Bearden High School Curriculum Guide Algebra I Revised (July 2016)

Bearden High School Curriculum Guide Algebra I Revised (July 2016) Common Core Arkansas Performance Standards: Curriculum Map for Algebra I ALGEBRA I 1 ST QUARTER UNIT 1: BASICS OF ALGEBRA, SIMPLIFYING EXPRESSIONS, SOLVING EQUATIONS, SOLVING LINEAR EQUATIONS (5 weeks) Essential Questions How can mathematical ideas be represented? Why is it helpful to represent the same mathematical idea in different ways? Content Standards AR July 2016 HSN.RN.B.3 Explain why The sum/difference or product/quotient (where defined) of two rational numbers is rational; The sum/difference of a rational number and an irrational number is irrational; The product/quotient of a nonzero rational number and an irrational number is irrational; and The product/quotient of two nonzero rationals is a nonzero rational HSN.Q.A.1 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. Vocabulary integer, order of operations, distributive property, commutative property, associative property, signs of numbers, integer rules, expression, equation, solution to an equation, no solution to an equation, multi-step equation Instructional Strategies Model Whole group practice Student explanations and presentations Peer work and small group Resources Text Supplemental Texts Calculator Assessments Daily formative assessments Mid unit quiz or quizzes Unit test HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. (I.E., Use units appropriate to the problem

being solved.) Limitation: This standard will be assessed in Algebra I by ensuring that some modeling tasks (involving Algebra I content or securely held content from grades 6-8) require the student to create a quantity of interest in the situation being described (i.e., a quantity of interest is not selected for the student by the task). For example, in a situation involving data, the student might autonomously decide that a measure of center is a key variable in a situation, and then choose to work with the mean. HSN.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. HSN.CED.A.4 Rearrange literal equations using the properties of equality. HSA.REI.A.1 Assuming that equations have a solution, construct a solution and justify the reasoning used. Note: Students are not required to use only one procedure to solve problems nor are they required to show each step of the process. Students should be able to justify their solution in their own words. (Limited to quadratics) HSA.REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. For example: The area of a square equals 49 square inches. The length of the side is 7 inches. Although -7 is a solution to the equation, x2 = 49, -7 is an extraneous solution Text Resources 1-1 Variables and Expressions 1-2 Order of Operations 1-4 The Distributive Property 1-5 Equations 2-1 Writing Equations 2-2 Solving One Step Equations 2-3 Solving Multi-Step Equations 2-4 Solving Equations with Variables on Both Sides 2-8 Literal Equations and Dimensional Analysis CCSS N.RN.3 1 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. Additional (NS) N.Q.1 2 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. Supporting (NS) N.Q.2 2 Define appropriate quantities for the purpose of descriptive modeling. ALC for N.Q.2: This standard will be assessed in Algebra I by ensuring that some modeling tasks (involving Algebra I content or securely held content from grades 6-8) require the student to create a quantity of interest in the situation being described (i.e., a quantity of interest is not selected for the student by the task). For example, in a situation involving data, the student might autonomously decide that a measure of center is a key variable in a situation, and then choose to work with the mean. Supporting (DS) N.Q.3 2 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Supporting (NS) A.CED.4 7 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange the formula D=RT to highlight R or T. Major (LCS) A.REI.1 8 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. ALC for A.REI.1: i) Major (LCS, NCS)

