™: What is an Explicit Formula?
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-2: Ex 2: Write a Linear Function Rule & Try It!
              Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-3: Ex 2: Horizontal Translations of Linear Functions & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: Virtual Nerd™: Transforming Linear Functions
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: MathXL for School: Enrichment
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-5: Ex 1: Understand Association & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: Virtual Nerd™: How Do You Use a Scatter Plot to Find a Positive Correlation?
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-1: Ex 2: Analyze Reasonable Domains and Ranges & Try It!
              Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            3-1: Virtual Nerd™: How Do You Make a Mapping Diagram for a Relation?
              Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            3-1: Ex 4: Identify Constraints on the Domain & Try It!
              Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            3-6: Ex 5: Correlation and Causation & Try It!
              Curriculum Standards: Distinguish between correlation and causation. 

            3-6: Ex 2: Understand Correlation Coefficients & Try It!
              Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

            3-6: Virtual Nerd™: What is the Correlation Coefficient?
              Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

            Topic 3: Assessment Form C
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Compute (using technology) and interpret the correlation coefficient of a linear fit. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Fit a linear function for a scatter plot that suggests a linear association. Distinguish between correlation and causation. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         Systems of Linear Equations and Inequalities

            Interactive Student Edition: Realize Reader: Topic 4

            1-5: Ex 1: Solve Inequalities & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-5: Virtual Nerd™: How Do You Solve and Graph a Two-Step Inequality?
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

            1-5: MathXL for School: Enrichment
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-2: Ex 1: Solve Linear Equations & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-2: Virtual Nerd™: How Do You Solve a Two-Step Equation with Fractions by Multiplying Away the Fraction?
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            2-1: Ex 4: Interpret Slope and y-Intercept & Try It!
              Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-3: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

            2-4: Ex 1: Write an Equation of a Line Parallel to a Given Line & Try It!
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: Virtual Nerd™: How Do You Know if Two Lines Are Parallel?
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            2-4: MathXL for School: Enrichment
              Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

            1-4: Ex 1: Rewrite Literal Equations & Try It!
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-4: Virtual Nerd™: How Do You Solve a Formula for a Variable?
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-4: MathXL for School: Enrichment
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            2-2: Ex 1: Understand Point-Slope Form of a Linear Equation & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: Ex 3: Understand Slope-Intercept Form & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-3: Ex 1: Understand Standard Form of a Linear Equation & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-3: Virtual Nerd™: How Do You Write an Equation of a Line in Standard Form from a Word Problem?
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: Ex 1: Graph a Linear Equation & Try It!
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            2-3: Virtual Nerd™: How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            3-2: MathXL for School: Enrichment
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            2-1: Ex 2: Write an Equation from a Graph & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: Virtual Nerd™: How Do You Write an Equation of a Line in Slope-Intercept Form if You Have a Graph?
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            5-5: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            5-3: Virtual Nerd™: How Do You Solve a System of Equations Using the Substitution Method?
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            5-5: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Addition Method?
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            5-2: Virtual Nerd™: How Do You Solve a System of Equations by Graphing?
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            5-2: Example 1 & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            5-4: Example 1 & Try It!
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            5-3: Example 1 & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            2-8: Example 1
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 

            5-4: Example 3 & Try It!
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            Topic 4: Readiness Assessment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            Topic 4: enVision STEM Project

               Topic 4: enVision STEM Video

            Solving Systems of Equations by Graphing

               Interactive Student Edition: Realize Reader: Lesson 4-1
                 Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

               Explore

                  4-1: Explore & Reason
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. 

               Understand and Apply

                  4-1: Ex 1: Solve a System of Equations by Graphing & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Ex 2: Graph Systems of Equations With Infinitely Many Solutions or No Solution & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Additional Example 2 with Try Another One
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Ex 3: Write a System of Equations & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Additional Example 3
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Ex 4: Solve a System of Equations Approximately & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Concept Summary
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Do You Understand?
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Do You Know How?
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

               Practice and Problem-Solving

                  4-1: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  4-1: MathXL for School: Mixed Review
                    Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. Graph linear and quadratic functions and show intercepts, maxima, and minima. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Fit a linear function for a scatter plot that suggests a linear association. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Assess & Differentiate

                  4-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  4-1: MathXL for School: Enrichment
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Ex 1: Solve a System of Equations by Graphing & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Virtual Nerd™: How Do You Solve a System of Equations by Graphing?
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  5-2: Example 1 & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  5-2: Virtual Nerd™: How Do You Solve a System of Equations by Graphing?
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Lesson Quiz
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  4-1: MathXL for School: Additional Practice
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  4-1: MathXL for School: Enrichment
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Virtual Nerd™: How Do You Solve a System of Equations by Graphing?
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Virtual Nerd™: How Do You Show that a System of Equations has No Solution?
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            Solving Systems of Equations by Substitution

               Interactive Student Edition: Realize Reader: Lesson 4-2
                 Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

               Explore

                  4-2: Model & Discuss
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Understand and Apply

                  4-2: Ex 1: Solve Systems of Equations Using Substitution & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: Ex 2: Compare Graphing and Substitution Methods & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: Ex 3: Systems With Infinitely Many Solutions or No Solution & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: Additional Example 3 with Try Another One
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: Ex 4: Model Using Systems of Equations & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: Additional Example 4
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: Concept Summary
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: Do You Understand?
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: Do You Know How?
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

               Practice and Problem-Solving

                  4-2: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  4-2: MathXL for School: Mixed Review
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Assess & Differentiate

                  4-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: MathXL for School: Enrichment
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  4-2: Ex 1: Solve Systems of Equations Using Substitution & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: Virtual Nerd™: What is Another Way of Solving a System of Equations Using the Substitution Method?
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Ex 3: Write a System of Equations & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Additional Example 2 with Try Another One
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Ex 2: Graph Systems of Equations With Infinitely Many Solutions or No Solution & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: MathXL for School: Enrichment
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: Lesson Quiz
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: MathXL for School: Additional Practice
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  4-2: MathXL for School: Enrichment
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  4-2: Virtual Nerd™: What is Another Way of Solving a System of Equations Using the Substitution Method?
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            Solving Systems of Equations by Elimination

               Interactive Student Edition: Realize Reader: Lesson 4-3
                 Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

               Explore

                  4-3: Critique & Explain
                    Curriculum Standards: Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (io – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. 

               Understand and Apply

                  4-3: Ex 1: Solve a System of Equations by Adding & Try It!
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: Additional Example 1 with Try Another One
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: Ex 2: Understand Equivalent Systems of Equations & Try It!
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: Ex 3: Apply Elimination & Try It!
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: Additional Example 3
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: Ex 4: Choose a Method of Solving & Try It!
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: Concept Summary
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: Do You Understand?
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: Do You Know How?
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

               Practice and Problem-Solving

                  4-3: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-3: MathXL for School: Mixed Review
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

               Assess & Differentiate

                  4-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: MathXL for School: Enrichment
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Ex 3: Write a System of Equations & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-1: Additional Example 2 with Try Another One
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: Ex 4: Model Using Systems of Equations & Try It!
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-2: MathXL for School: Enrichment
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  5-4: Example 1 & Try It!
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  5-5: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Addition Method?
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: Lesson Quiz
                    Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: MathXL for School: Additional Practice
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: MathXL for School: Enrichment
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

                  4-3: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  4-3: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Addition Method?
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            Linear Inequalities in Two Variables

               Interactive Student Edition: Realize Reader: Lesson 4-4
                 Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

               Explore

                  4-4: Model & Discuss
                    Curriculum Standards: Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)( – + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Understand and Apply

                  4-4: Ex 1: Understand an Inequality in Two Variables & Try It!
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Additional Example 1 with Try Another One
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Ex 2: Rewrite an Inequality to Graph It & Try It!
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Ex 3: Write an Inequality From a Graph & Try It!
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Additional Example 3
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Ex 4: Inequalities in One Variable in the Coordinate Plane & Try It!
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Concept Summary
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Do You Understand?
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Do You Know How?
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

               Practice and Problem-Solving

                  4-4: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: MathXL for School: Mixed Review
                    Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

               Assess & Differentiate

                  4-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: MathXL for School: Enrichment
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Ex 1: Understand an Inequality in Two Variables & Try It!
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Additional Example 1 with Try Another One
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Ex 2: Rewrite an Inequality to Graph It & Try It!
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Virtual Nerd™: How Do You Solve and Graph Inequalities from a Word Problem?
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Lesson Quiz
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: MathXL for School: Additional Practice
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: MathXL for School: Enrichment
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Virtual Nerd™: How Do You Graph a Greater Than Inequality on the Coordinate Plane?
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-4: Virtual Nerd™: How Do You Solve and Graph Inequalities from a Word Problem?
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            Mathematical Modeling in 3 Acts: Get Up There!

               Topic 4: Get Up There! - Act 1 Video with Questions

               Topic 4: Get Up There! - Act 2 Content

               Topic 4: Get Up There! - Act 2 Questions

               Topic 4: Get Up There! - Act 3 Video

               Topic 4: Get Up There! - Act 3 Questions

            Systems of Linear Inequalities

               Interactive Student Edition: Realize Reader: Lesson 4-5
                 Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

               Explore

                  4-5: Explore & Reason
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Understand and Apply

                  4-5: Ex 1: Graph a System of Inequalities & Try It!
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Additional Example 1 with Try Another One
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Ex 2: Write a System of Inequalities From a Graph & Try It!
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Additional Example 2
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Ex 3: Use a System of Inequalities & Try It!
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Concept Summary
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Do You Understand?
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Do You Know How?
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

               Practice and Problem-Solving

                  4-5: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: MathXL for School: Mixed Review
                    Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Assess & Differentiate

                  4-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: MathXL for School: Enrichment
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Ex 1: Graph a System of Inequalities & Try It!
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Virtual Nerd™: How Do You Write a System of Inequalities From a Graph?
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Ex 2: Write a System of Inequalities From a Graph & Try It!
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Virtual Nerd™: How Do You Solve a System of Inequalities by Graphing?
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Lesson Quiz
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: MathXL for School: Additional Practice
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: MathXL for School: Enrichment
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Virtual Nerd™: How Do You Solve a System of Inequalities by Graphing?
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

                  4-5: Virtual Nerd™: How Do You Write a System of Inequalities From a Graph?
                    Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            Topic 4: MathXL for School: Topic Review
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            Topic 4: Performance Assessment Form A
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-3: Ex 1: Solve a System of Equations by Adding & Try It!
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            4-3: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            4-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            4-3: MathXL for School: Enrichment
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-1: Ex 3: Write a System of Equations & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-1: Additional Example 2 with Try Another One
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-1: Ex 2: Graph Systems of Equations With Infinitely Many Solutions or No Solution & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: MathXL for School: Enrichment
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            4-5: Ex 2: Write a System of Inequalities From a Graph & Try It!
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-5: Virtual Nerd™: How Do You Solve a System of Inequalities by Graphing?
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-4: MathXL for School: Enrichment
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-2: Ex 1: Solve Systems of Equations Using Substitution & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: Virtual Nerd™: What is Another Way of Solving a System of Equations Using the Substitution Method?
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-4: Ex 2: Rewrite an Inequality to Graph It & Try It!
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-4: Virtual Nerd™: How Do You Solve and Graph Inequalities from a Word Problem?
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            5-2: Example 1 & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            5-2: Virtual Nerd™: How Do You Solve a System of Equations by Graphing?
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            Topic 4: Assessment Form A
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-3: Ex 1: Solve a System of Equations by Adding & Try It!
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            4-3: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            4-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            4-3: MathXL for School: Enrichment
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-1: Ex 3: Write a System of Equations & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-1: Additional Example 2 with Try Another One
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-1: Ex 2: Graph Systems of Equations With Infinitely Many Solutions or No Solution & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: MathXL for School: Enrichment
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            4-5: Ex 2: Write a System of Inequalities From a Graph & Try It!
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-5: Virtual Nerd™: How Do You Solve a System of Inequalities by Graphing?
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-4: MathXL for School: Enrichment
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-2: Ex 1: Solve Systems of Equations Using Substitution & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: Virtual Nerd™: What is Another Way of Solving a System of Equations Using the Substitution Method?
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-4: Ex 2: Rewrite an Inequality to Graph It & Try It!
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-4: Virtual Nerd™: How Do You Solve and Graph Inequalities from a Word Problem?
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            5-2: Example 1 & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            5-2: Virtual Nerd™: How Do You Solve a System of Equations by Graphing?
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            Topic 4: Assessment Form C
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

         2-4: Ex 2: Understand the Slopes of Perpendicular Lines & Try It!
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

         1-4: Ex 1: Rewrite Literal Equations & Try It!
           Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

         1-4: MathXL for School: Enrichment
           Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

         3-4: Ex 1: Connect Sequences and Functions & Try It!
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

         3-6: Ex 2: Understand Correlation Coefficients & Try It!
           Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

         2-1: Ex 1: Graph a Linear Equation & Try It!
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

         4-3: Ex 1: Solve a System of Equations by Adding & Try It!
           Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

         2-1: Ex 3: Understand Slope-Intercept Form & Try It!
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         3-1: Ex 1: Recognize Domain and Range & Try It!
           Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

         1-7: Ex 1: Understand Absolute Value Equations & Try It!
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         4-4: Ex 2: Rewrite an Inequality to Graph It & Try It!
           Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

         4-2: Ex 1: Solve Systems of Equations Using Substitution & Try It!
           Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         1-2: Ex 1: Solve Linear Equations & Try It!
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         3-3: Ex 2: Horizontal Translations of Linear Functions & Try It!
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         3-5: Ex 1: Understand Association & Try It!
           Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

         3-1: Additional Example 4
           Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

         3-6: Virtual Nerd™: What is the Correlation Coefficient?
           Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

         2-4: MathXL for School: Enrichment
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

         3-3: MathXL for School: Enrichment
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         4-3: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

         4-3: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
           Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

         4-2: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         1-2: Virtual Nerd™: How Do You Solve a Two-Step Equation with Fractions by Multiplying Away the Fraction?
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         3-3: Virtual Nerd™: Transforming Linear Functions
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         3-5: Virtual Nerd™: How Do You Use a Scatter Plot to Find a Positive Correlation?
           Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

         4-2: Virtual Nerd™: What is Another Way of Solving a System of Equations Using the Substitution Method?
           Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         1-7: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         4-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

         4-4: Virtual Nerd™: How Do You Solve and Graph Inequalities from a Word Problem?
           Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

         2-3: Virtual Nerd™: How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

         3-2: MathXL for School: Enrichment
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

         3-4: MathXL for School: Enrichment
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

         3-3: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         3-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         4-3: MathXL for School: Enrichment
           Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         3-4: Additional Example 3A
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         2-1: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         1-7: Ex 2: Apply an Absolute Value Equation & Try It!
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         1-7: MathXL for School: Enrichment
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         3-2: Ex 2: Write a Linear Function Rule & Try It!
           Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

         4-1: Ex 3: Write a System of Equations & Try It!
           Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         3-6: Ex 5: Correlation and Causation & Try It!
           Curriculum Standards: Distinguish between correlation and causation. 

         3-5: Ex 3: Write the Equation of a Trend Line & Try It!
           Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

         4-5: Ex 2: Write a System of Inequalities From a Graph & Try It!
           Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

         1-4: Virtual Nerd™: How Do You Solve a Formula for a Variable?
           Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

         4-5: Virtual Nerd™: How Do You Solve a System of Inequalities by Graphing?
           Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

         4-1: Ex 2: Graph Systems of Equations With Infinitely Many Solutions or No Solution & Try It!
           Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         4-1: Additional Example 2 with Try Another One
           Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         2-4: Virtual Nerd™: How Do You Know if Two Lines Are Perpendicular?
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

         4-5: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

         1-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

         2-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         3-6: Ex 1: Find the Line of Best Fit & Try It!
           Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

         3-5: MathXL for School: Enrichment
           Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

         4-4: MathXL for School: Enrichment
           Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

         4-2: MathXL for School: Enrichment
           Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         3-5: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

         Benchmark Test 2
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Compute (using technology) and interpret the correlation coefficient of a linear fit. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Graph linear and quadratic functions and show intercepts, maxima, and minima. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Distinguish between correlation and causation. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Fit a linear function for a scatter plot that suggests a linear association. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         Piecewise Functions

            Interactive Student Edition: Realize Reader: Topic 5

            4-1: Ex 3: Write a System of Equations & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-1: Additional Example 2 with Try Another One
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-1: Ex 2: Graph Systems of Equations With Infinitely Many Solutions or No Solution & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: MathXL for School: Enrichment
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            4-5: Ex 1: Graph a System of Inequalities & Try It!
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-5: Virtual Nerd™: How Do You Write a System of Inequalities From a Graph?
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-5: MathXL for School: Enrichment
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            1-5: Ex 1: Solve Inequalities & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-5: Virtual Nerd™: How Do You Solve and Graph a Two-Step Inequality?
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 

            1-5: MathXL for School: Enrichment
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            4-5: Ex 2: Write a System of Inequalities From a Graph & Try It!
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-5: Virtual Nerd™: How Do You Solve a System of Inequalities by Graphing?
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-4: MathXL for School: Enrichment
              Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

            4-2: Ex 1: Solve Systems of Equations Using Substitution & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: Virtual Nerd™: What is Another Way of Solving a System of Equations Using the Substitution Method?
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-3: MathXL for School: Enrichment
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            2-8: Example 1
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 

            Topic 5: Readiness Assessment
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            Topic 5: enVision STEM Project

               Topic 5: enVision STEM Video

            The Absolute Value Functions

               Interactive Student Edition: Realize Reader: Lesson 5-1
                 Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Explore

                  5-1: Explore & Reason
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 

               Understand and Apply

                  5-1: Ex 1: Graph the Absolute Value Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-1: Ex 2: Transform the Absolute Value Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-1: Additional Example 2 with Try Another One
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-1: Ex 3: Interpret the Graph of a Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-1: Additional Example 3
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-1: Ex 4: Determine Rate of Change & Try It!
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  5-1: Concept Summary
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-1: Do You Understand?
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-1: Do You Know How?
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Practice and Problem-Solving

                  5-1: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-1: MathXL for School: Mixed Review
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Assess & Differentiate

                  5-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-1: MathXL for School: Enrichment
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-1: Ex 4: Determine Rate of Change & Try It!
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  5-1: Lesson Quiz
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-1: MathXL for School: Additional Practice
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-1: MathXL for School: Enrichment
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-1: Virtual Nerd™: What is an Absolute Value Function?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-1: Virtual Nerd™: How Do You Graph an Absolute Value Function?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            Mathematical Modeling in 3 Acts:The Mad Runner

               Topic 5: The Mad Runner - Act 1 Video with Questions

               Topic 5: The Mad Runner - Act 2 Content

               Topic 5: The Mad Runner - Act 2 Questions

               Topic 5: The Mad Runner - Act 3 Video

               Topic 5: The Mad Runner - Act 3 Questions

            Piecewise-Defined Functions

               Interactive Student Edition: Realize Reader: Lesson 5-2
                 Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Explore

                  5-2: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 

               Understand and Apply

                  5-2: Ex 1: Understand Piecewise-Defined Functions & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: Additional Example 1 with Try Another One
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: Ex 2: Graph a Piecewise-Defined Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-2: Ex 3: Analyze the Graph of a Piecewise-Defined Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-2: Ex 4: Apply a Piecewise-Defined Function & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: Additional Example 4
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: Concept Summary
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: Do You Understand?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: Do You Know How?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Practice and Problem-Solving

                  5-2: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: MathXL for School: Mixed Review
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Assess & Differentiate

                  5-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: MathXL for School: Enrichment
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-2: Ex 1: Understand Piecewise-Defined Functions & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: Virtual Nerd™: What is a Piecewise Linear Function?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: Ex 2: Graph a Piecewise-Defined Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-2: Lesson Quiz
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: MathXL for School: Additional Practice
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  5-2: MathXL for School: Enrichment
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-2: Virtual Nerd™: What is a Piecewise Linear Function?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            Step Functions

               Interactive Student Edition: Realize Reader: Lesson 5-3
                 Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Explore

                  5-3: Critique & Explain
                    Curriculum Standards: Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 

               Understand and Apply

                  5-3: Ex 1: Understand Step Functions & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Additional Example 1 with Try Another One
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Ex 2: Use a Step Function to Represent a Real-World Situation & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Additional Example 2
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Ex 3: Use a Step Function to Solve Problems & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Concept Summary
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Do You Understand?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Do You Know How?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Practice and Problem-Solving

                  5-3: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: MathXL for School: Mixed Review
                    Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Assess & Differentiate

                  5-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: MathXL for School: Enrichment
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Ex 2: Use a Step Function to Represent a Real-World Situation & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Virtual Nerd™: What is a Step Function?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Ex 1: Understand Step Functions & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Virtual Nerd™: How Do You Graph a Real-World Example of a Step Function?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-1: Ex 4: Determine Rate of Change & Try It!
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  5-3: Lesson Quiz
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: MathXL for School: Additional Practice
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: MathXL for School: Enrichment
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Virtual Nerd™: How Do You Graph a Real-World Example of a Step Function?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-3: Virtual Nerd™: What is a Step Function?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            Transformations of Piecewise-Defined Functions

               Interactive Student Edition: Realize Reader: Lesson 5-4
                 Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Explore

                  5-4: Model & Discuss
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. 

               Understand and Apply

                  5-4: Ex 1: Translate Step Functions & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  5-4: Ex 2: Vertical Translations of the Absolute Value Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Additional Example 2 with Try Another One
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Ex 3: Horizontal Translations of the Absolute Value Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Ex 4: Understand Vertical and Horizontal Translations & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Additional Example 4
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Ex 5: Understand Vertical Stretches and Compressions & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Ex 6: Understand Transformations of the Absolute Value
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Concept Summary
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? +  +) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Do You Understand?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Do You Know How?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Practice and Problem-Solving

                  5-4: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: MathXL for School: Mixed Review
                    Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Assess & Differentiate

                  5-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: MathXL for School: Enrichment
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Ex 2: Vertical Translations of the Absolute Value Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-1: Virtual Nerd™: What is an Absolute Value Function?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Lesson Quiz
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: MathXL for School: Additional Practice
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: MathXL for School: Enrichment
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Virtual Nerd™: How Do You Write an Equation for a Translation of an Absolute Value Function?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  5-4: Virtual Nerd™: What Does the Constant 'a' do in y = a|x|?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            Topic 5: MathXL for School: Topic Review
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

            Topic 5: Performance Assessment Form A
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            5-3: Ex 2: Use a Step Function to Represent a Real-World Situation & Try It!
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-3: Virtual Nerd™: What is a Step Function?
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-3: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-2: Ex 4: Apply a Piecewise-Defined Function & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            5-2: Virtual Nerd™: What is a Piecewise Linear Function?
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            5-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            5-1: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            5-4: Ex 2: Vertical Translations of the Absolute Value Function & Try It!
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-4: Virtual Nerd™: How Do You Write an Equation for a Translation of an Absolute Value Function?
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-4: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-3: Ex 1: Understand Step Functions & Try It!
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-4: Virtual Nerd™: What Does the Constant 'a' do in y = a|x|?
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-2: Ex 3: Analyze the Graph of a Piecewise-Defined Function & Try It!
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-2: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-1: Ex 4: Determine Rate of Change & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            Topic 5: Assessment Form A
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            5-3: Ex 2: Use a Step Function to Represent a Real-World Situation & Try It!
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-3: Virtual Nerd™: What is a Step Function?
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-3: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-2: Ex 4: Apply a Piecewise-Defined Function & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            5-2: Virtual Nerd™: What is a Piecewise Linear Function?
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            5-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            5-1: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            5-4: Ex 2: Vertical Translations of the Absolute Value Function & Try It!
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-4: Virtual Nerd™: How Do You Write an Equation for a Translation of an Absolute Value Function?
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-4: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-3: Ex 1: Understand Step Functions & Try It!
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-4: Virtual Nerd™: What Does the Constant 'a' do in y = a|x|?
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-2: Ex 3: Analyze the Graph of a Piecewise-Defined Function & Try It!
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-2: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-1: Ex 4: Determine Rate of Change & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            Topic 5: Assessment Form C
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         Exponents and Exponential Functions

            Interactive Student Edition: Realize Reader: Topic 6

            5-1: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            3-3: Ex 2: Horizontal Translations of Linear Functions & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: Virtual Nerd™: Transforming Linear Functions
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: MathXL for School: Enrichment
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-1: Ex 1: Recognize Domain and Range & Try It!
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            5-1: Ex 4: Determine Rate of Change & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            3-2: Ex 2: Write a Linear Function Rule & Try It!
              Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            2-1: Ex 2: Write an Equation from a Graph & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: Virtual Nerd™: How Do You Write an Equation of a Line in Slope-Intercept Form if You Have a Graph?
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            3-4: Ex 3: Apply the Explicit Formula & Try It!
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-4: Virtual Nerd™: What is an Explicit Formula?
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-1: Ex 3: Classify Relations and Functions & Try It!
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: MathXL for School: Enrichment
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-4: Ex 1: Connect Sequences and Functions & Try It!
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-4: Additional Example 3A
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-4: MathXL for School: Enrichment
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-4: Ex 2: Apply the Recursive Formula & Try It!
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-4: Virtual Nerd™: How Do You Find the Nth Term in an Arithmetic Sequence?
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            Topic 6: Readiness Assessment
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of )  (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

            Topic 6: enVision STEM Project

               Topic 6: enVision STEM Video

            Rational Exponents and Properties of Exponents

               Interactive Student Edition: Realize Reader: Lesson 6-1
                 Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

               Explore

                  6-1: Critique & Explain
                    Curriculum Standards: Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. 

               Understand and Apply

                  6-1: Ex 1: Write Radicals Using Rational Exponents & Try It!
                    Curriculum Standards: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

                  6-1: Ex 2: Use the Product of Powers Property to Solve Equations With Rational Exponents & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Additional Example 2 with Try Another One
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Ex 3: Use the Power of a Power Property to Solve Equations With Rational Exponents & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Ex 4: Use the Power of a Product Property to Solve Equations With Rational Exponents & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Additional Example 4
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Ex 5: Use the Quotient of Powers Property to Solve Equations With Rational Exponents & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Concept Summary
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

                  6-1: Do You Understand?
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

                  6-1: Do You Know How?
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

               Practice and Problem-Solving

                  6-1: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

                  6-1: MathXL for School: Mixed Review
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Assess & Differentiate

                  6-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

                  6-1: MathXL for School: Enrichment
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Ex 1: Write Radicals Using Rational Exponents & Try It!
                    Curriculum Standards: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

                  6-1: Ex 3: Use the Power of a Power Property to Solve Equations With Rational Exponents & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Virtual Nerd™: What are Rational Exponents?
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Lesson Quiz
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

                  6-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

                  6-1: MathXL for School: Additional Practice
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

                  6-1: MathXL for School: Enrichment
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Virtual Nerd™: What are Rational Exponents?
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Virtual Nerd™: What are the Properties of Rational Exponents?
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            Exponential Functions

               Interactive Student Edition: Realize Reader: Lesson 6-2
                 Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Explore

                  6-2: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

               Understand and Apply

                  6-2: Ex 1: Key Features of ??(??) = 2? & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: Additional Example 1 with Try Another One
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: Concept: Exponential Function

                  6-2: Ex 2: Graph Exponential Functions & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: Ex 3: Write Exponential Functions & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: Additional Example 3
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: Ex 4: Compare Linear and Exponential Functions & Try It!
                    Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

                  6-2: Concept Summary
                    Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: Do You Understand?
                    Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: Do You Know How?
                    Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Practice and Problem-Solving

                  6-2: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: MathXL for School: Mixed Review
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Assess & Differentiate

                  6-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: MathXL for School: Enrichment
                    Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

                  6-2: Ex 1: Key Features of ??(??) = 2? & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: Virtual Nerd™: How Do You Graph an Exponential Function Using a Table?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: Lesson Quiz
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: MathXL for School: Additional Practice
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: MathXL for School: Enrichment
                    Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

                  6-2: Virtual Nerd™: How Do You Find the Asymptotes of a Rational Function if You Have a Graph?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-2: Virtual Nerd™: How Do You Graph an Exponential Function Using a Table?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            Exponential Growth and Decay

               Interactive Student Edition: Realize Reader: Lesson 6-3
                 Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

               Explore

                  6-3: Explore & Reason
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret complicated expressions by viewing one or more of their parts as a single entity. Example: 
For example, interpret ??(1+??)n as the product of ?? and a factor not depending on ??. Interpret the parameters in a linear or exponential function in terms of a context. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Use the properties of exponents to transform expressions for exponential functions. Example: 
For example the expression 1.15 to the ?? power can be rewritten as ((1.15 to the 1/12 power) to the 12?? power) is approximately equal to (1.012 to the 12?? power) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 

               Understand and Apply

                  6-3: Ex 1: Exponential Growth & Try It!
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Additional Example 1 with Try Another One
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Concept: Interest

                  6-3: Ex 2: Exponential Models of Growth & Try It!
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Ex 3: Exponential Decay & Try It!
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Ex 4: Exponential Models of Decay & Try It!
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Ex 5: Exponential Growth and Decay & Try It!
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Additional Example 5
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Concept Summary
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Do You Understand?
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Do You Know How?
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

               Practice and Problem-Solving

                  6-3: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: MathXL for School: Mixed Review
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Assess & Differentiate

                  6-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: MathXL for School: Enrichment
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Ex 1: Exponential Growth & Try It!
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Virtual Nerd™: What is Exponential Growth?
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  5-1: Ex 4: Determine Rate of Change & Try It!
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  6-3: Lesson Quiz
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: MathXL for School: Additional Practice
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: MathXL for School: Enrichment
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Virtual Nerd™: What is Exponential Growth?
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

                  6-3: Virtual Nerd™: How do you solve a word problem with exponential decay?
                    Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

            Geometric Sequences

               Interactive Student Edition: Realize Reader: Lesson 6-4
                 Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

               Explore

                  6-4: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)( –² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. 

               Understand and Apply

                  6-4: Ex 1: Identify Arithmetic and Geometric Sequences & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Additional Example 1
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Ex 2: Write the Recursive Formula For a Sequence & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Additional Example 2 with Try Another One
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Ex 3: Use the Explicit Formula & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Ex 4: Connect Geometric Sequences and Exponential Functions & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Ex 5: Apply the Recursive and Explicit Formulas & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Concept Summary
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Do You Understand?
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Do You Know How?
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

               Practice and Problem-Solving

                  6-4: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-4: MathXL for School: Mixed Review
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

               Assess & Differentiate

                  6-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: MathXL for School: Enrichment
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Ex 4: Connect Geometric Sequences and Exponential Functions & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Ex 2: Write the Recursive Formula For a Sequence & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Additional Example 2 with Try Another One
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Ex 3: Use the Explicit Formula & Try It!
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Virtual Nerd™: How Do You Find the Common Ratio of a Geometric Sequence?
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Lesson Quiz
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: MathXL for School: Additional Practice
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-4: MathXL for School: Enrichment
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Virtual Nerd™: How Do You Find the Common Ratio of a Geometric Sequence?
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

                  6-4: Virtual Nerd™: How Do You Find the nth Term in a Geometric Sequence?
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            Transformations of Exponential Functions

               Interactive Student Edition: Realize Reader: Lesson 6-5
                 Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Explore

                  6-5: Model & Discuss
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. 

               Understand and Apply

                  6-5: Ex 1: Vertical Translations of Graphs of Exponential Functions & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  6-5: Additional Example 1 with Try Another One
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  6-5: Ex 2: Horizontal Translations of Graphs of Exponential Functions & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of  ( given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  6-5: Ex 3: Compare Two Different Transformations of ??(??) = 2? & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: Additional Example 3
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: Concept Summary
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: Do You Understand?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: Do You Know How?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Practice and Problem-Solving

                  6-5: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: MathXL for School: Mixed Review
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

               Assess & Differentiate

                  6-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: Ex 3: Compare Two Different Transformations of ??(??) = 2? & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: Virtual Nerd™: What Does the Value of 'a' Do in the Exponential Function a•bx?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: Ex 2: Horizontal Translations of Graphs of Exponential Functions & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  6-5: Ex 1: Vertical Translations of Graphs of Exponential Functions & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  6-5: Additional Example 1 with Try Another One
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  6-5: Lesson Quiz
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??((?), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: MathXL for School: Additional Practice
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing   (??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: Virtual Nerd™: What Does the Value of 'a' Do in the Exponential Function a•bx?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  6-5: Virtual Nerd™: What Does the Constant 'h' Do in the Exponential Function f(x)=bx-h?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            Mathematical Modeling in 3 Acts: Big Time Pay Back

               Topic 6: Big Time Pay Back - Act 1 Video with Questions

               Topic 6: Big Time Pay Back - Act 2 Content

               Topic 6: Big Time Pay Back - Act 2 Questions

               Topic 6: Big Time Pay Back - Act 3 Video

               Topic 6: Big Time Pay Back - Act 3 Questions

            Topic 6: MathXL for School: Topic Review
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Interpret the parameters in a linear or exponential function in terms of a context. 

            Topic 6: Performance Assessment Form A
              Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            6-3: Ex 2: Exponential Models of Growth & Try It!
              Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

            6-3: Virtual Nerd™: What is Exponential Growth?
              Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

            6-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

            6-3: MathXL for School: Enrichment
              Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

            6-5: Ex 3: Compare Two Different Transformations of ??(??) = 2? & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            6-5: Virtual Nerd™: What Does the Constant 'h' Do in the Exponential Function f(x)=bx-h?
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            6-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            6-5: MathXL for School: Enrichment
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            6-1: Ex 1: Write Radicals Using Rational Exponents & Try It!
              Curriculum Standards: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

            6-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

            6-1: Ex 4: Use the Power of a Product Property to Solve Equations With Rational Exponents & Try It!
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            6-1: Virtual Nerd™: What are Rational Exponents?
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            6-1: MathXL for School: Enrichment
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            6-4: Ex 2: Write the Recursive Formula For a Sequence & Try It!
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: Additional Example 2 with Try Another One
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: Ex 3: Use the Explicit Formula & Try It!
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: Virtual Nerd™: How Do You Find the Common Ratio of a Geometric Sequence?
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: MathXL for School: Enrichment
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: Ex 1: Identify Arithmetic and Geometric Sequences & Try It!
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: Virtual Nerd™: How Do You Find the nth Term in a Geometric Sequence?
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            5-1: Ex 4: Determine Rate of Change & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            Topic 6: Assessment Form A
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

            6-1: Ex 1: Write Radicals Using Rational Exponents & Try It!
              Curriculum Standards: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

            6-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

            6-1: Ex 4: Use the Power of a Product Property to Solve Equations With Rational Exponents & Try It!
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            6-1: Virtual Nerd™: What are Rational Exponents?
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            6-1: MathXL for School: Enrichment
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            6-5: Ex 3: Compare Two Different Transformations of ??(??) = 2? & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            6-5: Virtual Nerd™: What Does the Constant 'h' Do in the Exponential Function f(x)=bx-h?
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            6-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            6-5: MathXL for School: Enrichment
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            6-3: Ex 2: Exponential Models of Growth & Try It!
              Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

            6-3: Virtual Nerd™: What is Exponential Growth?
              Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

            6-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

            6-3: MathXL for School: Enrichment
              Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

            5-1: Ex 4: Determine Rate of Change & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            6-4: Ex 1: Identify Arithmetic and Geometric Sequences & Try It!
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: Virtual Nerd™: How Do You Find the nth Term in a Geometric Sequence?
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: Ex 2: Write the Recursive Formula For a Sequence & Try It!
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: Additional Example 2 with Try Another One
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: Ex 3: Use the Explicit Formula & Try It!
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: Virtual Nerd™: How Do You Find the Common Ratio of a Geometric Sequence?
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-4: MathXL for School: Enrichment
              Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            6-5: Ex 1: Vertical Translations of Graphs of Exponential Functions & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            6-5: Additional Example 1 with Try Another One
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            6-5: Ex 2: Horizontal Translations of Graphs of Exponential Functions & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            Topic 6: Assessment Form C
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

         1-1: Ex 3: Operations With Rational Numbers & Try It!
           Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

         2-1: Ex 3: Understand Slope-Intercept Form & Try It!
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         1-2: Virtual Nerd™: How Do You Solve a Two-Step Equation with Fractions by Multiplying Away the Fraction?
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         1-3: Virtual Nerd™: How Do You Solve a Word Problem Using an Equation With Variables on Both Sides?
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         2-1: Ex 1: Graph a Linear Equation & Try It!
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

         1-6: Ex 1: Understand Compound Inequalities & Try It!
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         3-4: Ex 1: Connect Sequences and Functions & Try It!
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

         6-4: Ex 1: Identify Arithmetic and Geometric Sequences & Try It!
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         3-1: Ex 1: Recognize Domain and Range & Try It!
           Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

         2-4: Ex 1: Write an Equation of a Line Parallel to a Given Line & Try It!
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

         1-7: Ex 1: Understand Absolute Value Equations & Try It!
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         4-2: Ex 1: Solve Systems of Equations Using Substitution & Try It!
           Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         6-4: Ex 2: Write the Recursive Formula For a Sequence & Try It!
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         6-1: Ex 4: Use the Power of a Product Property to Solve Equations With Rational Exponents & Try It!
           Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

         1-2: Ex 1: Solve Linear Equations & Try It!
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         3-3: Ex 2: Horizontal Translations of Linear Functions & Try It!
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         10-3: Ex 4: Analyze End Behaviors of Graphs & Try It!
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         10-3: Ex 2: Analyze Maximum and Minimum Values & Try It!
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         5-2: Ex 4: Apply a Piecewise-Defined Function & Try It!
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         9-6: Ex 3: Find Approximate Solutions & Try It!
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         3-5: Ex 1: Understand Association & Try It!
           Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

         3-1: Additional Example 4
           Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

         6-1: Virtual Nerd™: What are Rational Exponents?
           Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

         2-4: MathXL for School: Enrichment
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

         3-3: MathXL for School: Enrichment
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         4-2: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         10-3: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         3-3: Virtual Nerd™: Transforming Linear Functions
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??((?) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         3-5: Virtual Nerd™: How Do You Use a Scatter Plot to Find a Positive Correlation?
           Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

         4-2: Virtual Nerd™: What is Another Way of Solving a System of Equations Using the Substitution Method?
           Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         1-7: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         5-2: Virtual Nerd™: What is a Piecewise Linear Function?
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         1-6: MathXL for School: Enrichment
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         2-4: Virtual Nerd™: How Do You Know if Two Lines Are Parallel?
           Curriculum Standards: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 

         10-3: MathXL for School: Enrichment
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         5-2: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         2-3: Virtual Nerd™: How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

         3-2: MathXL for School: Enrichment
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

         1-6: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         3-4: MathXL for School: Enrichment
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

         1-6: Virtual Nerd™: How Do You Solve an AND Compound Inequality and Graph It On a Number Line?
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         6-4: Virtual Nerd™: How Do You Find the nth Term in a Geometric Sequence?
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         6-4: Additional Example 2 with Try Another One
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         3-3: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ) (??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         3-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         6-1: MathXL for School: Enrichment
           Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

         6-1: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

         4-3: MathXL for School: Enrichment
           Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         3-4: Additional Example 3A
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         2-1: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         1-7: Ex 2: Apply an Absolute Value Equation & Try It!
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         1-7: MathXL for School: Enrichment
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         Mid-Year Assessment
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Fit a linear function for a scatter plot that suggests a linear association. 

         Polynomials and Factoring

            Interactive Student Edition: Realize Reader: Topic 7

            4-7: Virtual Nerd™: What are the Commutative Properties of Addition and Multiplication?
              Curriculum Standards: Use the relation ??² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

            4-7: Virtual Nerd™: What is the Distributive Property?
              Curriculum Standards: Use the relation ??² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

            Topic 7: Readiness Assessment
              Curriculum Standards: Use the relation ??² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Evaluate and compare strategies on the basis of expected values. Example: 
For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. 

            Topic 7: enVision STEM Project

               Topic 7: enVision STEM Video

            Adding and Subtracting Polynomials

               Interactive Student Edition: Realize Reader: Lesson 7-1
                 Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

               Explore

                  7-1: Explore & Reason
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. 