Bearden High School Curriculum Guide Algebra I Common Core Arkansas Performance Standards: Curriculum Map for Algebra I ALGEBRA I 1 ST QUARTER UNIT 2: SOLVING LINEAR INEQUALITIES, ABSOLUTE VALUE EQUATIONS & INEQUALITIES (3 weeks) Essential Questions Why is it helpful to represent the same mathematical idea in different ways? Content Standards AR July 2016 HSA.REI.B.3 Solve linear equations, inequalities and absolute value equations in one variable, including equations with coefficients represented by letters. CCSS A.REI.3 9 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Major (LCS) Vocabulary distributive property, expression, equation, solution to an equation, no solution to an equation, multi-step equation, inequality, greater than, greater than or equal to, less than, less than or equal to, not equal to, solution(s) to an inequality, number line, compound inequality, and/or compound inequality, absolute value equation, absolute value inequality Instructional Strategies Model Whole group practice Student explanations and presentations Peer work and small group Resources Text Supplemental Texts Calculator Graphing calculator Graph paper Text Resources 2-5 Solving Equations Involving Absolute Value 5-1 Solving Inequalities by Addition and Subtraction 5-2 Solving Inequalities by Multiplication and Division 5-3 Solving Multi-step Inequalities 5-4 Solving Compound Inequalities

5-5 Inequalities Involving Absolute Value Assessments Daily formative assessments Mid unit quiz or quizzes Unit test

Bearden High School Curriculum Guide Algebra I Common Core Arkansas Performance Standards: Curriculum Map for Algebra I ALGEBRA I 2nd QUARTER UNIT 3: LINEAR EQUATIONS, LINEAR INEQUALITIES (3 weeks) Essential Questions Why is it helpful to represent the same mathematical idea in different ways? Why is math used to model real-world situations? Why are graphs useful? Content Standards AR July 2016 HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Note: Including but not limited to equations arising from: Linear functions Quadratic functions Exponential functions Absolute value functions HSA.REI.C.6 Solve systems of equations algebraically and graphically. Limitation: i) Tasks have a real-world context. ii) Tasks have hallmarks of modeling as a mathematical practice (less defined tasks, more of the modeling cycle, etc.). HSA.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. HSA.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the Vocabulary (X,Y) coordinate, coordinate plane, coordinate system, x-axis, y- axis, slope, intercept, slope-intercept form, y=mx+b, y-intercept, parallel lines, perpendicular lines, rate of change, reciprocal, vertical line, horizontal line, undefined slope, origin, direct variation Instructional Strategies Model Whole group practice Student explanations and presentations Peer work and small group Resources Text Supplemental Texts Calculator Graphing calculator Graph paper Ruler Text Resources 1-7 Functions 3-1 Graphing Linear Equations 3-2 Solve Linear Equations by Graphing 3-3 Rate of Change and Slope

solutions of the equation f(x) = g(x); Find the solutions approximately by Using technology to graph the functions Making tables of values Finding successive approximations Include cases (but not limited to) where f(x) and/or g(x) are Linear Polynomial Absolute value Exponential (Introduction in Algebra 1, Mastery in Algebra 2) Teacher notes: Modeling should be applied throughout this standard. 3-4 Direct Variation 3-5 Arithmetic Sequences as linear Functions 4-1 Graphing Equations in Slope-Intercept Form 4-2 Writing Equations in Slope-Intercept Form 4-3 Wiring Equations in Point-Slope Form 4-4 Parallel and Perpendicular Lines 5-6 Graphing Inequalities in Two Variables HSF.IF.A.1 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. Understand that if f is a function and xx is an element of its domain, then f(xx) denotes the output of f corresponding to the input xx. Understand that the graph of ff is the graph of the equation yy = ff(xx). HSF.IF.A.2 In terms of a real-world context: Use function notation, Evaluate functions for inputs in their domains, and Interpret statements that use function notation. HSF.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example: The Fibonacci sequence is defined recursively by ff(0) = ff(1) = 1, ff(nn + 1) = ff(nn) + (nn 1) for nn 1. HSF.IF.A.4 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. Note: Key features may include but not limited to: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* Limitation: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, square

root functions, cube root functions, piecewise-defined functions (including step functions and absolute value functions), and exponential functions with domains in the integers. Compare note (ii) with standard F-IF.7. The function types listed here are the same as those listed in the Algebra I column for standards F- IF.6 and F-IF.9. HSF.IF.A.5 Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes. For example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* HSF.IF.A.6 Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. * Estimate the rate of change from a graph.* Limitation: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, square root functions, cube root functions, piecewise-defined functions (including step functions and absolute value functions), and exponential functions with domains in the integers. The function types listed here are the same as those listed in the Algebra I column for standards F-IF.4 and F-IF.9 HSF.IF.A.7 Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph linear and quadratic functions and, when applicable, show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior.

HSF.BF.A.1 Write a function that describes a relationship between two quantities. * From a context, determine an explicit expression, a recursive process, or steps for calculation. Limitation: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, and exponential functions with domains in the integers. HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit CCSS A.CED.1 7 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. ALC for A.CED.1: i) Tasks are limited to linear, quadratic, or exponential equations with integer exponents. Major (LCM, NCM) ALC for A.REI.6: i) Tasks have a real-world context. ii) Tasks have hallmarks of modeling as a mathematical practice (less defined tasks, more of the modeling cycle, etc.). Additional (LCS) A.REI.10 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). Major (FLCA) (LCA, NCA) A.REI.12 11 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. Major (LCS)

F.IF.1 12 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 f is a function and g is an element of its domain, then f(g) denotes the output of f corresponding to the input g. The graph of f is the graph of the equation y =f(g). Major (FLCS, FNCS) F.IF.2 12 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Major (FLCS, FNCS) F.IF.3 12 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. This standard is part of the Major work in Algebra I and will be assessed accordingly. Major (FLCA, FNCA) F.IF.4 13 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.* ALC for F.IF.4: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, square root functions, cube root functions, piecewise-defined functions (including step functions and absolute value functions), and exponential functions with domains in the integers. Compare note (ii) with standard F-IF.7. The function types listed here are the same as those listed in the Algebra I column for standards F-IF.6 and F-IF.9. Major (FLCA, FNCA) F.IF.5 13 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(x) gives the number of person-hours it

takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* Major (FLCA, FNCA) F.IF.6 13 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.* ALC for F.IF.6: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, square root functions, cube root functions, piecewise-defined functions (including step functions and absolute value functions), and exponential functions with domains in the integers. The function types listed here are the same as those listed in the Algebra I column for standards F-IF.4 and F-IF.9. Major (FLCA, FNCA) F.IF.7 14 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Supporting (FLCM, FNCM, NCM) F.BF.1 15 Write a function that describes a relationship between two quantities.* a. Determine an explicit expression, a recursive process, or steps for calculation from a context. ALC for F.BF.1a: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, and exponential functions with domains in the integers. Supporting (FLCA, FNCM) S.ID.7 21 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Major (LCA) S.ID.8 21 Compute (using technology) and interpret the correlation coefficient of a linear fit. Major (LCA) S.ID.9 21 Distinguish between correlation and causation. Major (LCA)

Assessments Daily formative assessments Mid unit quiz or quizzes Unit test ASSESSMENTS WILL INCLULE A MID-UNIT QUIZ OVER GRAPHING LINEAR EQUATIONS, SLOPE, AND INTERCEPTS. THE UNIT TEST WILL GO ON TO COVER GRAPHING AND WRITING LINEAR EQUATIONS IN SLOPE-INTERCEPT FORM, POINT-SLOPE FORM, AND STANDARD FORM, AS WELL AS GRAPHING AND WRITING LINEAR INEQUALITIES.