               Understand and Apply

                  7-1: Ex 1: Understand Polynomials & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Ex 2: Write Polynomials in Standard Form & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Ex 3: Add and Subtract Monomials & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Ex 4: Add Polynomials & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Ex 5: Subtract Polynomials & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Additional Example 5 with Try Another One
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Ex 6: Apply Polynomials & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Additional Example 6
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Concept Summary
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Do You Understand?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Do You Know How?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

               Practice and Problem-Solving

                  7-1: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: MathXL for School: Mixed Review
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

               Assess & Differentiate

                  7-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: MathXL for School: Enrichment
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Ex 4: Add Polynomials & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Additional Example 6
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Ex 5: Subtract Polynomials & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Virtual Nerd™: How Do You Subtract Polynomials?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Ex 1: Understand Polynomials & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Virtual Nerd™: What's the Standard Form of a Polynomial?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Lesson Quiz
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: MathXL for School: Additional Practice
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: MathXL for School: Enrichment
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Virtual Nerd™: What's the Standard Form of a Polynomial?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-1: Virtual Nerd™: How Do You Subtract Polynomials?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            Multiplying Polynomials

               Interactive Student Edition: Realize Reader: Lesson 7-2
                 Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

               Explore

                  7-2: Model & Discuss
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. 

               Understand and Apply

                  7-2: Ex 1: Multiply a Monomial and a Trinomial & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Ex 2: Use a Table to Find the Product of Polynomials & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Additional Example 2
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Ex 3: Multiply Binomials & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Ex 4: Multiply a Trinomial and a Binomial & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Ex 5: Closure and Multiplication & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Ex 6: Apply Multiplication of Binomials & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Additional Example 6 with Try Another One
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Concept Summary
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Do You Understand?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Do You Know How?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

               Practice and Problem-Solving

                  7-2: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: MathXL for School: Mixed Review
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

               Assess & Differentiate

                  7-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: MathXL for School: Enrichment
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Ex 4: Multiply a Trinomial and a Binomial & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Virtual Nerd™: How Do You Multiply a Binomial and a Trinomial Using the Grid Method?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Lesson Quiz
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: MathXL for School: Additional Practice
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: MathXL for School: Enrichment
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Virtual Nerd™: How Do You Multiply a Binomial and a Trinomial Using the Grid Method?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-2: Virtual Nerd™: How Do You Multiply Binomials Using the Distributive Property?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            Multiplying Special Cases

               Interactive Student Edition: Realize Reader: Lesson 7-3
                 Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

               Explore

                  7-3: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. 

               Understand and Apply

                  7-3: Ex 1: Determine the Square of a Binomial & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Additional Example 1C with Try Another One
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Ex 2: Find the Product of a Sum and a Difference & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Ex 3: Apply the Square of a Binomial & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Additional Example 3
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Concept Summary
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Do You Understand?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Do You Know How?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

               Practice and Problem-Solving

                  7-3: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: MathXL for School: Mixed Review
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

               Assess & Differentiate

                  7-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: MathXL for School: Enrichment
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Ex 2: Find the Product of a Sum and a Difference & Try It!
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Virtual Nerd™: What's the Formula for the Product of a Sum and a Difference?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Lesson Quiz
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: MathXL for School: Additional Practice
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: MathXL for School: Enrichment
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Virtual Nerd™: What's the Formula for the Product of a Sum and a Difference?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

                  7-3: Virtual Nerd™: How Do You Use the Formula for the Product of a Sum and a Difference?
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            Factoring Polynomials

               Interactive Student Edition: Realize Reader: Lesson 7-4
                 Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

               Explore

                  7-4: Model & Discuss
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

               Understand and Apply

                  7-4: Ex 1: Find the Greatest Common Factor & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: Ex 2: Factor Out the Greatest Common Factor & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: Additional Example 2 with Try Another One
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: Ex 3: Factor a Polynomial Model & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ² ²). 

                  7-4: Additional Example 3A
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: Concept Summary
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: Do You Understand?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: Do You Know How?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

               Practice and Problem-Solving

                  7-4: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: MathXL for School: Mixed Review
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

               Assess & Differentiate

                  7-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ² ²). 

                  7-4: MathXL for School: Enrichment
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: Ex 3: Factor a Polynomial Model & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: Virtual Nerd™: How Do You Factor the Greatest Common Factor Out of Monomials?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: Lesson Quiz
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: MathXL for School: Additional Practice
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: MathXL for School: Enrichment
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ² ²). 

                  7-4: Virtual Nerd™: How Do You Factor the Greatest Common Factor Out of Monomials?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-4: Virtual Nerd™: How Do You Factor the Greatest Common Factor out of a Polynomial?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            Factor ??² + ???? + ??

               Interactive Student Edition: Realize Reader: Lesson 7-5
                 Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

               Explore

                  7-5: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Interpret parts of an expression, such as terms, factors, and coefficients. 

               Understand and Apply

                  7-5: Ex 1: Understand Factoring a Trinomial & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Additional Example 1B
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Ex 2: Factor x² + ???? + c , When ?? < 0 and ?? > 0 & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Ex 3: Factor x² + ???? + c , When ?? < 0 & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Additional Example 3 with Try Another One
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Ex 4: Factor ?? Trinomial With Two Variables & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Ex 5: Apply Factoring Trinomials & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Concept Summary
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Do You Understand?
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Do You Know How?
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

               Practice and Problem-Solving

                  7-5: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: MathXL for School: Mixed Review
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

               Assess & Differentiate

                  7-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Ex 1: Understand Factoring a Trinomial & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Virtual Nerd™: How Do You Factor a Trinomial?
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Lesson Quiz
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: MathXL for School: Additional Practice
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: MathXL for School: Enrichment
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-5: Virtual Nerd™: How Do You Factor a Trinomial?
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: Virtual Nerd™: How Do You Factor a Perfect Square Trinomial by Guess and Check?
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

            Mathematical Modeling in 3 Acts: Who's Right?

               Topic 7: Who's Right? - Act 1 Video with Questions

               Topic 7: Who's Right? - Act 2 Content

               Topic 7: Who's Right? - Act 2 Questions

               Topic 7: Who's Right? - Act 3 Video

               Topic 7: Who's Right? - Act 3 Questions

            Factoring ????² + ???? + ??

               Interactive Student Edition: Realize Reader: Lesson 7-6
                 Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

               Explore

                  7-6: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Interpret parts of an expression, such as terms, factors, and coefficients. 

               Understand and Apply

                  7-6: Ex 1: Factor Out a Common Factor & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-6: Additional Example 1 with Try Another One
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-6: Ex 2: Understand Factoring by Grouping & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-6: Additional Example 2
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-6: Ex 3: Factor ?? Trinomial Using Substitution & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-6: Concept Summary
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-6: Do You Understand?
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-6: Do You Know How?
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

               Practice and Problem-Solving

                  7-6: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-6: MathXL for School: Mixed Review
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Interpret parts of an expression, such as terms, factors, and coefficients. 

               Assess & Differentiate

                  7-6: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-6: Ex 1: Factor Out a Common Factor & Try It!
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-6: Virtual Nerd™: How Do You Factor a Common Factor Out Of a Difference of Squares?
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-6: Lesson Quiz
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  7-6: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-6: MathXL for School: Additional Practice
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-6: Virtual Nerd™: How Do You Factor a Common Factor Out Of a Difference of Squares?
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

                  7-6: Virtual Nerd™: How Do You Factor a Polynomial by Guessing and Checking?
                    Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

            Factoring Special Cases

               Interactive Student Edition: Realize Reader: Lesson 7-7
                 Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

               Explore

                  7-7: Critique & Explain
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Interpret complicated expressions by viewing one or more of their parts as a single entity. Example: 
For example, interpret ??(1+??)n as the product of ?? and a factor not depending on ??. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. 

               Understand and Apply

                  7-7: Ex 1: Understand Factoring a Perfect Square & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Ex 2: Factor to Find a Dimension & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Ex 3: Factor a Difference of Two Squares & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Additional Example 3 with Try Another One
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Ex 4: Factor Out a Common Factor & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Additional Example 4
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Concept Summary
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Do You Understand?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Do You Know How?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

               Practice and Problem-Solving

                  7-7: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: MathXL for School: Mixed Review
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

               Assess & Differentiate

                  7-7: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: MathXL for School: Enrichment
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Ex 3: Factor a Difference of Two Squares & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Additional Example 3 with Try Another One
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Ex 1: Understand Factoring a Perfect Square & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Virtual Nerd™: How Do You Determine if You Have a Perfect Square Trinomial?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Ex 2: Factor to Find a Dimension & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Lesson Quiz
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: MathXL for School: Additional Practice
                    Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: MathXL for School: Enrichment
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Virtual Nerd™: How Do You Determine if You Have a Perfect Square Trinomial?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

                  7-7: Virtual Nerd™: What is a Perfect Square Trinomial?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            Topic 7: MathXL for School: Topic Review
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

            Topic 7: Performance Assessment Form A
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Interpret parts of an expression, such as terms, factors, and coefficients. 

            7-5: Ex 1: Understand Factoring a Trinomial & Try It!
              Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

            7-5: Virtual Nerd™: How Do You Factor a Trinomial?
              Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

            7-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

            7-1: Ex 4: Add Polynomials & Try It!
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-1: Additional Example 6
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-1: MathXL for School: Enrichment
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-1: Ex 5: Subtract Polynomials & Try It!
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-1: Virtual Nerd™: How Do You Subtract Polynomials?
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-7: Ex 3: Factor a Difference of Two Squares & Try It!
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: Additional Example 3 with Try Another One
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: MathXL for School: Enrichment
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: Ex 1: Understand Factoring a Perfect Square & Try It!
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: Virtual Nerd™: How Do You Determine if You Have a Perfect Square Trinomial?
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-2: Ex 4: Multiply a Trinomial and a Binomial & Try It!
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-2: Virtual Nerd™: How Do You Multiply Binomials Using the Distributive Property?
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-3: MathXL for School: Enrichment
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-4: Ex 3: Factor a Polynomial Model & Try It!
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-4: Virtual Nerd™: How Do You Factor the Greatest Common Factor Out of Monomials?
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-4: MathXL for School: Enrichment
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: Ex 2: Factor to Find a Dimension & Try It!
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ² ²)(??² + ??²). 

            7-1: Ex 1: Understand Polynomials & Try It!
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-1: Virtual Nerd™: What's the Standard Form of a Polynomial?
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            Topic 7: Assessment Form A
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

            7-1: Ex 1: Understand Polynomials & Try It!
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-1: Virtual Nerd™: What's the Standard Form of a Polynomial?
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-1: Ex 5: Subtract Polynomials & Try It!
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-1: Virtual Nerd™: How Do You Subtract Polynomials?
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-2: Ex 4: Multiply a Trinomial and a Binomial & Try It!
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-2: Virtual Nerd™: How Do You Multiply Binomials Using the Distributive Property?
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-3: MathXL for School: Enrichment
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

            7-4: Ex 3: Factor a Polynomial Model & Try It!
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-4: Virtual Nerd™: How Do You Factor the Greatest Common Factor Out of Monomials?
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-4: MathXL for School: Enrichment
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-5: Ex 1: Understand Factoring a Trinomial & Try It!
              Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

            7-5: Virtual Nerd™: How Do You Factor a Trinomial?
              Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

            7-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

            7-7: Ex 1: Understand Factoring a Perfect Square & Try It!
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: Virtual Nerd™: How Do You Determine if You Have a Perfect Square Trinomial?
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: Ex 3: Factor a Difference of Two Squares & Try It!
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: Additional Example 3 with Try Another One
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: MathXL for School: Enrichment
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            7-7: Ex 2: Factor to Find a Dimension & Try It!
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

            Topic 7: Assessment Form C
              Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

         Quadratic Functions

            Interactive Student Edition: Realize Reader: Topic 8

            3-2: Ex 1: Evaluate Functions in Function Notation & Try It!
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

            3-2: Virtual Nerd™: What is Function Notation?
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

            3-1: Ex 3: Classify Relations and Functions & Try It!
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: MathXL for School: Enrichment
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-2: Ex 4: Apply Linear Functions & Try It!
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

            3-2: Additional Example 2
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-2: Ex 2: Write a Linear Function Rule & Try It!
              Curriculum Standards: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-4: Ex 1: Connect Sequences and Functions & Try It!
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

            3-4: MathXL for School: Enrichment
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            2-8: Example 1
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 

            3-3: Example 1 & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            3-3: Virtual Nerd™: How Do You Find the Rate of Change Between Two Points on a Graph?
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            2-8: Virtual Nerd™: What's the Y-Intercept?
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 

            Topic 8: Readiness Assessment
              Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            Topic 8: enVision STEM Project

               Topic 8: enVision STEM Video
                 Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            Key Features of a Quadratic Function

               Interactive Student Edition: Realize Reader: Lesson 8-1
                 Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

               Explore

                  8-1: Explore & Reason
                    Curriculum Standards: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

               Understand and Apply

                  8-1: Ex 1: Identify a Quadratic Parent Function & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  8-1: Ex 2: Understand the Graph of f(??) = ????² and Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  8-1: Additional Example 2 with Try Another One
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  8-1: Ex 3: Interpret Quadratic Functions from Tables & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  8-1: Ex 4: Apply Quadratic Functions & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  8-1: Additional Example 4
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  8-1: Ex 5: Compare the Rate of Change & Try It!
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  8-1: Concept Summary
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 

                  8-1: Do You Understand?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  8-1: Do You Know How?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

               Practice and Problem-Solving

                  8-1: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  8-1: MathXL for School: Mixed Review
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

               Assess & Differentiate

                  8-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  8-1: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  8-1: Ex 5: Compare the Rate of Change & Try It!
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  8-1: Ex 2: Understand the Graph of f(??) = ????² and Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  8-1: Ex 3: Interpret Quadratic Functions from Tables & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  8-1: Virtual Nerd™: How Do You Graph the Parent Quadratic Function y=x2?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  5-4: Example 1 & Try It!
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  5-5: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Addition Method?
                    Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

                  8-1: Lesson Quiz
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  8-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  8-1: MathXL for School: Additional Practice
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  8-1: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  8-1: Virtual Nerd™: What is a Quadratic Function?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  8-1: Virtual Nerd™: How Do You Graph the Parent Quadratic Function y=x2?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            Quadratic Functions in Vertex Form

               Interactive Student Edition: Realize Reader: Lesson 8-2
                 Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

               Explore

                  8-2: Critique & Explain
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 

               Understand and Apply

                  8-2: Ex 1: Understand the Graph of ??(??) = ??² + ?? & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  8-2: Additional Example 1 with Try Another One
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  8-2: Ex 2: Understand the Graph of ??(??) = (?? - h)² & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  8-2: Ex 3: Understand the Graph of f(??) = )  (?? - h)² + ?? & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  8-2: Ex 4: Graph Using Vertex Form & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: Ex 5: Use Vertex Form to Solve Problems & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: Additional Example 5
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: Concept Summary
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: Do You Understand?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: Do You Know How?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

               Practice and Problem-Solving

                  8-2: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: MathXL for School: Mixed Review
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

               Assess & Differentiate

                  8-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  8-2: Ex 3: Understand the Graph of f(??) = ?? (?? - h)² + ?? & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  8-2: Ex 1: Understand the Graph of ??(??) = ??² + ?? & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  8-2: Ex 4: Graph Using Vertex Form & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: Virtual Nerd™: What is Vertex Form of a Quadratic Equation?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: Lesson Quiz
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: MathXL for School: Additional Practice
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  8-2: Virtual Nerd™: What is Vertex Form of a Quadratic Equation?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-2: Virtual Nerd™: How Do You Graph a Quadratic Equation in Vertex Form?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            Quadratic Functions in Standard Form

               Interactive Student Edition: Realize Reader: Lesson 8-3
                 Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

               Explore

                  8-3: Explore & Reason
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Factor a quadratic expression to reveal the zeros of the function it defines. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

               Understand and Apply

                  8-3: Ex 1: Relate c to the Graph of f(??) = ????² + ???? + ?? & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Additional Example 1 with Try Another One
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Concept: Standard Form of a Quadratic Equation
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 

                  8-3: Ex 2: Graph a Quadratic Function in Standard Form & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Additional Example 2
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Ex 3: Compare Properties of Quadratic Functions & Try It!
                    Curriculum Standards: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

                  8-3: Ex 4: Analyze the Structure of Different Forms & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Concept Summary
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Do You Understand?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Do You Know How?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

               Practice and Problem-Solving

                  8-3: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: MathXL for School: Mixed Review
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

               Assess & Differentiate

                  8-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  8-3: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Ex 1: Relate c to the Graph of f(??) = ????² + ???? + ?? & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Ex 4: Analyze the Structure of Different Forms & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Ex 3: Compare Properties of Quadratic Functions & Try It!
                    Curriculum Standards: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

                  8-3: Virtual Nerd™: What is the Standard Form of a Quadratic?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

                  8-3: Lesson Quiz
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  8-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  8-3: MathXL for School: Additional Practice
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

                  8-3: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Virtual Nerd™: What is the Standard Form of a Quadratic?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

                  8-3: Virtual Nerd™: How Do You Graph a Quadratic Function?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

            Modeling With Quadratic Functions

               Interactive Student Edition: Realize Reader: Lesson 8-4
                 Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Informally assess the fit of a function by plotting and analyzing residuals. 

               Explore

                  8-4: Model & Discuss
                    Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Informally assess the fit of a function by plotting and analyzing residuals. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. 

               Understand and Apply

                  8-4: Ex 1: Use Quadratic Functions to Model Area & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  8-4: Additional Example 1 with Try Another One
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  8-4: Concept: Vertical Motion Model
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  8-4: Ex 2: Model Vertical Motion & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  8-4: Additional Example 2
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  8-4: Ex 3: Assess the Fit of a Function by Analyzing Residuals & Try It!
                    Curriculum Standards: Informally assess the fit of a function by plotting and analyzing residuals. 

                  8-4: Ex 4: Fit a Quadratic Function to Data & Try It!
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  8-4: Concept Summary
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Informally assess the fit of a function by plotting and analyzing residuals. 

                  8-4: Do You Understand?
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Informally assess the fit of a function by plotting and analyzing residuals. 

                  8-4: Do You Know How?
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Informally assess the fit of a function by plotting and analyzing residuals. 

               Practice and Problem-Solving

                  8-4: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. Informally assess the fit of a function by plotting and analyzing residuals. 

                  8-4: MathXL for School: Mixed Review
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Informally assess the fit of a function by plotting and analyzing residuals. 

               Assess & Differentiate

                  8-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

                  8-4: MathXL for School: Enrichment
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-4: Ex 1: Use Quadratic Functions to Model Area & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  8-4: Ex 3: Assess the Fit of a Function by Analyzing Residuals & Try It!
                    Curriculum Standards: Informally assess the fit of a function by plotting and analyzing residuals. 

                  8-4: Ex 4: Fit a Quadratic Function to Data & Try It!
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  8-4: Lesson Quiz
                    Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

                  8-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

                  8-4: MathXL for School: Additional Practice
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Informally assess the fit of a function by plotting and analyzing residuals. 

                  8-4: MathXL for School: Enrichment
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-4: Virtual Nerd™: How do you solve for the displacement of an object that rises and falls near Earth, given initial upward velocity, and time?
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Informally assess the fit of a function by plotting and analyzing residuals. 

            Mathematical Modeling in 3 Acts: The Long Shot

               Topic 8: The Long Shot - Act 1 Video with Questions
                 Curriculum Standards: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). 

               Topic 8: The Long Shot - Act 2 Content
                 Curriculum Standards: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). 

               Topic 8: The Long Shot - Act 2 Questions

               Topic 8: The Long Shot - Act 3 Video
                 Curriculum Standards: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). 