Bearden High School Curriculum Guide Algebra I Common Core Arkansas Performance Standards: Curriculum Map for Algebra I ALGEBRA I 2nd QUARTER UNIT 4: INTRODUCTION TO NONLINEAR GRAPHS (1 week) Essential Questions Content Standards AR JULY 2016 HSA.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. HSA.REI.D.12 Solve linear inequalities and systems of linear inequalities in two variables by graphing. HSF.IF.A.1 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. Understand that if f is a function and xx is an element of its domain, then f(xx) denotes the output of f corresponding to the input xx. Vocabulary (X,Y) coordinate, coordinate plane, coordinate system, x-axis, y- axis, slope, intercept, slope-intercept form, y=mx+b, y-intercept, parallel lines, perpendicular lines, rate of change, reciprocal, vertical line, horizontal line, undefined slope, origin, direct variation, exponential graphs, absolute value graphs, piece-wise graph, step graph, *EVERY GRAPH IS NOT LINEAR* Instructional Strategies Model Whole group practice Student explanations and presentations Peer work and small group Resources Text Supplemental Texts Calculator Graphing calculator Graph paper Ruler Assessments Daily formative assessments Mid unit quiz or quizzes

Understand that the graph of ff is the graph of the equation yy = ff(xx). Unit test HSF.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example: The Fibonacci sequence is defined recursively by ff(0) = ff(1) = 1, ff(nn + 1) = ff(nn) + (nn 1) for nn 1. HSF.IF.A.4 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. Note: Key features may include but not limited to: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* Limitation: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, square root functions, cube root functions, piecewise-defined functions (including step functions and absolute value functions), and exponential functions with domains in the integers. Compare note (ii) with standard F-IF.7. The function types listed here are the same as those listed in the Algebra I column for standards F- IF.6 and F-IF.9. HSF.IF.A.5 Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes. For example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* HSF.IF.A.6 Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified

interval. * Estimate the rate of change from a graph.* Limitation: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, square root functions, cube root functions, piecewise-defined functions (including step functions and absolute value functions), and exponential functions with domains in the integers. The function types listed here are the same as those listed in the Algebra I column for standards F-IF.4 and F-IF.9. HSF.IF.A.7 Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph linear and quadratic functions and, when applicable, show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior. HSF.BF.A.1 Write a function that describes a relationship between two quantities. * From a context, determine an explicit expression, a recursive process, or steps for calculation. Limitation: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, and exponential functions with domains in the integers CCSS A.REI.10 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). Major (FLCA) (LCA, NCA) A.REI.12 11 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. Major (LCS)

F.IF.1 12 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 f is a function and g is an element of its domain, then f(g) denotes the output of f corresponding to the input g. The graph of f is the graph of the equation y =f(g). Major (FLCS, FNCS) F.IF.3 12 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. This standard is part of the Major work in Algebra I and will be assessed accordingly. Major (FLCA, FNCA) F.IF.4 13 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.* ALC for F.IF.4: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, square root functions, cube root functions, piecewise-defined functions (including step functions and absolute value functions), and exponential functions with domains in the integers. Compare note (ii) with standard F-IF.7. The function types listed here are the same as those listed in the Algebra I column for standards F-IF.6 and F-IF.9. Major (FLCA, FNCA) F.IF.5 13 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(x) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* Major (FLCA, FNCA)

F.IF.6 13 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.* ALC for F.IF.6: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, square root functions, cube root functions, piecewise-defined functions (including step functions and absolute value functions), and exponential functions with domains in the integers. The function types listed here are the same as those listed in the Algebra I column for standards F-IF.4 and F-IF.9. Major (FLCA, FNCA) F.IF.7 14 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Supporting (FLCM, FNCM, NCM) F.BF.1 15 Write a function that describes a relationship between two quantities.* a. Determine an explicit expression, a recursive process, or steps for calculation from a context. ALC for F.BF.1a: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, and exponential functions with domains in the integers. Supporting (FLCA, FNCM)