               Topic 8: The Long Shot - Act 3 Questions

            Linear, Exponential, and Quadratic Models

               Interactive Student Edition: Realize Reader: Lesson 8-5
                 Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

               Explore

                  8-5: Model & Discuss
                    Curriculum Standards: Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

               Understand and Apply

                  8-5: Ex 1: Determine Which Function Type Represents Data & Try It!
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 

                  8-5: Additional Example 1 with Try Another One
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 

                  8-5: Ex 2: Choose a Function Type for Real-World Data & Try It!
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  8-5: Additional Example 2
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  8-5: Ex 3: Compare Linear, Exponential, and Quadratic Growth & Try It!
                    Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

                  8-5: Concept Summary
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 

                  8-5: Do You Understand?
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

                  8-5: Do You Know How?
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

               Practice and Problem-Solving

                  8-5: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

                  8-5: MathXL for School: Mixed Review
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

               Assess & Differentiate

                  8-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  8-5: MathXL for School: Enrichment
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  8-5: Ex 1: Determine Which Function Type Represents Data & Try It!
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 

                  8-5: Ex 3: Compare Linear, Exponential, and Quadratic Growth & Try It!
                    Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

                  8-5: Virtual Nerd™: How Do You Determine if a Graph Represents a Linear, Exponential, or Quadratic Function?
                    Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

                  8-5: Lesson Quiz
                    Curriculum Standards: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 

                  8-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  8-5: MathXL for School: Additional Practice
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

                  8-5: MathXL for School: Enrichment
                    Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

                  8-5: Virtual Nerd™: How Do You Determine if a Graph Represents a Linear, Exponential, or Quadratic Function?
                    Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

            Topic 8: MathXL for School: Topic Review
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph linear and quadratic functions and show intercepts, maxima, and minima. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Informally assess the fit of a function by plotting and analyzing residuals. 

            Topic 8: Performance Assessment Form A
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Graph linear and quadratic functions and show intercepts, maxima, and minima. Informally assess the fit of a function by plotting and analyzing residuals. 

            8-4: Ex 1: Use Quadratic Functions to Model Area & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

            8-1: Ex 2: Understand the Graph of f(??) = ????² and Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??((?) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            8-1: Virtual Nerd™: How Do You Graph the Parent Quadratic Function y=x2?
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            8-1: MathXL for School: Enrichment
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            8-1: Ex 5: Compare the Rate of Change & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            8-1: Ex 3: Interpret Quadratic Functions from Tables & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            8-2: Ex 3: Understand the Graph of f(??) = ?? (?? - h)² + ?? & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            8-2: Ex 2: Understand the Graph of ??(??) = (?? - h)² & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            8-3: Ex 2: Graph a Quadratic Function in Standard Form & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            8-3: Additional Example 1 with Try Another One
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            8-3: Additional Example 2
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            8-3: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            8-4: Additional Example 1 with Try Another One
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            8-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

            8-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

            8-4: MathXL for School: Enrichment
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            8-3: Ex 3: Compare Properties of Quadratic Functions & Try It!
              Curriculum Standards: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

            8-3: Virtual Nerd™: How Do You Graph a Quadratic Function?
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

            8-4: Ex 4: Fit a Quadratic Function to Data & Try It!
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

            8-4: Ex 3: Assess the Fit of a Function by Analyzing Residuals & Try It!
              Curriculum Standards: Informally assess the fit of a function by plotting and analyzing residuals. 

            8-5: Ex 3: Compare Linear, Exponential, and Quadratic Growth & Try It!
              Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

            8-5: Virtual Nerd™: How Do You Determine if a Graph Represents a Linear, Exponential, or Quadratic Function?
              Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

            8-5: Ex 1: Determine Which Function Type Represents Data & Try It!
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 

            8-5: Additional Example 1 with Try Another One
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 

            Topic 8: Assessment Form A
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            8-1: Ex 2: Understand the Graph of f(??) = ????² and Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            8-1: Virtual Nerd™: How Do You Graph the Parent Quadratic Function y=x2?
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            8-1: MathXL for School: Enrichment
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            8-1: Ex 5: Compare the Rate of Change & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            8-1: Ex 3: Interpret Quadratic Functions from Tables & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            8-2: Ex 3: Understand the Graph of f(??) = ?? (?? - h)² + ?? & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            8-2: Ex 2: Understand the Graph of ??(??) = (?? - h)² & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            8-3: Ex 2: Graph a Quadratic Function in Standard Form & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            8-3: Additional Example 1 with Try Another One
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            8-3: Additional Example 2
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            8-3: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            8-4: Ex 1: Use Quadratic Functions to Model Area & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

            8-4: Additional Example 1 with Try Another One
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            8-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

            8-4: MathXL for School: Enrichment
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            8-3: Ex 3: Compare Properties of Quadratic Functions & Try It!
              Curriculum Standards: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

            8-3: Virtual Nerd™: How Do You Graph a Quadratic Function?
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

            8-4: Ex 4: Fit a Quadratic Function to Data & Try It!
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

            8-4: Ex 3: Assess the Fit of a Function by Analyzing Residuals & Try It!
              Curriculum Standards: Informally assess the fit of a function by plotting and analyzing residuals. 

            8-5: Ex 3: Compare Linear, Exponential, and Quadratic Growth & Try It!
              Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

            8-5: Virtual Nerd™: How Do You Determine if a Graph Represents a Linear, Exponential, or Quadratic Function?
              Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

            8-5: Ex 1: Determine Which Function Type Represents Data & Try It!
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 

            8-5: Additional Example 1 with Try Another One
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 

            8-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

            Topic 8: Assessment Form C
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph linear and quadratic functions and show intercepts, maxima, and minima. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Informally assess the fit of a function by plotting and analyzing residuals. 

         10-4: Ex 3: Combine Translations & Try It!
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         2-3: Ex 1: Understand Standard Form of a Linear Equation & Try It!
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         1-6: Ex 1: Understand Compound Inequalities & Try It!
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         6-4: Ex 2: Write the Recursive Formula For a Sequence & Try It!
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         10-3: Ex 2: Analyze Maximum and Minimum Values & Try It!
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         7-5: Ex 1: Understand Factoring a Trinomial & Try It!
           Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

         2-3: Virtual Nerd™: How Do You Write an Equation of a Line in Standard Form from a Word Problem?
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         9-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         10-3: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         1-6: MathXL for School: Enrichment
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         10-3: MathXL for School: Enrichment
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         10-4: Virtual Nerd™: What Does the Constant '??' Do in the Function ??(??)=v(??)+???
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         7-5: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

         1-6: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         1-6: Virtual Nerd™: How Do You Solve an AND Compound Inequality and Graph It On a Number Line?
           Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

         6-4: Additional Example 2 with Try Another One
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         4-3: MathXL for School: Enrichment
           Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

         7-5: Virtual Nerd™: How Do You Factor a Trinomial?
           Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

         8-4: Ex 4: Fit a Quadratic Function to Data & Try It!
           Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

         10-4: Ex 2: Analyze Horizontal Translations & Try It!
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         3-6: Ex 2: Understand Correlation Coefficients & Try It!
           Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

         8-5: Ex 1: Determine Which Function Type Represents Data & Try It!
           Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 

         7-4: Ex 3: Factor a Polynomial Model & Try It!
           Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

         4-3: Ex 1: Solve a System of Equations by Adding & Try It!
           Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

         7-2: Ex 4: Multiply a Trinomial and a Binomial & Try It!
           Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

         8-4: Ex 1: Use Quadratic Functions to Model Area & Try It!
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

         8-5: Ex 3: Compare Linear, Exponential, and Quadratic Growth & Try It!
           Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

         8-1: Ex 2: Understand the Graph of f(??) = ????² and Try It!
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         8-4: Ex 3: Assess the Fit of a Function by Analyzing Residuals & Try It!
           Curriculum Standards: Informally assess the fit of a function by plotting and analyzing residuals. 

         7-7: Ex 1: Understand Factoring a Perfect Square & Try It!
           Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

         7-1: Ex 5: Subtract Polynomials & Try It!
           Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

         5-3: Ex 2: Use a Step Function to Represent a Real-World Situation & Try It!
           Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

         6-3: Ex 2: Exponential Models of Growth & Try It!
           Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

         8-1: Ex 5: Compare the Rate of Change & Try It!
           Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

         9-4: Ex 4: Determine a Reasonable Solution & Try It!
           Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         8-4: MathXL for School: Enrichment
           Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

         3-6: Virtual Nerd™: What is the Correlation Coefficient?
           Curriculum Standards: Compute (using technology) and interpret the correlation coefficient of a linear fit. 

         10-4: Virtual Nerd™: What Does the Constant 'h' Do in the Function ??(??)=v(??-h)?
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         4-3: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

         4-3: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
           Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

         7-1: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

         6-3: Virtual Nerd™: What is Exponential Growth?
           Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

         6-3: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

         7-1: Virtual Nerd™: How Do You Subtract Polynomials?
           Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

         6-3: MathXL for School: Enrichment
           Curriculum Standards: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

         8-1: Virtual Nerd™: How Do You Graph the Parent Quadratic Function y=x2?
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         7-2: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

         8-5: Additional Example 1 with Try Another One
           Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 

         10-4: MathXL for School: Enrichment
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         10-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         5-3: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

         8-5: Virtual Nerd™: How Do You Determine if a Graph Represents a Linear, Exponential, or Quadratic Function?
           Curriculum Standards: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 

         7-3: MathXL for School: Enrichment
           Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

         7-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

         8-1: MathXL for School: Enrichment
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         8-4: Additional Example 1 with Try Another One
           Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         5-3: MathXL for School: Enrichment
           Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

         7-7: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

         7-4: Virtual Nerd™: How Do You Factor the Greatest Common Factor Out of Monomials?
           Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

         7-4: MathXL for School: Enrichment
           Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

         7-7: Virtual Nerd™: How Do You Determine if You Have a Perfect Square Trinomial?
           Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ² ²)(??² + ??²). 

         8-5: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

         7-2: Virtual Nerd™: How Do You Multiply Binomials Using the Distributive Property?
           Curriculum Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

         8-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: 
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 

         5-3: Virtual Nerd™: What is a Step Function?
           Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

         Benchmark Test 3
           Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Compute (using technology) and interpret the correlation coefficient of a linear fit. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Informally assess the fit of a function by plotting and analyzing residuals. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Interpret parts of an expression, such as terms, factors, and coefficients. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         Solving Quadratic Equations

            Interactive Student Edition: Realize Reader: Topic 9

            4-2: Ex 1: Solve Systems of Equations Using Substitution & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: Virtual Nerd™: What is Another Way of Solving a System of Equations Using the Substitution Method?
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-3: MathXL for School: Enrichment
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            6-1: Ex 1: Write Radicals Using Rational Exponents & Try It!
              Curriculum Standards: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

            6-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

            2-2: Ex 1: Understand Point-Slope Form of a Linear Equation & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            4-3: Ex 1: Solve a System of Equations by Adding & Try It!
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            4-3: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            4-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            2-3: Ex 1: Understand Standard Form of a Linear Equation & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-3: Virtual Nerd™: How Do You Write an Equation of a Line in Standard Form from a Word Problem?
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            7-5: Ex 1: Understand Factoring a Trinomial & Try It!
              Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

            7-5: Virtual Nerd™: How Do You Factor a Trinomial?
              Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

            7-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

            1-1: Ex 3: Operations With Rational Numbers & Try It!
              Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            1-4: Ex 1: Rewrite Literal Equations & Try It!
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-4: Virtual Nerd™: How Do You Solve a Formula for a Variable?
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            1-4: MathXL for School: Enrichment
              Curriculum Standards: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. 

            3-2: Ex 4: Apply Linear Functions & Try It!
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

            3-2: Additional Example 2
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            3-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 

            2-2: Ex 2: Write an Equation in Point-Slope Form & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-2: Virtual Nerd™: How do you write an equation of a line in point-slope form if you have the slope and one point?
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: Ex 2: Write an Equation from a Graph & Try It!
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: Virtual Nerd™: How Do You Write an Equation of a Line in Slope-Intercept Form if You Have a Graph?
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            2-1: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            1-2: Ex 1: Solve Linear Equations & Try It!
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            1-2: Virtual Nerd™: How Do You Solve a Two-Step Equation with Fractions by Multiplying Away the Fraction?
              Curriculum Standards: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

            Topic 9: Readiness Assessment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. Interpret parts of an expression, such as terms, factors, and coefficients. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            Topic 9: enVision STEM Project

               Topic 9: enVision STEM Video
                 Curriculum Standards: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??² + 9?? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?? – ??)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?? and ??. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: 
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Interpret parts of an expression, such as terms, factors, and coefficients. 

            Solving Quadratic Equations Using Graphs and Tables

               Interactive Student Edition: Realize Reader: Lesson 9-1
                 Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

               Explore

                  9-1: Explore & Reason

               Understand and Apply

                  9-1: Ex 1: Recognize Solutions of Quadratic Equations & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-1: Additional Example 1 with Try Another One
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-1: Ex 2: Solve Quadratic Equations Using Tables & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  9-1: Ex 3: Use Approximate Solutions & Try It!
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 

                  9-1: Additional Example 3
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 

                  9-1: Concept Summary
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  9-1: Do You Understand?
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  9-1: Do You Know How?
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

               Practice and Problem-Solving

                  9-1: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  9-1: MathXL for School: Mixed Review
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

               Assess & Differentiate

                  9-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  9-1: MathXL for School: Enrichment
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  8-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  8-3: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  9-1: Ex 2: Solve Quadratic Equations Using Tables & Try It!
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  9-1: Virtual Nerd™: How Do You Solve a Word Problem by Graphing a Quadratic Equation?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  8-2: MathXL for School: Enrichment
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  8-3: Ex 2: Graph a Quadratic Function in Standard Form & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Additional Example 1 with Try Another One
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  8-3: Additional Example 2
                    Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  9-1: Ex 3: Use Approximate Solutions & Try It!
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations -c = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 

                  9-1: Additional Example 3
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 

                  8-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  9-1: Lesson Quiz
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

                  9-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  9-1: MathXL for School: Additional Practice
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  9-1: MathXL for School: Enrichment
                    Curriculum Standards: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-1: Virtual Nerd™: How Do You Solve a Word Problem by Graphing a Quadratic Equation?
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

                  9-1: Virtual Nerd™: How Do You Solve a Quadratic Equation With Two Solutions by Graphing?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            Solving Quadratic Equations by Factoring

               Interactive Student Edition: Realize Reader: Lesson 9-2
                 Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Factor a quadratic expression to reveal the zeros of the function it defines. 

               Explore

                  9-2: Model & Discuss

               Understand and Apply

                  9-2: Ex 1: Use the Zero-Product Property & Try It!
                    Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

                  9-2: Additional Example 1 with Try Another One
                    Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

                  9-2: Ex 2: Solve by Factoring & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-2: Ex 3: Use Factoring to Solve a Real-World Problem & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-2: Additional Example 3
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-2: Ex 4: Use Factored Form to Graph a Quadratic Function & Try It!
                    Curriculum Standards: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 

                  9-2: Ex 5: Write the Factored Form of a Quadratic Function & Try It!
                    Curriculum Standards: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 

                  9-2: Concept Summary
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Factor a quadratic expression to reveal the zeros of the function it defines. 

                  9-2: Do You Understand?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Factor a quadratic expression to reveal the zeros of the function it defines. 

                  9-2: Do You Know How?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Factor a quadratic expression to reveal the zeros of the function it defines. 

               Practice and Problem-Solving

                  9-2: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Factor a quadratic expression to reveal the zeros of the function it defines. 

                  9-2: MathXL for School: Mixed Review
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Graph linear and quadratic functions and show intercepts, maxima, and minima. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

               Assess & Differentiate

                  9-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-2: MathXL for School: Enrichment
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-2: Ex 1: Use the Zero-Product Property & Try It!
                    Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

                  9-2: Additional Example 1 with Try Another One
                    Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

                  9-2: Virtual Nerd™: What's the Zero Product Property?
                    Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

                  9-2: Ex 2: Solve by Factoring & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-2: Virtual Nerd™: How Do You Solve a Word Problem by Factoring a Quadratic Equation?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-2: Lesson Quiz
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Factor a quadratic expression to reveal the zeros of the function it defines. 

                  9-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-2: MathXL for School: Additional Practice
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 

                  9-2: MathXL for School: Enrichment
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-2: Virtual Nerd™: How Do You Solve a Word Problem by Factoring a Quadratic Equation?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-2: Virtual Nerd™: What's the Zero Product Property?
                    Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

            Rewriting Radical Expressions

               Interactive Student Edition: Realize Reader: Lesson 9-3
                 Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

               Explore

                  9-3: Explore & Reason

               Understand and Apply

                  9-3: Ex 1: Use Properties to Rewrite Radical Expressions & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Ex 2: Write Equivalent Radical Expressions & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Additional Example 2 with Try Another One
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Ex 3: Write Equivalent Radical Expressions With Variables & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Ex 4: Multiply Radical Expressions & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Additional Example 4
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Ex 5: Write a Radical Expression & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Concept Summary
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Do You Understand?
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Do You Know How?
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

               Practice and Problem-Solving

                  9-3: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: MathXL for School: Mixed Review
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

               Assess & Differentiate

                  9-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: MathXL for School: Enrichment
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Ex 4: Multiply Radical Expressions & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Virtual Nerd™: How Do You Multiply Two Radicals?
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Ex 4: Use the Power of a Product Property to Solve Equations With Rational Exponents & Try It!
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: Virtual Nerd™: What are Rational Exponents?
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  6-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

                  6-1: MathXL for School: Enrichment
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Lesson Quiz
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: MathXL for School: Additional Practice
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: MathXL for School: Enrichment
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Virtual Nerd™: How Do You Multiply Two Radicals?
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

                  9-3: Virtual Nerd™: What is the Product Property of Square Roots?
                    Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            Solving Quadratic Equations Using Square Roots

               Interactive Student Edition: Realize Reader: Lesson 9-4
                 Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Explore

                  9-4: Explore & Reason

               Understand and Apply

                  9-4: Ex 1: Solve Equations of the Form ??² = ?? & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-4: Additional Example 1 with Try Another One
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-4: Ex 2: Solve Equations of the Form ??x² = ?? & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-4: Additional Example 2
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-4: Ex 3: Solve Equations of the Form ????² + ?? = ?? & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-4: Ex 4: Determine a Reasonable Solution & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-4: Concept Summary
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-4: Do You Understand?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-4: Do You Know How?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Practice and Problem-Solving

                  9-4: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-4: MathXL for School: Mixed Review
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). 

               Assess & Differentiate

                  9-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-4: MathXL for School: Enrichment
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-4: Ex 4: Determine a Reasonable Solution & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-4: Ex 2: Solve Equations of the Form ??x² = ?? & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-4: Virtual Nerd™: How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions if a?1?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-4: Lesson Quiz
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-4: MathXL for School: Additional Practice
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-4: MathXL for School: Enrichment
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-4: Virtual Nerd™: How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions if a?1?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-4: Virtual Nerd™: What is the Square Root Property?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            Completing the Square

               Interactive Student Edition: Realize Reader: Lesson 9-5
                 Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

               Explore

                  9-5: Critique & Explain

               Understand and Apply

                  9-5: Ex 1: Complete the Square & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-5: Ex 2: Solve ??² + ???? + ?? = 0 & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-5: Ex 3: Complete the Square When a ? 1 Initially & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-5: Additional Example 3 with Try Another One
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-5: Ex 4: Use Completing the Square to Write a Quadratic Function In Vertex Form & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-5: Ex 5: Write Vertex Form When a ? 1 & Try It!
                    Curriculum Standards: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

                  9-5: Additional Example 5
                    Curriculum Standards: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

                  9-5: Concept Summary
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

                  9-5: Do You Understand?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

                  9-5: Do You Know How?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

               Practice and Problem-Solving

                  9-5: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

                  9-5: MathXL for School: Mixed Review
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

               Assess & Differentiate

                  9-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ² ²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-5: MathXL for School: Enrichment
                    Curriculum Standards: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

                  9-5: Ex 2: Solve ??² + ???? + ?? = 0 & Try It!
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-5: Virtual Nerd™: How Do You Solve a Quadratic Equation by Completing the Square?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-5: Ex 5: Write Vertex Form When a ? 1 & Try It!
                    Curriculum Standards: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

                  9-5: Additional Example 5
                    Curriculum Standards: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

                  9-5: Lesson Quiz
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

                  9-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-5: MathXL for School: Additional Practice
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

                  9-5: MathXL for School: Enrichment
                    Curriculum Standards: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

                  9-5: Virtual Nerd™: How Do You Solve a Quadratic Equation by Completing the Square?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-5: Virtual Nerd™: How Do You Solve a Word Problem by Completing the Square?
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

            The Quadratic Formula and the Discriminant

               Interactive Student Edition: Realize Reader: Lesson 9-6
                 Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Explore

                  9-6: Explore & Reason

               Understand and Apply

                  9-6: Ex 1: Derive the Quadratic Formula & Try It!
                    Curriculum Standards: Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-6: Ex 2: Use the Quadratic Formula & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-6: Ex 3: Find Approximate Solutions & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-6: Additional Example 3
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-6: Ex 4: Understand and Use the Discriminant & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-6: Additional Example 4 with Try Another One
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-6: Concept Summary
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-6: Do You Understand?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-6: Do You Know How?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

               Practice and Problem-Solving

                  9-6: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-6: MathXL for School: Mixed Review
                    Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ² ²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 

               Assess & Differentiate

                  9-6: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-6: MathXL for School: Enrichment
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-6: Ex 4: Understand and Use the Discriminant & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-6: Virtual Nerd™: How Do You Use the Discriminant to Determine the Number of Solutions of a Quadratic Equation?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-6: Ex 3: Find Approximate Solutions & Try It!
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  1-3: Virtual Nerd™: How Do You Solve a Word Problem Using an Equation With Variables on Both Sides?
                    Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-6: Ex 2: Use the Quadratic Formula & Try It!
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-6: Lesson Quiz
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-6: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-6: MathXL for School: Additional Practice
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for   ² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

                  9-6: MathXL for School: Enrichment
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

                  9-6: Virtual Nerd™: How was the Quadratic Formula Derived?
                    Curriculum Standards: Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

                  9-6: Virtual Nerd™: How Do You Use the Discriminant to Determine the Number of Solutions of a Quadratic Equation?
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            Mathematical Modeling in 3 Acts: Unwrapping Change

               Topic 9: Unwrapping Change - Act 1 Video With Questions

               Topic 9: Unwrapping Change - Act 2 Content

               Topic 9: Unwrapping Change - Act 2 Questions

               Topic 9: Unwrapping Change - Act 3 Video

               Topic 9: Unwrapping Change - Act 3 Questions

            Solving Systems of Linear and Quadratic Equations

               Interactive Student Edition: Realize Reader: Lesson 9-7
                 Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

               Explore

                  9-7: Model & Discuss

               Understand and Apply

                  9-7: Ex 1: Understand Linear-Quadratic Systems of Equations & Try It!
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Additional Example 1
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Ex 2: Solve a Linear-Quadratic Equation by Graphing & Try It!
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Additional Example 2 with Try Another One
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Ex 3: Solve Systems of Equations Using Elimination & Try It!
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Ex 4: Solve Systems Using Substitution & Try It!
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Concept Summary
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Do You Understand?
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Do You Know How?
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

               Practice and Problem-Solving

                  9-7: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: MathXL for School: Mixed Review
                    Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

               Assess & Differentiate

                  9-7: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: MathXL for School: Enrichment
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Ex 2: Solve a Linear-Quadratic Equation by Graphing & Try It!
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Virtual Nerd™: How Do You Solve a System of Equations by Graphing if One Equation is a Quadratic?
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Ex 1: Understand Linear-Quadratic Systems of Equations & Try It!
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Virtual Nerd™: How Do You Solve a System of Equations Using Elimination if One Equation is a Quadratic?
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Lesson Quiz
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: MathXL for School: Additional Practice
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: MathXL for School: Enrichment
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Virtual Nerd™: How Do You Solve a System of Equations by Graphing if One Equation is a Quadratic?
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

                  9-7: Virtual Nerd™: How Do You Solve a System of Equations Using Elimination if One Equation is a Quadratic?
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            Topic 9: MathXL for School: Topic Review
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ) (??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            Topic 9: Performance Assessment Form A
              Curriculum Standards: Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            9-7: Ex 2: Solve a Linear-Quadratic Equation by Graphing & Try It!
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-7: Virtual Nerd™: How Do You Solve a System of Equations by Graphing if One Equation is a Quadratic?
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-7: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-7: MathXL for School: Enrichment
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-7: Ex 1: Understand Linear-Quadratic Systems of Equations & Try It!
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-7: Virtual Nerd™: How Do You Solve a System of Equations Using Elimination if One Equation is a Quadratic?
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-6: Ex 4: Understand and Use the Discriminant & Try It!
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-6: Virtual Nerd™: How Do You Use the Discriminant to Determine the Number of Solutions of a Quadratic Equation?
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-6: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-6: MathXL for School: Enrichment
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-5: Ex 2: Solve ??² + ???? + ?? = 0 & Try It!
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

            9-5: Virtual Nerd™: How Do You Solve a Quadratic Equation by Completing the Square?
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

            9-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

            9-4: Ex 1: Solve Equations of the Form ??² = ?? & Try It!
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-4: Additional Example 1 with Try Another One
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            8-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            8-3: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            9-4: Ex 4: Determine a Reasonable Solution & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            9-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            9-4: Ex 2: Solve Equations of the Form ??x² = ?? & Try It!
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-4: Virtual Nerd™: How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions if a?1?
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-4: MathXL for School: Enrichment
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-2: Ex 1: Use the Zero-Product Property & Try It!
              Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

            9-2: Additional Example 1 with Try Another One
              Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

            9-2: Virtual Nerd™: What's the Zero Product Property?
              Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

            9-6: Ex 2: Use the Quadratic Formula & Try It!
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-2: Ex 2: Solve by Factoring & Try It!
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-2: Virtual Nerd™: How Do You Solve a Word Problem by Factoring a Quadratic Equation?
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-2: MathXL for School: Enrichment
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            6-1: Ex 4: Use the Power of a Product Property to Solve Equations With Rational Exponents & Try It!
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            6-1: Virtual Nerd™: What are Rational Exponents?
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            6-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

            6-1: MathXL for School: Enrichment
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            8-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            Topic 9: Assessment Form A
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Factor a quadratic expression to reveal the zeros of the function it defines. Rewrite expressions involving radicals and rational exponents using the properties of exponents. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            9-7: Ex 2: Solve a Linear-Quadratic Equation by Graphing & Try It!
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-7: Virtual Nerd™: How Do You Solve a System of Equations by Graphing if One Equation is a Quadratic?
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-7: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-7: MathXL for School: Enrichment
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-7: Ex 1: Understand Linear-Quadratic Systems of Equations & Try It!
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-7: Virtual Nerd™: How Do You Solve a System of Equations Using Elimination if One Equation is a Quadratic?
              Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

            9-6: Ex 4: Understand and Use the Discriminant & Try It!
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-6: Virtual Nerd™: How Do You Use the Discriminant to Determine the Number of Solutions of a Quadratic Equation?
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-6: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-6: MathXL for School: Enrichment
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-5: Ex 2: Solve ??² + ???? + ?? = 0 & Try It!
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

            9-5: Virtual Nerd™: How Do You Solve a Quadratic Equation by Completing the Square?
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

            9-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. 

            9-4: Ex 1: Solve Equations of the Form ??² = ?? & Try It!
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-4: Additional Example 1 with Try Another One
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            8-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            8-3: MathXL for School: Enrichment
              Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            9-4: Ex 4: Determine a Reasonable Solution & Try It!
              Curriculum Standards: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            9-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

            9-4: Ex 2: Solve Equations of the Form ??x² = ?? & Try It!
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-4: Virtual Nerd™: How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions if a?1?
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-4: MathXL for School: Enrichment
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-2: Ex 1: Use the Zero-Product Property & Try It!
              Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

            9-2: Additional Example 1 with Try Another One
              Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

            9-2: Virtual Nerd™: What's the Zero Product Property?
              Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

            9-6: Ex 2: Use the Quadratic Formula & Try It!
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-2: Ex 2: Solve by Factoring & Try It!
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-2: Virtual Nerd™: How Do You Solve a Word Problem by Factoring a Quadratic Equation?
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            9-2: MathXL for School: Enrichment
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

            6-1: Ex 4: Use the Power of a Product Property to Solve Equations With Rational Exponents & Try It!
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            6-1: Virtual Nerd™: What are Rational Exponents?
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            6-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

            6-1: MathXL for School: Enrichment
              Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

            8-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            Topic 9: Assessment Form C
              Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ² ²)(??² + ??²). Use the method of completing the square to transform any quadratic equation in ?? into an equation of the form (?? – ??)² = ?? that has the same solutions. Derive the quadratic formula from this form. Factor a quadratic expression to reveal the zeros of the function it defines. Rewrite expressions involving radicals and rational exponents using the properties of exponents. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         Working With Functions

            Interactive Student Edition: Realize Reader: Topic 10

            5-1: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            4-2: Ex 1: Solve Systems of Equations Using Substitution & Try It!
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: Virtual Nerd™: What is Another Way of Solving a System of Equations Using the Substitution Method?
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-3: MathXL for School: Enrichment
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 

            4-3: Ex 1: Solve a System of Equations by Adding & Try It!
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            4-3: Virtual Nerd™: How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            4-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 

            2-1: Ex 1: Graph a Linear Equation & Try It!
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            2-3: Virtual Nerd™: How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            2-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

            3-2: MathXL for School: Enrichment
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. 

            3-3: Ex 2: Horizontal Translations of Linear Functions & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: Virtual Nerd™: Transforming Linear Functions
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of  ( given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            3-3: MathXL for School: Enrichment
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            8-1: Ex 5: Compare the Rate of Change & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            5-1: Ex 4: Determine Rate of Change & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            5-2: Ex 3: Analyze the Graph of a Piecewise-Defined Function & Try It!
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            5-2: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            3-1: Ex 3: Classify Relations and Functions & Try It!
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            3-1: MathXL for School: Enrichment
              Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

            5-4: Ex 2: Vertical Translations of the Absolute Value Function & Try It!
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-4: Virtual Nerd™: How Do You Write an Equation for a Translation of an Absolute Value Function?
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            5-4: MathXL for School: Enrichment
              Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            Topic 10: Readiness Assessment
              Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            Topic 10: enVision STEM Project

               Topic 10: enVision STEM Video
                 Curriculum Standards: Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Compose functions. Example: 
For example, if ??(??) is the temperature in the atmosphere as a function of height, and ??(??) is the height of a weather balloon as a function of time, then ??(??(??)) is the temperature at the location of the weather balloon as a function of time. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            The Square Root Function

               Interactive Student Edition: Realize Reader: Lesson 10-1
                 Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Explore

                  10-1: Explore & Reason

               Understand and Apply

                  10-1: Ex 1: Key Features of the Square Root Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-1: Additional Example 1 with Try Another One
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-1: Ex 2: Translations of the Square Root Function & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-1: Additional Example 2
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-1: Ex 3: Rate of Change of the Square Root Function & Try It!
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  10-1: Ex 4: Compare Functions & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-1: Concept Summary
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-1: Do You Understand?
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-1: Do You Know How?
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Practice and Problem-Solving

                  10-1: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-1: MathXL for School: Mixed Review
                    Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

               Assess & Differentiate

                  10-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-1: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-1: Ex 2: Translations of the Square Root Function & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-1: Additional Example 2
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-1: Ex 3: Rate of Change of the Square Root Function & Try It!
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  10-1: Virtual Nerd™: How Do You Graph a Square Root Function Using a Table?
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  10-1: Ex 1: Key Features of the Square Root Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-1: Virtual Nerd™: What Does the Parent Function Graph of a Square Root Function Look Like?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-1: Lesson Quiz
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-1: MathXL for School: Additional Practice
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-1: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-1: Virtual Nerd™: What Does the Parent Function Graph of a Square Root Function Look Like?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-1: Virtual Nerd™: How Do You Graph a Square Root Function Using a Table?
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            The Cube Root Function

               Interactive Student Edition: Realize Reader: Lesson 10-2
                 Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Explore

                  10-2: Critique & Explain

               Understand and Apply

                  10-2: Ex 1: Key Features of the Cube Root Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-2: Ex 2: Translations of the Cube Root Function & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: Additional Example 2 with Try Another One
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: Ex 3: Model a Problem Using the Cube Root Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-2: Ex 4: Compare Rates of Change of a Function & Try It!
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  10-2: Additional Example 4
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  10-2: Ex 5: Compare Rates of Change of Two Functions & Try It!
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  10-2: Concept Summary
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: Do You Understand?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: Do You Know How?
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Practice and Problem-Solving

                  10-2: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: MathXL for School: Mixed Review
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Graph linear and quadratic functions and show intercepts, maxima, and minima. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Assess & Differentiate

                  10-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  10-2: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: Ex 1: Key Features of the Cube Root Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-2: Ex 4: Compare Rates of Change of a Function & Try It!
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  10-2: Virtual Nerd™: How Do You Graph a Cube Root Function Using a Table?
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  10-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: Ex 2: Translations of the Cube Root Function & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: Additional Example 2 with Try Another One
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: Ex 3: Model a Problem Using the Cube Root Function & Try It!
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-2: Lesson Quiz
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

                  10-2: MathXL for School: Additional Practice
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-2: Virtual Nerd™: How Do You Graph a Cube Root Function Using a Table?
                    Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            Analyzing Functions Graphically

               Interactive Student Edition: Realize Reader: Lesson 10-3
                 Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Explore

                  10-3: Model & Discuss

               Understand and Apply

                  10-3: Ex 1: Analyze Domain and Range & Try It!
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  10-3: Additional Example 1 with Try Another One
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  10-3: Ex 2: Analyze Maximum and Minimum Values & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Additional Example 2
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Ex 3: Understand Axes of Symmetry & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Ex 4: Analyze End Behaviors of Graphs & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Concept Summary
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Do You Understand?
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Do You Know How?
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

               Practice and Problem-Solving

                  10-3: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

                  10-3: MathXL for School: Mixed Review
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Assess & Differentiate

                  10-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: MathXL for School: Enrichment
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Ex 4: Analyze End Behaviors of Graphs & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Ex 2: Analyze Maximum and Minimum Values & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Ex 3: Understand Axes of Symmetry & Try It!
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Virtual Nerd™: What is the Axis of Symmetry of a Quadratic Function?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Ex 1: Analyze Domain and Range & Try It!
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  10-3: Additional Example 1 with Try Another One
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

                  10-3: Lesson Quiz
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: MathXL for School: Additional Practice
                    Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: MathXL for School: Enrichment
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

                  10-3: Virtual Nerd™: What is the Axis of Symmetry of a Quadratic Function?
                    Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            Translations of Functions

               Interactive Student Edition: Realize Reader: Lesson 10-4
                 Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Explore

                  10-4: Critique & Explain

               Understand and Apply

                  10-4: Ex 1: Vertical Translations & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Additional Example 1 with Try Another One
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Ex 2: Analyze Horizontal Translations & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Additional Example 2
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Ex 3: Combine Translations & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Concept Summary
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Do You Understand?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ) (??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Do You Know How?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Practice and Problem-Solving

                  10-4: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: MathXL for School: Mixed Review
                    Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 

               Assess & Differentiate

                  10-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Ex 2: Analyze Horizontal Translations & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Virtual Nerd™: What Does the Constant 'h' Do in the Function ??(??)=v(??-h)?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Ex 1: Vertical Translations & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Additional Example 1 with Try Another One
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Ex 3: Combine Translations & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Virtual Nerd™: What Does the Constant '??' Do in the Function ??(??)=v(??)+???
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Lesson Quiz
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: MathXL for School: Additional Practice
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Virtual Nerd™: What Does the Constant 'h' Do in the Function ??(??)=v(??-h)?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-4: Virtual Nerd™: What Does the Constant '??' Do in the Function ??(??)=v(??)+???
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            Compressions and Stretches of Functions

               Interactive Student Edition: Realize Reader: Lesson 10-5
                 Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Explore

                  10-5: Explore & Reason

               Understand and Apply

                  10-5: Ex 1: Analyze Reflections Across the ??-Axis & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Ex 2: Analyze Vertical Stretches of Graphs & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Ex 3: Analyze Vertical Compressions of Graphs & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Additional Example 3
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Ex 4: Analyze Horizontal Stretches of Graphs & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Additional Example 4 with Try Another One
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Ex 5: Analyze Horizontal Compressions of Graphs & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Concept Summary
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Do You Understand?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Do You Know How?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

               Practice and Problem-Solving

                  10-5: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: MathXL for School: Mixed Review
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 

               Assess & Differentiate

                  10-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Ex 2: Analyze Vertical Stretches of Graphs & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Additional Example 3
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Ex 4: Analyze Horizontal Stretches of Graphs & Try It!
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Additional Example 4 with Try Another One
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??((?) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Lesson Quiz
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: MathXL for School: Additional Practice
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: MathXL for School: Enrichment
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

                  10-5: Virtual Nerd™: What Does the Value of 'a' Do in the Function ??(??)=av(??)?
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            Mathematical Modeling in 3 Acts: Edgy Tiles

               Topic 10: Edgy Tiles - Act 1 Video With Questions

               Topic 10: Edgy Tiles - Act 2 Content

               Topic 10: Edgy Tiles - Act 2 Questions

               Topic 10: Edgy Tiles - Act 3 Video

               Topic 10: Edgy Tiles - Act 3 Questions

            Operations With Functions

               Interactive Student Edition: Realize Reader: Lesson 10-6
                 Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

               Explore

                  10-6: Explore & Reason

               Understand and Apply

                  10-6: Ex 1: Add and Subtract Functions & Try It!
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Ex 2: Multiply Functions & Try It!
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Additional Example 2 with Try Another One
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Ex 3: Apply Function Operations & Try It!
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Additional Example 3
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Concept Summary
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Do You Understand?
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Do You Know How?
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

               Practice and Problem-Solving

                  10-6: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: MathXL for School: Mixed Review
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Assess & Differentiate

                  10-6: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: MathXL for School: Enrichment
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Ex 1: Add and Subtract Functions & Try It!
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Virtual Nerd™: How Do You Find the Product of Two Functions?
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Lesson Quiz
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: MathXL for School: Additional Practice
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: MathXL for School: Enrichment
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Virtual Nerd™: How Do You Find the Sum of Two Functions?
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

                  10-6: Virtual Nerd™: How Do You Find the Product of Two Functions?
                    Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

            Inverse Functions

               Interactive Student Edition: Realize Reader: Lesson 10-7
                 Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

               Explore

                  10-7: Explore & Reason

               Understand and Apply

                  10-7: Ex 1: Understand Inverse Functions & Try It!
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Ex 2: Graph Inverse Functions & Try It!
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Additional Example 2
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Ex 3: Find the Inverse of a Function Algebraically & Try It!
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Ex 4: Interpret Inverse Functions & Try It!
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Additional Example 4 with Try Another One
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Concept Summary
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Do You Understand?
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Do You Know How?
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

               Practice and Problem-Solving

                  10-7: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: MathXL for School: Mixed Review
                    Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Assess & Differentiate

                  10-7: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: MathXL for School: Enrichment
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Ex 2: Graph Inverse Functions & Try It!
                    Curriculum Standards: Solve an equation of the form ??(??) = )  for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Additional Example 2
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Ex 1: Understand Inverse Functions & Try It!
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Lesson Quiz
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: MathXL for School: Additional Practice
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: MathXL for School: Enrichment
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ³ (??) = (??+1)/(??–1) for ?? ? 1. 