Bearden High School Curriculum Guide Algebra I Common Core Arkansas Performance Standards: Curriculum Map for Algebra I Algebra I 2nd QUARTER UNIT 5: DATA GRAPHS & CENTRAL TENDENCY (2 weeks) Essential Questions Vocabulary domain, range, independent variable, dependent variable, bar graph, divided bar graph, line graph, circle graph, box & whisker plot, stem & leaf plot, outlier, frequency table, histogram, central tendency, mean, median, mode, range. Content Standards AR JULY 2016 HSA.CED.A.2 Create equations in two or more variables to represent relationships between quantities Graph equations, in two variables, on a coordinate plane. HSA.CED.A.3 Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context. HSA.REI.C.6 Solve systems of equations algebraically and graphically. Limitation: i) Tasks have a real-world context. ii) Tasks Instructional Strategies Model Whole group practice Student explanations and presentations Peer work and small group Resources document camera, paper, pencil, calculator, graph paper, ruler, computer, text, and supplemental resources Assessments Daily formative assessments Mid unit quiz or quizzes Unit test

have hallmarks of modeling as a mathematical practice (less defined tasks, more of the modeling cycle, etc.). HSF.IF.B.5 Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes. For example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* HSF.LE.B.5 In terms of a context, interpret the parameters (rates of growth or decay, domain and range restrictions where applicable, etc.) in a function. Limitation: i) Tasks have a realworld context. ii) Exponential functions are limited to those with domains in the integers. HSS.ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). HSS.ID.A.2 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. HSS.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). For example: Be able to explain the effects of extremes or outliers on the measures of center and spread HSS.ID.A.5 Summarize categorical data for two categories in twoway 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

HSS.ID.A.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Note: Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. The focus of Algebra I should be on linear and exponential models while the focus of Algebra II is more on quadratic and exponential models. HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data CCSS A.CED.2 7 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Major (FLCM, FNCM) A.CED.3 7 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Major (LCS) ALC for A.REI.6: i) Tasks have a real-world context. ii) Tasks have hallmarks of modeling as a mathematical practice (less defined tasks, more of the modeling cycle, etc.). Additional (LCS) F.IF.5 13 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h( ) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* Major (FLCA, FNCA)

F.LE.5 18 Interpret the parameters in a linear or exponential function in terms of a context. ALC for F.LE.5: i) Tasks have a realworld context. ii) Exponential functions are limited to those with domains in the integers. Supporting (LCA, NCA) S.ID.1 19 Represent data with plots on the real number line (dot plots, histograms, and box plots). Additional (DS) S.ID.2 19 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. Additional (DS) S.ID.3 19 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Additional (DS) S.ID.5 20 Summarize categorical data for two categories in twoway 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. Supporting (DS) S.ID.6 20 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 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. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. ALC for S.ID.6a: i) Tasks have a real-world context. ii) Exponential functions are limited to those with domains in the integers. Supporting (LCA, FNCM)

S.ID.7 21 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Major (LCA) S.ID.8 21 Compute (using technology) and interpret the correlation coefficient of a linear fit. Major (LCA) S.ID.9 21 Distinguish between correlation and causation. Major (LCA)

Bearden High School Curriculum Guide Algebra I Common Core Arkansas Performance Standards: Curriculum Map for Algebra I Algebra I 2nd QUARTER UNIT 6: SYSTEMS OF EQUATIONS & INEQUALITIES (2 weeks) Essential Questions How can you find the solution to a math problem? Content Standards AR July 2016 HSA.CED.A.3 Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context. HSA.REI.C.5 Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination HSA.REI.C.6 Solve systems of equations algebraically and graphically. Limitation: i) Tasks have a real-world context. ii) Tasks Vocabulary (X,Y) coordinate, coordinate plane, coordinate system, x-axis, y- axis, slope, intercept, slope-intercept form, y=mx+b, y-intercept, system of equations, systems of parallel lines have no solution, intersection of lines, intersection of lines IS THE SOLUTION to the system, graphing method, substitution method, elimination method, linear combination method, Cramers Rule for 2x2 matrices method Instructional Strategies Model Whole group practice Student explanations and presentations Peer work and small group Resources Materials: document camera, paper, pencil, calculator, graph paper, ruler, computer, text, and supplemental resources Text Resources 6-1 Graphing Systems of Equations 6-2 Substitution 6-3 Elimination using Addition and Subtraction 6-4 Elimination using Multiplication