                  10-7: Virtual Nerd™: How Do You Find the Inverse of a Linear Function?
                    Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

            Topic 10: MathXL for School: Topic Review
              Curriculum Standards: Identify the effect on the graph of replacing ??((?) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            Topic 10: Performance Assessment Form A
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

            10-5: Ex 2: Analyze Vertical Stretches of Graphs & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-5: Additional Example 3
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-5: MathXL for School: Enrichment
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-3: Ex 4: Analyze End Behaviors of Graphs & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-3: Ex 2: Analyze Maximum and Minimum Values & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-3: MathXL for School: Enrichment
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-7: Ex 2: Graph Inverse Functions & Try It!
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

            10-7: Additional Example 2
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

            10-7: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

            10-7: MathXL for School: Enrichment
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

            10-3: Ex 3: Understand Axes of Symmetry & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-3: Virtual Nerd™: What is the Axis of Symmetry of a Quadratic Function?
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-4: Ex 1: Vertical Translations & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-4: Additional Example 1 with Try Another One
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-4: Ex 3: Combine Translations & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-4: Virtual Nerd™: What Does the Constant '??' Do in the Function ??(??)=v(??)+???
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-7: Ex 1: Understand Inverse Functions & Try It!
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

            10-3: Ex 1: Analyze Domain and Range & Try It!
              Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            10-3: Additional Example 1 with Try Another One
              Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            10-6: Ex 1: Add and Subtract Functions & Try It!
              Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

            10-6: Virtual Nerd™: How Do You Find the Product of Two Functions?
              Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

            10-6: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

            10-6: MathXL for School: Enrichment
              Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

            10-2: Ex 4: Compare Rates of Change of a Function & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            10-2: Virtual Nerd™: How Do You Graph a Cube Root Function Using a Table?
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            10-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing   (??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-2: Ex 2: Translations of the Cube Root Function & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-2: Additional Example 2 with Try Another One
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ,  ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-2: MathXL for School: Enrichment
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-5: Ex 4: Analyze Horizontal Stretches of Graphs & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-5: Additional Example 4 with Try Another One
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            Topic 10: Assessment Form A
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-3: Ex 4: Analyze End Behaviors of Graphs & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-3: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-3: Ex 2: Analyze Maximum and Minimum Values & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-3: MathXL for School: Enrichment
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-7: Ex 2: Graph Inverse Functions & Try It!
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

            10-7: Additional Example 2
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

            10-7: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

            10-7: MathXL for School: Enrichment
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

            10-3: Ex 3: Understand Axes of Symmetry & Try It!
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-3: Virtual Nerd™: What is the Axis of Symmetry of a Quadratic Function?
              Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

            10-4: Ex 1: Vertical Translations & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-4: Additional Example 1 with Try Another One
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-4: Ex 3: Combine Translations & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-4: Virtual Nerd™: What Does the Constant '??' Do in the Function ??(??)=v(??)+???
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-7: Ex 1: Understand Inverse Functions & Try It!
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

            10-3: Ex 1: Analyze Domain and Range & Try It!
              Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            10-3: Additional Example 1 with Try Another One
              Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

            10-6: Ex 1: Add and Subtract Functions & Try It!
              Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

            10-6: Virtual Nerd™: How Do You Find the Product of Two Functions?
              Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

            10-6: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

            10-6: MathXL for School: Enrichment
              Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

            10-2: Ex 4: Compare Rates of Change of a Function & Try It!
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            10-2: Virtual Nerd™: How Do You Graph a Cube Root Function Using a Table?
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

            10-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-2: Ex 2: Translations of the Cube Root Function & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-2: Additional Example 2 with Try Another One
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-2: MathXL for School: Enrichment
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-5: Ex 4: Analyze Horizontal Stretches of Graphs & Try It!
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-5: Additional Example 4 with Try Another One
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            10-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

            Topic 10: Assessment Form C
              Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         2-3: Ex 1: Understand Standard Form of a Linear Equation & Try It!
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         2-3: Virtual Nerd™: How Do You Write an Equation of a Line in Standard Form from a Word Problem?
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         2-2: MathXL for School: Enrichment
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         2-2: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph linear and quadratic functions and show intercepts, maxima, and minima. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         9-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 

         1-1: Ex 3: Operations With Rational Numbers & Try It!
           Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

         3-1: Ex 1: Recognize Domain and Range & Try It!
           Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). 

         6-1: Ex 4: Use the Power of a Product Property to Solve Equations With Rational Exponents & Try It!
           Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

         10-3: Ex 2: Analyze Maximum and Minimum Values & Try It!
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         3-1: Additional Example 4
           Curriculum Standards: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

         6-1: Virtual Nerd™: What are Rational Exponents?
           Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

         10-3: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         10-3: MathXL for School: Enrichment
           Curriculum Standards: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

         6-1: MathXL for School: Enrichment
           Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 

         6-1: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: 
For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. 

         10-7: Ex 1: Understand Inverse Functions & Try It!
           Curriculum Standards: Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. 

         9-7: Ex 1: Understand Linear-Quadratic Systems of Equations & Try It!
           Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

         9-2: Ex 2: Solve by Factoring & Try It!
           Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

         10-4: Ex 3: Combine Translations & Try It!
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         10-2: Ex 4: Compare Rates of Change of a Function & Try It!
           Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

         9-7: Ex 2: Solve a Linear-Quadratic Equation by Graphing & Try It!
           Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

         2-2: Ex 1: Understand Point-Slope Form of a Linear Equation & Try It!
           Curriculum Standards: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

         9-4: Ex 2: Solve Equations of the Form ??x² = ?? & Try It!
           Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

         6-4: Ex 3: Use the Explicit Formula & Try It!
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         10-6: Ex 1: Add and Subtract Functions & Try It!
           Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

         4-4: Ex 2: Rewrite an Inequality to Graph It & Try It!
           Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

         10-3: Ex 1: Analyze Domain and Range & Try It!
           Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

         9-2: Ex 1: Use the Zero-Product Property & Try It!
           Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

         10-2: Ex 2: Translations of the Cube Root Function & Try It!
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ) , ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         5-4: Ex 2: Vertical Translations of the Absolute Value Function & Try It!
           Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

         7-5: Ex 1: Understand Factoring a Trinomial & Try It!
           Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

         10-1: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Identify the effect on the graph of replacing ??((?) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         9-2: Virtual Nerd™: What's the Zero Product Property?
           Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

         9-2: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

         9-2: Additional Example 1 with Try Another One
           Curriculum Standards: Factor a quadratic expression to reveal the zeros of the function it defines. 

         5-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

         9-7: Virtual Nerd™: How Do You Solve a System of Equations Using Elimination if One Equation is a Quadratic?
           Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

         9-7: Virtual Nerd™: How Do You Solve a System of Equations by Graphing if One Equation is a Quadratic?
           Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

         10-6: Virtual Nerd™: How Do You Find the Product of Two Functions?
           Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

         10-3: Additional Example 1 with Try Another One
           Curriculum Standards: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

         10-6: MathXL for School: Enrichment
           Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

         5-4: Virtual Nerd™: How Do You Write an Equation for a Translation of an Absolute Value Function?
           Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

         9-4: MathXL for School: Enrichment
           Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

         10-6: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 

         5-4: MathXL for School: Enrichment
           Curriculum Standards: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

         9-4: Virtual Nerd™: How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions if a?1?
           Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

         9-2: Virtual Nerd™: How Do You Solve a Word Problem by Factoring a Quadratic Equation?
           Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

         6-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         9-7: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

         4-4: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

         4-4: Virtual Nerd™: How Do You Solve and Graph Inequalities from a Word Problem?
           Curriculum Standards: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 

         6-4: MathXL for School: Enrichment
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         10-2: Virtual Nerd™: How Do You Graph a Cube Root Function Using a Table?
           Curriculum Standards: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 

         9-7: MathXL for School: Enrichment
           Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. 

         10-4: Virtual Nerd™: What Does the Constant '??' Do in the Function ??((?)=v(??)+???
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         7-5: MathXL for School: Reteach to Build Understanding
           Curriculum Standards: Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). Interpret parts of an expression, such as terms, factors, and coefficients. 

         10-2: MathXL for School: Enrichment
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         10-2: Additional Example 2 with Try Another One
           Curriculum Standards: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

         6-4: Virtual Nerd™: How Do You Find the Common Ratio of a Geometric Sequence?
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

         7-5: Virtual Nerd™: How Do You Factor a Trinomial?
           Curriculum Standards: Interpret parts of an expression, such as terms, factors, and coefficients. 

         9-2: MathXL for School: Enrichment
           Curriculum Standards: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. 

         Benchmark Test 4
           Curriculum Standards: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Factor a quadratic expression to reveal the zeros of the function it defines. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Interpret parts of an expression, such as terms, factors, and coefficients. 

         Statistics

            Interactive Student Edition: Realize Reader: Topic 11

            3-5: Ex 2: Understand Correlation & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: Ex 1: Understand Association & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: Virtual Nerd™: How Do You Use a Scatter Plot to Find a Positive Correlation?
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: Ex 3: Write the Equation of a Trend Line & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-6: Ex 1: Find the Line of Best Fit & Try It!
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-5: MathXL for School: Enrichment
              Curriculum Standards: Fit a linear function for a scatter plot that suggests a linear association. 

            3-6: Ex 4: Interpolate and Extrapolate Using Linear Models & Try It!
              Curriculum Standards: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

            8-7: Example 1 & Try It!
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            8-7: Virtual Nerd™: How Do You Figure Out Whether the Mean, Median, or Mode Best Describes a Data Set?
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            Topic 11: Readiness Assessment
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Represent data with plots on the real number line (dot plots, histograms, and box plots). Fit a linear function for a scatter plot that suggests a linear association. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 

            Topic 11: enVision STEM Project

               Topic 11: enVision STEM Video
                 Curriculum Standards: Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Compose functions. Example: 
For example, if ??(??) is the temperature in the atmosphere as a function of height, and ??(??) is the height of a weather balloon as a function of time, then ??((?(??)) is the temperature at the location of the weather balloon as a function of time. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (?? – 2)/(?? – 1) = 3. Noticing the regularity in the way terms cancel when expanding (?? – 1)(?? + 1), (?? – 1)(??² + ?? + 1), and (?? – 1)(??³ + ??² + ?? + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 

            Analyzing Data Displays

               Interactive Student Edition: Realize Reader: Lesson 11-1
                 Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

               Explore

                  11-1: Model & Discuss

               Understand and Apply

                  11-1: Ex 1: Represent and Interpret Data in a Dot Plot & Try It!
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Additional Example 1 with Try Another One
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Ex 2: Represent and Interpret Data in a Histogram & Try It!
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Ex 3: Represent and Interpret Data in a Box Plot & Try It!
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Ex 4: Choose a Data Display & Try It!
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Additional Example 4
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Concept Summary
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Do You Understand?
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Do You Know How?
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

               Practice and Problem-Solving

                  11-1: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: MathXL for School: Mixed Review
                    Curriculum Standards: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Explain why the ² -coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Assess & Differentiate

                  11-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: MathXL for School: Enrichment
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Ex 4: Choose a Data Display & Try It!
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Additional Example 4
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Ex 1: Represent and Interpret Data in a Dot Plot & Try It!
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Additional Example 1 with Try Another One
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Ex 2: Represent and Interpret Data in a Histogram & Try It!
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Virtual Nerd™: How Do You Make a Histogram?
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Ex 3: Represent and Interpret Data in a Box Plot & Try It!
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Virtual Nerd™: How Do You Find the Interquartile Range of a Data Set?
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Lesson Quiz
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: MathXL for School: Additional Practice
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: MathXL for School: Enrichment
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Virtual Nerd™: How Do You Make a Histogram?
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-1: Virtual Nerd™: How Do You Find the Interquartile Range of a Data Set?
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            Comparing Data Sets

               Interactive Student Edition: Realize Reader: Lesson 11-2
                 Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

               Explore

                  11-2: Critique & Explain

               Understand and Apply

                  11-2: Ex 1: Compare Data Sets Displayed in Dot Plots & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: Additional Example 1
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: Ex 2: Compare Data Sets Displayed in Box Plots & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: Additional Example 2 with Try Another One
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: Ex 3: Compare Data Sets Displayed in Histograms & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: Ex 4: Make Observations With Data Displays & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: Concept Summary
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: Do You Understand?
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: Do You Know How?
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

               Practice and Problem-Solving

                  11-2: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: MathXL for School: Mixed Review
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

               Assess & Differentiate

                  11-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: MathXL for School: Enrichment
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-2: Ex 4: Make Observations With Data Displays & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: Ex 1: Compare Data Sets Displayed in Dot Plots & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: Virtual Nerd™: How Do You Compare Two Data Sets Using Box-and-Whisker Plots?
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: Lesson Quiz
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: MathXL for School: Additional Practice
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-2: MathXL for School: Enrichment
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Represent data with plots on the real number line (dot plots, histograms, and box plots). 

                  11-2: Virtual Nerd™: How Do You Compare Two Data Sets Using Box-and-Whisker Plots?
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            Interpreting the Shapes of Data Displays

               Interactive Student Edition: Realize Reader: Lesson 11-3
                 Curriculum Standards: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

               Explore

                  11-3: Explore & Reason

               Understand and Apply

                  11-3: Ex 1: Interpret the Shape of a Distribution & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Additional Example 1 with Try Another One
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Ex 2: Interpret the Shape of a Skewed Data Display & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Ex 3: Compare Shapes of Skewed Data Displays & Try It!
                    Curriculum Standards: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). 

                  11-3: Ex 4: Interpret the Shape of a Symmetric Data Display & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Ex 5: Comparing the Shapes of Data Sets & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Additional Example 5
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Concept Summary
                    Curriculum Standards: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Do You Understand?
                    Curriculum Standards: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Do You Know How?
                    Curriculum Standards: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

               Practice and Problem-Solving

                  11-3: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: MathXL for School: Mixed Review
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Represent data with plots on the real number line (dot plots, histograms, and box plots). 

               Assess & Differentiate

                  11-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: MathXL for School: Enrichment
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Ex 1: Interpret the Shape of a Distribution & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Virtual Nerd™: What is a Normal Distribution?
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Lesson Quiz
                    Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: MathXL for School: Additional Practice
                    Curriculum Standards: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: MathXL for School: Enrichment
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-3: Virtual Nerd™: What is a Normal Distribution?
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            Standard Deviation

               Interactive Student Edition: Realize Reader: Lesson 11-4
                 Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

               Explore

                  11-4: Model & Discuss

               Understand and Apply

                  11-4: Ex 1: Interpret the Variability of a Data Set & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Ex 2: Calculate the Standard Deviation of a Sample & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Ex 3: Find Standard Deviation of a Population & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Additional Example 3
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Ex 4: Compare Data Sets Using Standard Deviation & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Additional Example 4 with Try Another One
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Concept Summary
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Do You Understand?
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Do You Know How?
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

               Practice and Problem-Solving

                  11-4: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: MathXL for School: Mixed Review
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Represent data with plots on the real number line (dot plots, histograms, and box plots). Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 

               Assess & Differentiate

                  11-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: MathXL for School: Enrichment
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Ex 1: Interpret the Variability of a Data Set & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Virtual Nerd™: How Do You Find the Standard Deviation of a Data Set?
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Ex 4: Compare Data Sets Using Standard Deviation & Try It!
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Additional Example 4 with Try Another One
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Lesson Quiz
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: MathXL for School: Additional Practice
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: MathXL for School: Enrichment
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Virtual Nerd™: How Do You Find the Standard Deviation of a Data Set?
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

                  11-4: Virtual Nerd™: What is Sigma Notation?
                    Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            Two-Way Frequency Tables

               Interactive Student Edition: Realize Reader: Lesson 11-5
                 Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 

               Explore

                  11-5: Explore & Reason

               Understand and Apply

                  11-5: Ex 1: Interpret a Two-Way Frequency Table & Try It!
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 

                  11-5: Additional Example 1
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 

                  11-5: Ex 2: Interpret a Two-Way Relative Frequency Table & Try It!
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: Ex 3: Calculate Conditional Relative Frequency & Try It!
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: Ex 4: Interpret Conditional Relative Frequency & Try It!
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: Ex 5: Interpret Data Frequencies & Try It!
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: Additional Example 5 with Try Another One
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: Concept Summary
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 

                  11-5: Do You Understand?
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 

                  11-5: Do You Know How?
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 

               Practice and Problem-Solving

                  11-5: MathXL for School: Practice and Problem-Solving
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 

                  11-5: MathXL for School: Mixed Review
                    Curriculum Standards: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Represent data with plots on the real number line (dot plots, histograms, and box plots). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. 

               Assess & Differentiate

                  11-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: MathXL for School: Enrichment
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: Ex 1: Interpret a Two-Way Frequency Table & Try It!
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 

                  11-5: Additional Example 1
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 

                  11-5: Ex 2: Interpret a Two-Way Relative Frequency Table & Try It!
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: Ex 4: Interpret Conditional Relative Frequency & Try It!
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: Virtual Nerd™: How Do You Find Relative Frequency?
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: Lesson Quiz
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 

                  11-5: MathXL for School: Reteach to Build Understanding
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: MathXL for School: Additional Practice
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 

                  11-5: MathXL for School: Enrichment
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

                  11-5: Virtual Nerd™: How Do You Find Relative Frequency?
                    Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            Mathematical Modeling in 3 Acts: Text Message

               Topic 11: Text Message - Act 1 Video With Questions

               Topic 11: Text Message - Act 2 Content

               Topic 11: Text Message - Act 2 Questions

               Topic 11: Text Message - Act 3 Video

               Topic 11: Text Message - Act 3 Questions

            Topic 11: MathXL for School: Topic Review
              Curriculum Standards: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: 
For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            Topic 11: Performance Assessment Form A
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-4: Ex 4: Compare Data Sets Using Standard Deviation & Try It!
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-4: Additional Example 4 with Try Another One
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-4: MathXL for School: Enrichment
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-1: Ex 1: Represent and Interpret Data in a Dot Plot & Try It!
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-1: Additional Example 1 with Try Another One
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-1: Ex 2: Represent and Interpret Data in a Histogram & Try It!
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-1: Virtual Nerd™: How Do You Make a Histogram?
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-5: Ex 2: Interpret a Two-Way Relative Frequency Table & Try It!
              Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            11-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            11-2: Ex 4: Make Observations With Data Displays & Try It!
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-3: Additional Example 5
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-2: MathXL for School: Enrichment
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-5: Ex 4: Interpret Conditional Relative Frequency & Try It!
              Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            11-5: Virtual Nerd™: How Do You Find Relative Frequency?
              Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            11-5: MathXL for School: Enrichment
              Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            11-4: Ex 1: Interpret the Variability of a Data Set & Try It!
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-4: Virtual Nerd™: How Do You Find the Standard Deviation of a Data Set?
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-1: Ex 3: Represent and Interpret Data in a Box Plot & Try It!
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-1: Virtual Nerd™: How Do You Find the Interquartile Range of a Data Set?
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            Topic 11: Assessment Form A
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Represent data with plots on the real number line (dot plots, histograms, and box plots). Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            11-4: Ex 4: Compare Data Sets Using Standard Deviation & Try It!
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-4: Additional Example 4 with Try Another One
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-2: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-4: MathXL for School: Enrichment
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-1: Ex 1: Represent and Interpret Data in a Dot Plot & Try It!
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-1: Additional Example 1 with Try Another One
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-1: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-1: Ex 2: Represent and Interpret Data in a Histogram & Try It!
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-1: Virtual Nerd™: How Do You Make a Histogram?
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-5: Ex 2: Interpret a Two-Way Relative Frequency Table & Try It!
              Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            11-5: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            11-2: Ex 4: Make Observations With Data Displays & Try It!
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-3: Additional Example 5
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-2: MathXL for School: Enrichment
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-5: Ex 4: Interpret Conditional Relative Frequency & Try It!
              Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            11-5: Virtual Nerd™: How Do You Find Relative Frequency?
              Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            11-5: MathXL for School: Enrichment
              Curriculum Standards: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

            11-4: Ex 1: Interpret the Variability of a Data Set & Try It!
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-4: Virtual Nerd™: How Do You Find the Standard Deviation of a Data Set?
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-4: MathXL for School: Reteach to Build Understanding
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 

            11-1: Ex 3: Represent and Interpret Data in a Box Plot & Try It!
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            11-1: Virtual Nerd™: How Do You Find the Interquartile Range of a Data Set?
              Curriculum Standards: Represent data with plots on the real number line (dot plots, histograms, and box plots). 

            Topic 11: Assessment Form C
              Curriculum Standards: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Represent data with plots on the real number line (dot plots, histograms, and box plots). Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

         End-of-Course Assessment
           Curriculum Standards: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: 
For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Compute (using technology) and interpret the correlation coefficient of a linear fit. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve an equation of the form ??(??) = ?? for a simple function ?? that has an inverse and write an expression for the inverse. Example: 
For example, ??(??) =2 ??³ or ??(??) = (??+1)/(??–1) for ?? ? 1. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: 
For example, find the points of intersection between the line ?? = –3?? and the circle ??² + ??² = 3. Graph linear and quadratic functions and show intercepts, maxima, and minima. Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ?? is a function and ?? is an element of its domain, then ??(??) denotes the output of ?? corresponding to the input ??. The graph of ?? is the graph of the equation ?? = ??(??). Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Represent data with plots on the real number line (dot plots, histograms, and box plots). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: 
For example, rearrange Ohm’s law ?? = ???? to highlight resistance ??. Distinguish between correlation and causation. Understand that two events ?? and ?? are independent if the probability of ?? and ?? occurring together is the product of their probabilities, and use this characterization to determine if they are independent. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Fit a linear function for a scatter plot that suggests a linear association. Combine standard function types using arithmetic operations. Example: 
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: 
For example, if the function ??(??) gives the number of person-hours it takes to assemble ?? engines in a factory, then the positive integers would be an appropriate domain for the function. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Use the structure of an expression to identify ways to rewrite it. Example: 
For example, see ??4 – ??4 as (??²)² – (??²)², thus recognizing it as a difference of squares that can be factored as (??² – ??²)(??² + ??²). For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Interpret the parameters in a linear or exponential function in terms of a context. 