have hallmarks of modeling as a mathematical practice (less defined tasks, more of the modeling cycle, etc.). 6-5 Applying Systems of linear Equations 6-6 Systems of Inequalities CCSS A.CED.3 7 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Major (LCS) A.REI.5 10 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. Additional (LCA) A.REI.6 10 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. ALC for A.REI.6: i) Tasks have a real-world context. ii) Tasks have hallmarks of modeling as a mathematical practice (less defined tasks, more of the modeling cycle, etc.). Additional (LCS) Assessments TEST OVER SOLVING SYSTEMS OF EQUATIONS, BOTH ON GRAPH PAPER AND REAL-WORLD PROBLEMS RELATED TO REAL EVENTS ADDITIONAL ASSESSMENTS: HOMEWORK, INDEPENDENT CLASSWORK, OBSERVATION, SCHOOL CONTENT INTERIM ASSESSMENTS

Bearden High School Curriculum Guide Algebra I Algebra I 3RD QUARTER UNIT 7: EXPONENT RULES (2 weeks) Common Core Arkansas Performance Standards: Curriculum Map for Algebra I Essential Questions How can you make good decisions? What factors can affect good decision making? Vocabulary exponent, base, power, zero exponent rule, negative exponent rule, multiply/divide with the same base rule, distributing a power rule, scientific notation, exponential growth, exponential decay Content Standards AR JULY 2016 HSF.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. Show that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another CCSS F.LE.1 17 Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal Instructional Strategies Model Whole group practice Student explanations and presentations Peer work and small group Resources document camera, paper, pencil, calculator, computer, text, and supplemental resources Text Resources 7-1 Multiplication Properties of Exponents 7-2 Division Properties of Exponents 7-3 Rational Exponents 7-4 Scientific Notation 7-5 Exponential Functions 7-6 Growth and Decay

intervals, and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Supporting (FLCA, FNCA) Assessments TEST OVER EXPONENT RULES, SCIENTIFIC NOTATION, AND EXPONENTIAL GROWTH & DECAY ADDITIONAL ASSESSMENTS: HOMEWORK, INDEPENDENT CLASSWORK, OBSERVATION, SCHOOL CONTENT INTERIM ASSESSMENTs

Bearden High School Curriculum Guide Algebra I Common Core Arkansas Performance Standards: Curriculum Map for Algebra I Algebra I 3RD QUARTER UNIT 8: SIMPLIFYING RADICALS & RADICAL FORM (2 weeks) Essential Questions How can you choose a model to represent a real world situation? Vocabulary square root, radical, perfect square Content Standards AR JULY 2016 HSN.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. HSA.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.* Interpret parts of an expression using appropriate vocabulary, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example: Interpret as the product of P and a factor not depending on P CCSS N.Q.3 2 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Supporting (NS) Instructional Strategies Model Whole group practice Student explanations and presentations Peer work and small group Resources document camera, paper, pencil, calculator, computer, text, and supplemental resources Text Resources 10-1 Square Root Functions 10-2 Simplifying Radical Expressions 10-3 Operations with Radical Expressions 10-4 Radical Equations A.SSE.1 3 Interpret expressions that represent a quantity in terms of its context.* a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by

viewing one or more of their parts as a single entity. For example, interpret the square root of 50 (in radical form) as the product of the square root of 25 and the square root of 2. Major (LCA) Assessments ADDITIONAL ASSESSMENTS: HOMEWORK, INDEPENDENT CLASSWORK, OBSERVATION, SCHOOL LED CONTENT INTERIM ASSESSMENTS

Bearden High School Curriculum Guide Algebra I Common Core Arkansas Performance Standards: Curriculum Map for Algebra I Algebra I 3RD QUARTER UNIT 9: POLYNOMIAL OPERATIONS & FACTORING (5 weeks) Essential Questions When could a nonlinear function be used to model a real-world situation? Vocabulary standard form, degree of a polynomial, sum, difference, product, quotient by long division, quotient by synthetic division, factoring, greatest common factor (GCF), monomial, binomial, trinomial, polynomial, perfect square binomial, perfect square trinomial, twins Content Standards AR JULY 2016 HSA.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.* Interpret parts of an expression using appropriate vocabulary, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example: Interpret as the product of P and a factor not depending on P HSA.SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example: See that (x + 3)(x + 3) is the same as (x + 3)2 OR x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2). Limitation: i) Tasks are limited to numerical expressions and polynomial expressions in one variable. ii) Examples: Recognize 532 472 as a difference of squares and see an opportunity to rewrite it in the Instructional Strategies Model Whole group practice Student explanations and presentations Peer work and small group Resources document camera, paper, pencil, calculator, computer, text, and supplemental resources Text Resources 8-1 Adding and Subtracting Polynomials 8-2 Multiplying a Polynomial by a Monomial 8-3 Multiplying Polynomials 8-4 Special Products 8-5 Using the Distributive Property 8-6 Solving x 2 +bx+c=0 8-7 Solving ax 2 +bx+c=0

easier-to-evaluate form (53 + 47)(53 47). See an opportunity to rewrite aa2 + 9aa + 14 as (aa + 7)(aa + 2). 8-8 Differences of Squares 8-9 Perfect Squares HSA.SSE.A.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Note: Students should be able to identify and use various forms of a quadratic expression to solve problems. o Standard Form: aaxx + bbxx + cc o Factored Form: aa(xx rr1)(xx rr2) o Vertex Form: aa (xx h ) + kk Limitation: i) Tasks have a real-world context. As described in the standard, there is an interplay between the mathematical structure of the expression and the structure of the situation such that choosing and producing an equivalent form of the expression reveals something about the situation. ii) Tasks are limited to exponential expressions with integer exponents. HSA.APR.A.1 Add, subtract, and multiply polynomials Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication Note: If p and q are polynomials p + q, p q, and pq are also polynomials CCSS A.SSE.1 3 Interpret expressions that represent a quantity in terms of its context.* a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret 4x+12 as the product of 4 and (x+3) Major (LCA) A.SSE.2 3 Use the structure of an expression to identify ways to rewrite it. For example, see x squared -9 as (x+3) and (x-3), thus

recognizing it as a difference of squares that can be factored. ALC for A.SSE.2: i) Tasks are limited to numerical expressions and polynomial expressions in one variable. Major (NCA) A.SSE.3 4 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15! can be rewritten as (1.15!/!")!"! 1.012!"!to reveal the approximate equivalent monthly interest rate if the annual rate is 15% ALC for A.SSE.3c: i) Tasks have a real-world context. As described in the standard, there is an interplay between the mathematical structure of the expression and the structure of the situation such that choosing and producing an equivalent form of the expression reveals something about the situation. ii) Tasks are limited to exponential expressions with integer exponents. Supporting (NCS) A.APR.1 5 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. Major (NCS) Assessments

TEST OVER ADDING, SUBTRACTING, MULTIPLYING, DIVIDING FACTORING POLYNOMIALS ADDITIONAL ASSESSMENTS: HOMEWORK, INDEPENDENT CLASSWORK, OBSERVATION, SCHOOL CONTENT INTERIM ASSESSMENTS