         Algebra 1 Next-Generation Practice Test

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            2-4: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            2-4: Additional Practice (PDF)
              Intended Role: Instructor

            2-4: Enrichment (PDF)
              Intended Role: Instructor

            2-4: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            Topic 2: Performance Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 2: Performance Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 2: Performance Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 2: Performance Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 2: Performance Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 2: Performance Assessment Form B: Answer Key
              Intended Role: Instructor

            2-2: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            Topic 2: Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 2: Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 2: Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 2: Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 2: Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 2: Assessment Form B: Answer Key
              Intended Role: Instructor

            2-2: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            Benchmark Test 1 (PDF)
              Intended Role: Instructor

            Benchmark Test 1 (Editable)
              Intended Role: Instructor

            Benchmark Test 1: Answer Key
              Intended Role: Instructor

            Benchmark Test 1 Item Analysis Chart
              Intended Role: Instructor

            CC Standards Practice Week 7
              Intended Role: Instructor

            CC Standards Practice Week 8
              Intended Role: Instructor

            CC Standards Practice Week 9
              Intended Role: Instructor

            CC Standards Practice Weeks 7-9: Answer Key
              Intended Role: Instructor

            Teacher's Edition eText: Topic 3
              Intended Role: Instructor

            Topic 3: Professional Development Video
              Intended Role: Instructor

            Topic 3: Readiness Assessment (PDF)
              Intended Role: Instructor

            Topic 3: Readiness Assessment (Editable)
              Intended Role: Instructor

            Topic 3: Readiness Assessment: Answer Key
              Intended Role: Instructor

            Topic 3: enVision STEM Project (PDF)
              Intended Role: Instructor

            Topic 3: enVision STEM Masters (PDF)
              Intended Role: Instructor

            Topic 3: enVision STEM Masters: Answer Key
              Intended Role: Instructor

            3-1: Lesson Plan (PDF)
              Intended Role: Instructor

            3-1: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 3-1
              Intended Role: Instructor

            3-1: Lesson Quiz (PDF)
              Intended Role: Instructor

            3-1: Lesson Quiz (Editable)
              Intended Role: Instructor

            3-1: Lesson Quiz: Answer Key
              Intended Role: Instructor

            3-1: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            3-1: Additional Practice (PDF)
              Intended Role: Instructor

            3-1: Enrichment (PDF)
              Intended Role: Instructor

            3-1: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            3-2: Lesson Plan (PDF)
              Intended Role: Instructor

            3-2: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 3-2
              Intended Role: Instructor

            3-2: Lesson Quiz (PDF)
              Intended Role: Instructor

            3-2: Lesson Quiz (Editable)
              Intended Role: Instructor

            3-2: Lesson Quiz: Answer Key
              Intended Role: Instructor

            3-2: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            3-2: Additional Practice (PDF)
              Intended Role: Instructor

            3-2: Enrichment (PDF)
              Intended Role: Instructor

            3-2: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            3-3: Lesson Plan (PDF)
              Intended Role: Instructor

            3-3: Lesson Plan (Editable)
              Intended Role: Instructor

            3-3: TI 83/84 Activity A (PDF)
              Intended Role: Instructor

            3-3: TI 83/84 Activity A (Editable)
              Intended Role: Instructor

            3-3: TI 83/84 Activity B (PDF)
              Intended Role: Instructor

            3-3: TI 83/84 Activity B (Editable)
              Intended Role: Instructor

            3-3: TI 83/84 Activity C (PDF)
              Intended Role: Instructor

            3-3: TI 83/84 Activity C (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 3-3
              Intended Role: Instructor

            3-3: Lesson Quiz (PDF)
              Intended Role: Instructor

            3-3: Lesson Quiz (Editable)
              Intended Role: Instructor

            3-3: Lesson Quiz: Answer Key
              Intended Role: Instructor

            3-3: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            3-3: Additional Practice (PDF)
              Intended Role: Instructor

            3-3: Enrichment (PDF)
              Intended Role: Instructor

            3-3: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            3-4: Lesson Plan (PDF)
              Intended Role: Instructor

            3-4: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 3-4
              Intended Role: Instructor

            3-4: Lesson Quiz (PDF)
              Intended Role: Instructor

            3-4: Lesson Quiz (Editable)
              Intended Role: Instructor

            3-4: Lesson Quiz: Answer Key
              Intended Role: Instructor

            3-4: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            3-4: Additional Practice (PDF)
              Intended Role: Instructor

            3-4: Enrichment (PDF)
              Intended Role: Instructor

            3-4: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            3-5: Lesson Plan (PDF)
              Intended Role: Instructor

            3-5: Lesson Plan (Editable)
              Intended Role: Instructor

            3-5: TI 83/84 Activity (PDF)
              Intended Role: Instructor

            3-5: TI 83/84 Activity (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 3-5
              Intended Role: Instructor

            3-5: Lesson Quiz (PDF)
              Intended Role: Instructor

            3-5: Lesson Quiz (Editable)
              Intended Role: Instructor

            3-5: Lesson Quiz: Answer Key
              Intended Role: Instructor

            3-5: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            3-5: Additional Practice (PDF)
              Intended Role: Instructor

            3-5: Enrichment (PDF)
              Intended Role: Instructor

            3-5: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            3-6: Lesson Plan (PDF)
              Intended Role: Instructor

            3-6: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 3-6
              Intended Role: Instructor

            3-6: Lesson Quiz (PDF)
              Intended Role: Instructor

            3-6: Lesson Quiz (Editable)
              Intended Role: Instructor

            3-6: Lesson Quiz: Answer Key
              Intended Role: Instructor

            3-6: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            3-6: Additional Practice (PDF)
              Intended Role: Instructor

            3-6: Enrichment (PDF)
              Intended Role: Instructor

            3-6: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            Topic 3: Performance Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 3: Performance Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 3: Performance Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 3: Performance Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 3: Performance Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 3: Performance Assessment Form B: Answer Key
              Intended Role: Instructor

            3-4: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            Topic 3: Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 3: Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 3: Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 3: Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 3: Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 3: Assessment Form B: Answer Key
              Intended Role: Instructor

            3-4: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            CC Standards Practice Week 10
              Intended Role: Instructor

            CC Standards Practice Week 11
              Intended Role: Instructor

            CC Standards Practice Weeks 10-11: Answer Key
              Intended Role: Instructor

            Teacher's Edition eText: Topic 4
              Intended Role: Instructor

            Topic 4: Professional Development Video
              Intended Role: Instructor

            Topic 4: Readiness Assessment (PDF)
              Intended Role: Instructor

            Topic 4: Readiness Assessment (Editable)
              Intended Role: Instructor

            Topic 4: Readiness Assessment: Answer Key
              Intended Role: Instructor

            Topic 4: enVision STEM Project (PDF)
              Intended Role: Instructor

            Topic 4: enVision STEM Masters (PDF)
              Intended Role: Instructor

            Topic 4: enVision STEM Masters: Answer Key
              Intended Role: Instructor

            4-1: Lesson Plan (PDF)
              Intended Role: Instructor

            4-1: Lesson Plan (Editable)
              Intended Role: Instructor

            4-1: TI 83/84 Activity A (PDF)
              Intended Role: Instructor

            4-1: TI 83/84 Activity A (Editable)
              Intended Role: Instructor

            4-1: TI 83/84 Activity B (PDF)
              Intended Role: Instructor

            4-1: TI 83/84 Activity B (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 4-1
              Intended Role: Instructor

            4-1: Lesson Quiz (PDF)
              Intended Role: Instructor

            4-1: Lesson Quiz (Editable)
              Intended Role: Instructor

            4-1: Lesson Quiz: Answer Key
              Intended Role: Instructor

            4-1: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            4-1: Additional Practice (PDF)
              Intended Role: Instructor

            4-1: Enrichment (PDF)
              Intended Role: Instructor

            4-1: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            4-2: Lesson Plan (PDF)
              Intended Role: Instructor

            4-2: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 4-2
              Intended Role: Instructor

            4-2: Lesson Quiz (PDF)
              Intended Role: Instructor

            4-2: Lesson Quiz (Editable)
              Intended Role: Instructor

            4-2: Lesson Quiz: Answer Key
              Intended Role: Instructor

            4-2: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            4-2: Additional Practice (PDF)
              Intended Role: Instructor

            4-2: Enrichment (PDF)
              Intended Role: Instructor

            4-2: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            4-3: Lesson Plan (PDF)
              Intended Role: Instructor

            4-3: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 4-3
              Intended Role: Instructor

            4-3: Lesson Quiz (PDF)
              Intended Role: Instructor

            4-3: Lesson Quiz (Editable)
              Intended Role: Instructor

            4-3: Lesson Quiz: Answer Key
              Intended Role: Instructor

            4-3: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            4-3: Additional Practice (PDF)
              Intended Role: Instructor

            4-3: Enrichment (PDF)
              Intended Role: Instructor

            4-3: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            4-4: Lesson Plan (PDF)
              Intended Role: Instructor

            4-4: Lesson Plan (Editable)
              Intended Role: Instructor

            4-4: TI 83/84 Activity (PDF)
              Intended Role: Instructor

            4-4: TI 83/84 Activity (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 4-4
              Intended Role: Instructor

            4-4: Lesson Quiz (PDF)
              Intended Role: Instructor

            4-4: Lesson Quiz (Editable)
              Intended Role: Instructor

            4-4: Lesson Quiz: Answer Key
              Intended Role: Instructor

            4-4: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            4-4: Additional Practice (PDF)
              Intended Role: Instructor

            4-4: Enrichment (PDF)
              Intended Role: Instructor

            4-4: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            4-5: Lesson Plan (PDF)
              Intended Role: Instructor

            4-5: Lesson Plan (Editable)
              Intended Role: Instructor

            4-5: TI 83/84 Activity (PDF)
              Intended Role: Instructor

            4-5: TI 83/84 Activity (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 4-5
              Intended Role: Instructor

            4-5: Lesson Quiz (PDF)
              Intended Role: Instructor

            4-5: Lesson Quiz (Editable)
              Intended Role: Instructor

            4-5: Lesson Quiz: Answer Key
              Intended Role: Instructor

            4-5: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            4-5: Additional Practice (PDF)
              Intended Role: Instructor

            4-5: Enrichment (PDF)
              Intended Role: Instructor

            4-5: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            Topic 4: Performance Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 4: Performance Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 4: Performance Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 4: Performance Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 4: Performance Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 4: Performance Assessment Form B: Answer Key
              Intended Role: Instructor

            Topic 4: Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 4: Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 4: Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 4: Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 4: Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 4: Assessment Form B: Answer Key
              Intended Role: Instructor

            Benchmark Test 2 (PDF)
              Intended Role: Instructor

            Benchmark Test 2 (Editable)
              Intended Role: Instructor

            Benchmark Test 2: Answer Key
              Intended Role: Instructor

            Benchmark Test 2 Item Analysis Chart
              Intended Role: Instructor

            CC Standards Practice Week 12
              Intended Role: Instructor

            CC Standards Practice Week 13
              Intended Role: Instructor

            CC Standards Practice Weeks 12-13: Answer Key
              Intended Role: Instructor

            Teacher's Edition eText: Topic 5
              Intended Role: Instructor

            Topic 5: Professional Development Video
              Intended Role: Instructor

            Topic 5: Readiness Assessment (PDF)
              Intended Role: Instructor

            Topic 5: Readiness Assessment (Editable)
              Intended Role: Instructor

            Topic 5: Readiness Assessment: Answer Key
              Intended Role: Instructor

            Topic 5: enVision STEM Project (PDF)
              Intended Role: Instructor

            Topic 5: enVision STEM Masters (PDF)
              Intended Role: Instructor

            Topic 5: enVision STEM Masters: Answer Key
              Intended Role: Instructor

            5-1: Lesson Plan (PDF)
              Intended Role: Instructor

            5-1: Lesson Plan (Editable)
              Intended Role: Instructor

            5-1: TI 83/84 Activity (PDF)
              Intended Role: Instructor

            5-1: TI 83/84 Activity (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 5-1
              Intended Role: Instructor

            5-1: Lesson Quiz (PDF)
              Intended Role: Instructor

            5-1: Lesson Quiz (Editable)
              Intended Role: Instructor

            5-1: Lesson Quiz: Answer Key
              Intended Role: Instructor

            5-1: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            5-1: Additional Practice (PDF)
              Intended Role: Instructor

            5-1: Enrichment (PDF)
              Intended Role: Instructor

            5-1: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            5-2: Lesson Plan (PDF)
              Intended Role: Instructor

            5-2: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 5-2
              Intended Role: Instructor

            5-2: Lesson Quiz (PDF)
              Intended Role: Instructor

            5-2: Lesson Quiz (Editable)
              Intended Role: Instructor

            5-2: Lesson Quiz: Answer Key
              Intended Role: Instructor

            5-2: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            5-2: Additional Practice (PDF)
              Intended Role: Instructor

            5-2: Enrichment (PDF)
              Intended Role: Instructor

            5-2: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            5-3: Lesson Plan (PDF)
              Intended Role: Instructor

            5-3: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 5-3
              Intended Role: Instructor

            5-3: Lesson Quiz (PDF)
              Intended Role: Instructor

            5-3: Lesson Quiz (Editable)
              Intended Role: Instructor

            5-3: Lesson Quiz: Answer Key
              Intended Role: Instructor

            5-3: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            5-3: Additional Practice (PDF)
              Intended Role: Instructor

            5-3: Enrichment (PDF)
              Intended Role: Instructor

            5-3: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            5-4: Lesson Plan (PDF)
              Intended Role: Instructor

            5-4: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 5-4
              Intended Role: Instructor

            5-4: Lesson Quiz (PDF)
              Intended Role: Instructor

            5-4: Lesson Quiz (Editable)
              Intended Role: Instructor

            5-4: Lesson Quiz: Answer Key
              Intended Role: Instructor

            5-4: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            5-4: Additional Practice (PDF)
              Intended Role: Instructor

            5-4: Enrichment (PDF)
              Intended Role: Instructor

            5-4: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            Topic 5: Performance Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 5: Performance Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 5: Performance Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 5: Performance Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 5: Performance Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 5: Performance Assessment Form B: Answer Key
              Intended Role: Instructor

            Topic 5: Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 5: Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 5: Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 5: Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 5: Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 5: Assessment Form B: Answer Key
              Intended Role: Instructor

            CC Standards Practice Week 14
              Intended Role: Instructor

            CC Standards Practice Week 15
              Intended Role: Instructor

            CC Standards Practice Week 16
              Intended Role: Instructor

            CC Standards Practice Weeks 14-16: Answer Key
              Intended Role: Instructor

            Teacher's Edition eText: Topic 6
              Intended Role: Instructor

            Topic 6: Professional Development Video
              Intended Role: Instructor

            Topic 6: Readiness Assessment (PDF)
              Intended Role: Instructor

            Topic 6: Readiness Assessment (Editable)
              Intended Role: Instructor

            Topic 6: Readiness Assessment: Answer Key
              Intended Role: Instructor

            Topic 6: enVision STEM Project (PDF)
              Intended Role: Instructor

            Topic 6: enVision STEM Masters (PDF)
              Intended Role: Instructor

            Topic 6: enVision STEM Masters: Answer Key
              Intended Role: Instructor

            6-1: Lesson Plan (PDF)
              Intended Role: Instructor

            6-1: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 6-1
              Intended Role: Instructor

            6-1: Lesson Quiz (PDF)
              Intended Role: Instructor

            6-1: Lesson Quiz (Editable)
              Intended Role: Instructor

            6-1: Lesson Quiz: Answer Key
              Intended Role: Instructor

            6-1: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            6-1: Additional Practice (PDF)
              Intended Role: Instructor

            6-1: Enrichment (PDF)
              Intended Role: Instructor

            6-1: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            6-2: Lesson Plan (PDF)
              Intended Role: Instructor

            6-2: Lesson Plan (Editable)
              Intended Role: Instructor

            6-2: TI 83/84 Activity A (PDF)
              Intended Role: Instructor

            6-2: TI 83/84 Activity A (Editable)
              Intended Role: Instructor

            6-2: TI 83/84 Activity B (PDF)
              Intended Role: Instructor

            6-2: TI 83/84 Activity B (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 6-2
              Intended Role: Instructor

            6-2: Lesson Quiz (PDF)
              Intended Role: Instructor

            6-2: Lesson Quiz (Editable)
              Intended Role: Instructor

            6-2: Lesson Quiz: Answer Key
              Intended Role: Instructor

            6-2: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            6-2: Additional Practice (PDF)
              Intended Role: Instructor

            6-2: Enrichment (PDF)
              Intended Role: Instructor

            6-2: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            6-3: Lesson Plan (PDF)
              Intended Role: Instructor

            6-3: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 6-3
              Intended Role: Instructor

            6-3: Lesson Quiz (PDF)
              Intended Role: Instructor

            6-3: Lesson Quiz (Editable)
              Intended Role: Instructor

            6-3: Lesson Quiz: Answer Key
              Intended Role: Instructor

            6-3: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            6-3: Additional Practice (PDF)
              Intended Role: Instructor

            6-3: Enrichment (PDF)
              Intended Role: Instructor

            6-3: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            6-4: Lesson Plan (PDF)
              Intended Role: Instructor

            6-4: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 6-4
              Intended Role: Instructor

            6-4: Lesson Quiz (PDF)
              Intended Role: Instructor

            6-4: Lesson Quiz (Editable)
              Intended Role: Instructor

            6-4: Lesson Quiz: Answer Key
              Intended Role: Instructor

            6-4: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            6-4: Additional Practice (PDF)
              Intended Role: Instructor

            6-4: Enrichment (PDF)
              Intended Role: Instructor

            6-4: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            6-5: Lesson Plan (PDF)
              Intended Role: Instructor

            6-5: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 6-5
              Intended Role: Instructor

            6-5: Lesson Quiz (PDF)
              Intended Role: Instructor

            6-5: Lesson Quiz (Editable)
              Intended Role: Instructor

            6-5: Lesson Quiz: Answer Key
              Intended Role: Instructor

            6-5: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            6-5: Additional Practice (PDF)
              Intended Role: Instructor

            6-5: Enrichment (PDF)
              Intended Role: Instructor

            6-5: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            Topic 6: Performance Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 6: Performance Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 6: Performance Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 6: Performance Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 6: Performance Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 6: Performance Assessment Form B: Answer Key
              Intended Role: Instructor

            Topic 6: Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 6: Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 6: Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 6: Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 6: Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 6: Assessment Form B: Answer Key
              Intended Role: Instructor

            Mid-Year Assessment (PDF)
              Intended Role: Instructor

            Mid-Year Assessment (Editable)
              Intended Role: Instructor

            Mid-Year Assessment: Answer Key
              Intended Role: Instructor

            Mid-Year Assessment Item Analysis Chart
              Intended Role: Instructor

            CC Standards Practice Week 17
              Intended Role: Instructor

            CC Standards Practice Week 18
              Intended Role: Instructor

            CC Standards Practice Week 19
              Intended Role: Instructor

            CC Standards Practice Weeks 17-19: Answer Key
              Intended Role: Instructor

            Teacher's Edition eText: Topic 7
              Intended Role: Instructor

            Topic 7: Professional Development Video
              Intended Role: Instructor

            Topic 7: Readiness Assessment (PDF)
              Intended Role: Instructor

            Topic 7: Readiness Assessment (Editable)
              Intended Role: Instructor

            Topic 7: Readiness Assessment: Answer Key
              Intended Role: Instructor