Bearden High School Curriculum Guide Algebra I Common Core Arkansas Performance Standards: Curriculum Map for Algebra I Algebra I 4TH QUARTER UNIT 10: SOLVING & GRAPHING QUADRATIC EQUATIONS (4 weeks) Essential Questions Why do we use different methods to solve math problems? Vocabulary solve by factoring, solve using quadratic formula, solve by completing the square, find the zeros of the equation, parabola, maximum, minimum, axis of symmetry, x-intercept(s), y- intercept Content Standards AR JULY 2016 HSA.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Note: Students should be able to identify and use various forms of a quadratic expression to solve problems. o Standard Form: aaxx + bbxx + cc o Factored Form: aa(xx rr1)(xx rr2) o Vertex Form: aa (xx h ) + kk Limitation: i) Tasks have a real-world context. As described in the standard, there is an interplay between the mathematical structure of the expression and the structure of the situation such that choosing and producing an equivalent form of Instructional Strategies Model Whole group practice Student explanations and presentations Peer work and small group Resources document camera, paper, pencil, calculator, graph paper, ruler, computer, text, and supplemental resources Text Resources 9-1 Graphing Quadratic Functions 9-2 Solving Quadratic Equations by Graphing 9-3 Transformations of Quadratic Functions 9-4 Solving Quadratic Equations by Using Quadratic Formula

the expression reveals something about the situation. ii) Tasks are limited to exponential expressions with integer exponents. HSA.APR.B.3 Identify zeros of polynomials (linear, quadratic only) when suitable factorizations are available Use the zeros to construct a rough graph of the function defined by the polynomial. HSA.REI.B.4 Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (xx pp)2 = qq that has the same solutions. Note: This would be a good opportunity to demonstrate/explore how the quadratic formula is derived. This standard also connects to the transformations of functions and identifying key features of a graph (F-BF3). Introduce this with a leading coefficient of 1 in Algebra I. Finish mastery in Algebra II. Solve quadratic equations (as appropriate to the initial form of the equation) by: o Inspection of a graph o Taking square roots o Completing the square o Using the quadratic formula o Factoring Recognize complex solutions and write them as aa ± bbbb for real numbers a and b. (Algebra 2 only) Limitation: i) Tasks do not require students to write solutions for quadratic equations that have roots with nonzero imaginary parts. However, tasks can require the student to recognize cases in which a quadratic equation has no real solutions. HSF.IF.C.7 Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph linear and quadratic functions and, when applicable, show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior

HSF.IF.C.8 Write expressions for functions in different but equivalent forms to reveal key features of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values (vertex), and symmetry of the graph, and interpret these in terms of a context. Note: Connection to A.SSE.B.3b HSF.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Limitation: i) Tasks are limited to linear functions, quadratic functions, square root functions, cube root functions, piecewise-defined functions (including step functions and absolute value functions), and exponential functions with domains in the integers. The function types listed here are the same as those listed in the Algebra I column for standards F-IF.4 and F-IF.6. HSF.BF.A.1 7 Write a function that describes a relationship between two quantities. * From a context, determine an explicit expression, a recursive process, or steps for calculation. Limitation: i) Tasks have a real-world context. ii) Tasks are limited to linear functions, quadratic functions, and exponential functions with domains in the integers CCSS A.SSE.3 4 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15! can be rewritten as (1.15!/!")!"! 1.012!"!to reveal the approximate equivalent

monthly interest rate if the annual rate is 15% ALC for A.SSE.3c: i) Tasks have a real-world context. As described in the standard, there is an interplay between the mathematical structure of the expression and the structure of the situation such that choosing and producing an equivalent form of the expression reveals something about the situation. ii) Tasks are limited to exponential expressions with integer exponents. Supporting (NCS) A.APR.3 6 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. ALC for A.APR.3 i) Tasks are limited to quadratic and cubic polynomials in which linear and quadratic factors are available. For example, find the zeros of (X 2)(X 9). Supporting (NCA) A.REI.4 9 Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation into an equation of the form (x 5)(x+3) =y that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x squared = 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 3 ±square root 20. ALC for A.REI.4b: i) Tasks do not require students to write solutions for quadratic equations that have roots with nonzero imaginary parts. However, tasks can require the student to recognize cases in which a quadratic equation has no real solutions. Note, solving a quadratic equation by factoring relies on the connection between zeros and factors of polynomials (cluster AAPR.B). Cluster A- APR.B is formally assessed in Algebra II. Major (NCS) F.IF.7 14 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* a. Graph linear and