            Topic 7: enVision STEM Project (PDF)
              Intended Role: Instructor

            Topic 7: enVision STEM Masters (PDF)
              Intended Role: Instructor

            Topic 7: enVision STEM Masters: Answer Key
              Intended Role: Instructor

            7-1: Lesson Plan (PDF)
              Intended Role: Instructor

            7-1: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 7-1
              Intended Role: Instructor

            7-1: Lesson Quiz (PDF)
              Intended Role: Instructor

            7-1: Lesson Quiz (Editable)
              Intended Role: Instructor

            7-1: Lesson Quiz: Answer Key
              Intended Role: Instructor

            7-1: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            7-1: Additional Practice (PDF)
              Intended Role: Instructor

            7-1: Enrichment (PDF)
              Intended Role: Instructor

            7-1: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            7-2: Lesson Plan (PDF)
              Intended Role: Instructor

            7-2: Lesson Plan (Editable)
              Intended Role: Instructor

            7-2: TI 83/84 Activity (PDF)
              Intended Role: Instructor

            7-2: TI 83/84 Activity (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 7-2
              Intended Role: Instructor

            7-2: Lesson Quiz (PDF)
              Intended Role: Instructor

            7-2: Lesson Quiz (Editable)
              Intended Role: Instructor

            7-2: Lesson Quiz: Answer Key
              Intended Role: Instructor

            7-2: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            7-2: Additional Practice (PDF)
              Intended Role: Instructor

            7-2: Enrichment (PDF)
              Intended Role: Instructor

            7-2: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            7-3: Lesson Plan (PDF)
              Intended Role: Instructor

            7-3: Lesson Plan (Editable)
              Intended Role: Instructor

            7-3: TI 83/84 Activity (PDF)
              Intended Role: Instructor

            7-3: TI 83/84 Activity (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 7-3
              Intended Role: Instructor

            7-3: Lesson Quiz (PDF)
              Intended Role: Instructor

            7-3: Lesson Quiz (Editable)
              Intended Role: Instructor

            7-3: Lesson Quiz: Answer Key
              Intended Role: Instructor

            7-3: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            7-3: Additional Practice (PDF)
              Intended Role: Instructor

            7-3: Enrichment (PDF)
              Intended Role: Instructor

            7-3: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            7-4: Lesson Plan (PDF)
              Intended Role: Instructor

            7-4: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 7-4
              Intended Role: Instructor

            7-4: Lesson Quiz (PDF)
              Intended Role: Instructor

            7-4: Lesson Quiz (Editable)
              Intended Role: Instructor

            7-4: Lesson Quiz: Answer Key
              Intended Role: Instructor

            7-4: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            7-4: Additional Practice (PDF)
              Intended Role: Instructor

            7-4: Enrichment (PDF)
              Intended Role: Instructor

            7-4: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            7-5: Lesson Plan (PDF)
              Intended Role: Instructor

            7-5: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 7-5
              Intended Role: Instructor

            7-5: Lesson Quiz (PDF)
              Intended Role: Instructor

            7-5: Lesson Quiz (Editable)
              Intended Role: Instructor

            7-5: Lesson Quiz: Answer Key
              Intended Role: Instructor

            7-5: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            7-5: Additional Practice (PDF)
              Intended Role: Instructor

            7-5: Enrichment (PDF)
              Intended Role: Instructor

            7-5: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            7-6: Lesson Plan (PDF)
              Intended Role: Instructor

            7-6: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 7-6
              Intended Role: Instructor

            7-6: Lesson Quiz (PDF)
              Intended Role: Instructor

            7-6: Lesson Quiz (Editable)
              Intended Role: Instructor

            7-6: Lesson Quiz: Answer Key
              Intended Role: Instructor

            7-6: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            7-6: Additional Practice (PDF)
              Intended Role: Instructor

            7-6: Enrichment (PDF)
              Intended Role: Instructor

            7-6: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            7-7: Lesson Plan (PDF)
              Intended Role: Instructor

            7-7: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 7-7
              Intended Role: Instructor

            7-7: Lesson Quiz (PDF)
              Intended Role: Instructor

            7-7: Lesson Quiz (Editable)
              Intended Role: Instructor

            7-7: Lesson Quiz: Answer Key
              Intended Role: Instructor

            7-7: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            7-7: Additional Practice (PDF)
              Intended Role: Instructor

            7-7: Enrichment (PDF)
              Intended Role: Instructor

            7-7: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            Topic 7: Performance Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 7: Performance Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 7: Performance Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 7: Performance Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 7: Performance Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 7: Performance Assessment Form B: Answer Key
              Intended Role: Instructor

            Topic 7: Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 7: Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 7: Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 7: Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 7: Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 7: Assessment Form B: Answer Key
              Intended Role: Instructor

            CC Standards Practice Week 20
              Intended Role: Instructor

            CC Standards Practice Week 21
              Intended Role: Instructor

            CC Standards Practice Week 22
              Intended Role: Instructor

            CC Standards Practice Weeks 20-22: Answer Key
              Intended Role: Instructor

            Teacher's Edition eText: Topic 8
              Intended Role: Instructor

            Topic 8: Professional Development Video
              Intended Role: Instructor

            Topic 8: Readiness Assessment (PDF)
              Intended Role: Instructor

            Topic 8: Readiness Assessment (Editable)
              Intended Role: Instructor

            Topic 8: Readiness Assessment: Answer Key
              Intended Role: Instructor

            Topic 8: enVision STEM Project (PDF)
              Intended Role: Instructor

            Topic 8: enVision STEM Masters (PDF)
              Intended Role: Instructor

            Topic 8: enVision STEM Masters: Answer Key
              Intended Role: Instructor

            8-1: Lesson Plan (PDF)
              Intended Role: Instructor

            8-1: Lesson Plan (Editable)
              Intended Role: Instructor

            8-1: TI 83/84 Activity A (PDF)
              Intended Role: Instructor

            8-1: TI 83/84 Activity A (Editable)
              Intended Role: Instructor

            8-1: TI 83/84 Activity B (PDF)
              Intended Role: Instructor

            8-1: TI 83/84 Activity B (Editable)
              Intended Role: Instructor

            8-1: TI 83/84 Activity C (PDF)
              Intended Role: Instructor

            8-1: TI 83/84 Activity C (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 8-1
              Intended Role: Instructor

            8-1: Lesson Quiz (PDF)
              Intended Role: Instructor

            8-1: Lesson Quiz (Editable)
              Intended Role: Instructor

            8-1: Lesson Quiz: Answer Key
              Intended Role: Instructor

            8-1: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            8-1: Additional Practice (PDF)
              Intended Role: Instructor

            8-1: Enrichment (PDF)
              Intended Role: Instructor

            8-1: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            8-2: Lesson Plan (PDF)
              Intended Role: Instructor

            8-2: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 8-2
              Intended Role: Instructor

            8-2: Lesson Quiz (PDF)
              Intended Role: Instructor

            8-2: Lesson Quiz (Editable)
              Intended Role: Instructor

            8-2: Lesson Quiz: Answer Key
              Intended Role: Instructor

            8-2: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            8-2: Additional Practice (PDF)
              Intended Role: Instructor

            8-2: Enrichment (PDF)
              Intended Role: Instructor

            8-2: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            8-3: Lesson Plan (PDF)
              Intended Role: Instructor

            8-3: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 8-3
              Intended Role: Instructor

            8-3: Lesson Quiz (PDF)
              Intended Role: Instructor

            8-3: Lesson Quiz (Editable)
              Intended Role: Instructor

            8-3: Lesson Quiz: Answer Key
              Intended Role: Instructor

            8-3: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            8-3: Additional Practice (PDF)
              Intended Role: Instructor

            8-3: Enrichment (PDF)
              Intended Role: Instructor

            8-3: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            8-4: Lesson Plan (PDF)
              Intended Role: Instructor

            8-4: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 8-4
              Intended Role: Instructor

            8-4: Lesson Quiz (PDF)
              Intended Role: Instructor

            8-4: Lesson Quiz (Editable)
              Intended Role: Instructor

            8-4: Lesson Quiz: Answer Key
              Intended Role: Instructor

            8-4: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            8-4: Additional Practice (PDF)
              Intended Role: Instructor

            8-4: Enrichment (PDF)
              Intended Role: Instructor

            8-4: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            8-5: Lesson Plan (PDF)
              Intended Role: Instructor

            8-5: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 8-5
              Intended Role: Instructor

            8-5: Lesson Quiz (PDF)
              Intended Role: Instructor

            8-5: Lesson Quiz (Editable)
              Intended Role: Instructor

            8-5: Lesson Quiz: Answer Key
              Intended Role: Instructor

            8-5: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            8-5: Additional Practice (PDF)
              Intended Role: Instructor

            8-5: Enrichment (PDF)
              Intended Role: Instructor

            8-5: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            Topic 8: Performance Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 8: Performance Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 8: Performance Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 8: Performance Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 8: Performance Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 8: Performance Assessment Form B: Answer Key
              Intended Role: Instructor

            Topic 8: Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 8: Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 8: Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 8: Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 8: Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 8: Assessment Form B: Answer Key
              Intended Role: Instructor

            Benchmark Test 3 (PDF)
              Intended Role: Instructor

            Benchmark Test 3 (Editable)
              Intended Role: Instructor

            Benchmark Test 3: Answer Key
              Intended Role: Instructor

            Benchmark Test 3 Item Analysis Chart
              Intended Role: Instructor

            CC Standards Practice Week 23
              Intended Role: Instructor

            CC Standards Practice Week 24
              Intended Role: Instructor

            CC Standards Practice Week 25
              Intended Role: Instructor

            CC Standards Practice Weeks 23-25: Answer Key
              Intended Role: Instructor

            Teacher's Edition eText: Topic 9
              Intended Role: Instructor

            Topic 9: Professional Development Video
              Intended Role: Instructor

            Topic 9: Readiness Assessment (PDF)
              Intended Role: Instructor

            Topic 9: Readiness Assessment (Editable)
              Intended Role: Instructor

            Topic 9: Readiness Assessment: Answer Key
              Intended Role: Instructor

            Topic 9: enVision STEM Project (PDF)
              Intended Role: Instructor

            Topic 9: enVision STEM Masters (PDF)
              Intended Role: Instructor

            Topic 9: enVision STEM Masters: Answer Key
              Intended Role: Instructor

            9-1: Lesson Plan (PDF)
              Intended Role: Instructor

            9-1: Lesson Plan (Editable)
              Intended Role: Instructor

            9-1: TI 83/84 Activity (PDF)
              Intended Role: Instructor

            9-1: TI 83/84 Activity (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 9-1
              Intended Role: Instructor

            9-1: Lesson Quiz (PDF)
              Intended Role: Instructor

            9-1: Lesson Quiz (Editable)
              Intended Role: Instructor

            9-1: Lesson Quiz: Answer Key
              Intended Role: Instructor

            9-1: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            9-1: Additional Practice (PDF)
              Intended Role: Instructor

            9-1: Enrichment (PDF)
              Intended Role: Instructor

            9-1: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            9-2: Lesson Plan (PDF)
              Intended Role: Instructor

            9-2: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 9-2
              Intended Role: Instructor

            9-2: Lesson Quiz (PDF)
              Intended Role: Instructor

            9-2: Lesson Quiz (Editable)
              Intended Role: Instructor

            9-2: Lesson Quiz: Answer Key
              Intended Role: Instructor

            9-2: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            9-2: Additional Practice (PDF)
              Intended Role: Instructor

            9-2: Enrichment (PDF)
              Intended Role: Instructor

            9-2: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            9-3: Lesson Plan (PDF)
              Intended Role: Instructor

            9-3: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 9-3
              Intended Role: Instructor

            9-3: Lesson Quiz (PDF)
              Intended Role: Instructor

            9-3: Lesson Quiz (Editable)
              Intended Role: Instructor

            9-3: Lesson Quiz: Answer Key
              Intended Role: Instructor

            9-3: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            9-3: Additional Practice (PDF)
              Intended Role: Instructor

            9-3: Enrichment (PDF)
              Intended Role: Instructor

            9-3: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            9-4: Lesson Plan (PDF)
              Intended Role: Instructor

            9-4: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 9-4
              Intended Role: Instructor

            9-4: Lesson Quiz (PDF)
              Intended Role: Instructor

            9-4: Lesson Quiz (Editable)
              Intended Role: Instructor

            9-4: Lesson Quiz: Answer Key
              Intended Role: Instructor

            9-4: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            9-4: Additional Practice (PDF)
              Intended Role: Instructor

            9-4: Enrichment (PDF)
              Intended Role: Instructor

            9-4: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            9-5: Lesson Plan (PDF)
              Intended Role: Instructor

            9-5: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 9-5
              Intended Role: Instructor

            9-5: Lesson Quiz (PDF)
              Intended Role: Instructor

            9-5: Lesson Quiz (Editable)
              Intended Role: Instructor

            9-5: Lesson Quiz: Answer Key
              Intended Role: Instructor

            9-5: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            9-5: Additional Practice (PDF)
              Intended Role: Instructor

            9-5: Enrichment (PDF)
              Intended Role: Instructor

            9-5: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            9-6: Lesson Plan (PDF)
              Intended Role: Instructor

            9-6: Lesson Plan (Editable)
              Intended Role: Instructor

            9-6: TI 83/84 Activity (PDF)
              Intended Role: Instructor

            9-6: TI 83/84 Activity (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 9-6
              Intended Role: Instructor

            9-6: Lesson Quiz (PDF)
              Intended Role: Instructor

            9-6: Lesson Quiz (Editable)
              Intended Role: Instructor

            9-6: Lesson Quiz: Answer Key
              Intended Role: Instructor

            9-6: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            9-6: Additional Practice (PDF)
              Intended Role: Instructor

            9-6: Enrichment (PDF)
              Intended Role: Instructor

            9-6: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            9-7: Lesson Plan (PDF)
              Intended Role: Instructor

            9-7: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 9-7
              Intended Role: Instructor

            9-7: Lesson Quiz (PDF)
              Intended Role: Instructor

            9-7: Lesson Quiz (Editable)
              Intended Role: Instructor

            9-7: Lesson Quiz: Answer Key
              Intended Role: Instructor

            9-7: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            9-7: Additional Practice (PDF)
              Intended Role: Instructor

            9-7: Enrichment (PDF)
              Intended Role: Instructor

            9-7: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            Topic 9: Performance Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 9: Performance Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 9: Performance Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 9: Performance Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 9: Performance Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 9: Performance Assessment Form B: Answer Key
              Intended Role: Instructor

            Topic 9: Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 9: Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 9: Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 9: Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 9: Assessment Form B (Editable)
              Intended Role: Instructor

            Topic 9: Assessment Form B: Answer Key
              Intended Role: Instructor

            CC Standards Practice Week 26
              Intended Role: Instructor

            CC Standards Practice Week 27
              Intended Role: Instructor

            CC Standards Practice Week 28
              Intended Role: Instructor

            CC Standards Practice Weeks 26-28: Answer Key
              Intended Role: Instructor

            Teacher's Edition eText: Topic 10
              Intended Role: Instructor

            Topic 10: Professional Development Video
              Intended Role: Instructor

            Topic 10: Readiness Assessment (PDF)
              Intended Role: Instructor

            Topic 10: Readiness Assessment (Editable)
              Intended Role: Instructor

            Topic 10: Readiness Assessment: Answer Key
              Intended Role: Instructor

            Topic 10: enVision STEM Project (PDF)
              Intended Role: Instructor

            Topic 10: enVision STEM Masters (PDF)
              Intended Role: Instructor

            Topic 10: enVision STEM Masters: Answer Key
              Intended Role: Instructor

            10-1: Lesson Plan (PDF)
              Intended Role: Instructor

            10-1: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 10-1
              Intended Role: Instructor

            10-1: Lesson Quiz (PDF)
              Intended Role: Instructor

            10-1: Lesson Quiz (Editable)
              Intended Role: Instructor

            10-1: Lesson Quiz: Answer Key
              Intended Role: Instructor

            10-1: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            10-1: Additional Practice (PDF)
              Intended Role: Instructor

            10-1: Enrichment (PDF)
              Intended Role: Instructor

            10-1: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            10-2: Lesson Plan (PDF)
              Intended Role: Instructor

            10-2: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 10-2
              Intended Role: Instructor

            10-2: Lesson Quiz (PDF)
              Intended Role: Instructor

            10-2: Lesson Quiz (Editable)
              Intended Role: Instructor

            10-2: Lesson Quiz: Answer Key
              Intended Role: Instructor

            10-2: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            10-2: Additional Practice (PDF)
              Intended Role: Instructor

            10-2: Enrichment (PDF)
              Intended Role: Instructor

            10-2: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            10-3: Lesson Plan (PDF)
              Intended Role: Instructor

            10-3: Lesson Plan (Editable)
              Intended Role: Instructor

            10-3: TI 83/84 Activity (PDF)
              Intended Role: Instructor

            10-3: TI 83/84 Activity (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 10-3
              Intended Role: Instructor

            10-3: Lesson Quiz (PDF)
              Intended Role: Instructor

            10-3: Lesson Quiz (Editable)
              Intended Role: Instructor

            10-3: Lesson Quiz: Answer Key
              Intended Role: Instructor

            10-3: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            10-3: Additional Practice (PDF)
              Intended Role: Instructor

            10-3: Enrichment (PDF)
              Intended Role: Instructor

            10-3: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            10-4: Lesson Plan (PDF)
              Intended Role: Instructor

            10-4: Lesson Plan (Editable)
              Intended Role: Instructor

            10-4: TI 83/84 Activity (PDF)
              Intended Role: Instructor

            10-4: TI 83/84 Activity (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 10-4
              Intended Role: Instructor

            10-4: Lesson Quiz (PDF)
              Intended Role: Instructor

            10-4: Lesson Quiz (Editable)
              Intended Role: Instructor

            10-4: Lesson Quiz: Answer Key
              Intended Role: Instructor

            10-4: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            10-4: Additional Practice (PDF)
              Intended Role: Instructor

            10-4: Enrichment (PDF)
              Intended Role: Instructor

            10-4: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            10-5: Lesson Plan (PDF)
              Intended Role: Instructor

            10-5: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 10-5
              Intended Role: Instructor

            10-5: Lesson Quiz (PDF)
              Intended Role: Instructor

            10-5: Lesson Quiz (Editable)
              Intended Role: Instructor

            10-5: Lesson Quiz: Answer Key
              Intended Role: Instructor

            10-5: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            10-5: Additional Practice (PDF)
              Intended Role: Instructor

            10-5: Enrichment (PDF)
              Intended Role: Instructor

            10-5: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            10-6: Lesson Plan (PDF)
              Intended Role: Instructor

            10-6: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 10-6
              Intended Role: Instructor

            10-6: Lesson Quiz (PDF)
              Intended Role: Instructor

            10-6: Lesson Quiz (Editable)
              Intended Role: Instructor

            10-6: Lesson Quiz: Answer Key
              Intended Role: Instructor

            10-6: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            10-6: Additional Practice (PDF)
              Intended Role: Instructor

            10-6: Enrichment (PDF)
              Intended Role: Instructor

            10-6: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            10-7: Lesson Plan (PDF)
              Intended Role: Instructor

            10-7: Lesson Plan (Editable)
              Intended Role: Instructor

            Teacher's Edition eText: Lesson 10-7
              Intended Role: Instructor

            10-7: Lesson Quiz (PDF)
              Intended Role: Instructor

            10-7: Lesson Quiz (Editable)
              Intended Role: Instructor

            10-7: Lesson Quiz: Answer Key
              Intended Role: Instructor

            10-7: Reteach to Build Understanding (PDF)
              Intended Role: Instructor

            10-7: Additional Practice (PDF)
              Intended Role: Instructor

            10-7: Enrichment (PDF)
              Intended Role: Instructor

            10-7: Mathematical Literacy and Vocabulary (PDF)
              Intended Role: Instructor

            Topic 10: Performance Assessment Form A (PDF)
              Intended Role: Instructor

            Topic 10: Performance Assessment Form A (Editable)
              Intended Role: Instructor

            Topic 10: Performance Assessment Form A: Answer Key
              Intended Role: Instructor

            Topic 10: Performance Assessment Form B (PDF)
              Intended Role: Instructor

            Topic 10: Performance Assessment Form B (Editable)
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            Topic 10: Performance Assessment Form B: Answer Key
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