Algebra I: A Common Core Program Software and Textbook Scope & Sequence

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1 Unit 1: Relationships Between Quantities and Reasoning with Equations Chapter Lesson Title A Picture is Worth a Thousand Words Key Math Objective Quantities and Relationships Understanding Quantities and Their Relationships 1.2 A Sort of Sorts Analyzing and Sorting Graphs CCSS Key Terms Worked Peer Talk the Examples Analysis Talk This chapter introduces non-linear functions, including exponential, quadratic, linear piecewise, and linear absolute value functions. Students will classify each function family using graphing calculators, equations and graphs. Each function family is then defined and graphic organizers are created. Section 1: Recognizing Non-Numeric N.Q.2 Section 2: Recognizing Numeric dependent quantity, independent quantity Relations and F.LE.1.b Section 3: Recognizing Graphs of Section 4: Classifying Relations and F.IF.1 discrete graph, continuous graph, relation, domain, Graphs of Section 1: Identifying Key Characteristics of Graphs of F.IF.5 range, function, Vertical Line Test 1.3 There Are Many Ways to Represent Recognizing Algebraic and Graphical Representations of F.IF.5 F.IF.9 A.REI.10 F.IF.1 F.IF.2 F.IF.7.a function notation, increasing function, decreasing function, constant function, function family, linear functions, exponential functions, absolute minimum, absolute maximum, quadratic functions, linear absolute value functions, linear piecewise functions Function Families for 200 Alex Recognizing by Characteristics 2.1 The Plane! Modeling Linear Situations 2.2 What Goes UP Must Come Down Problem Solving Using Multiple Methods 2.3 Scouting for Prizes! Modeling Inequalities 2.4 We're Shipping Out 2.5 Play Ball! 2.6 Choose Wisely! Graphs, Equations & Inequalities Solving and Graphing Compound Inequalities Absolute Value Equations and Inequalities Understanding Non-Linear Graphs and Inequalities F.IF.1, F.IF.4, F.IF.7.a, F.IF.9 F.LE.1.b, A.CED.2 This chapter begins with a review of solving linear equations algebraically. A graphical method for solving linear equations or inequalities, which involves graphing the left and right side of a linear equation or inequality, is introduced. This graphical method is then generalized to non-linear equations and inequalities. A.REI.1, A.CED.1 A.CED.2 N.Q.1 A.SSE.1 A.REI.3, A.CED.1, A.CED.2 N.Q.1, A.SSE.1 A.CED.1, A.CED.2, A.CED.3 A.CED.1 A.CED.2 A.REI.3 A.CED.1 A.CED.2 A.CED.3 N.Q.1 A.CED.1 A.CED.2 A.CED.3 first differences, solution, point of intersection solve an inequality solution of a compound inequality, conjunction, disjunction opposites; absolute value; linear absolute value equation; linear absolute value inequality; equivalent compound inequality Linear and Four Quadrant Graphs Linear Equation and Inequality Solving with Graphs Linear Inequalities Absolute Value Equations and Inequalities Non-Linear Equation and Inequality Solving with Graphs Section 1: Graphing with Positive Integer Rates of Change Section 2: Graphing with Positive Fractional Rates of Change Section 3: Graphing with Negative Rates of Change Section 1: Solving Linear Equations and Inequalities Graphically Section 1: Graphing Inequalities Section 2: Graphing Compound Inequalities Section 3: Graphing Compound Inequalities with Non-Standard Solutions Section 4: Solving Linear Inequalities Section 5: Solving Compound Linear Inequalities Section 1: Solving Simple Absolute Value Equations Section 2: Solving Absolute Value Equations Section 3: Solving Simple Absolute Value Inequalities Section 4: Solving Simple Absolute Value Inequalities with Non-Standard Solutions Section 5: Solving Absolute Value Inequalities Section 1: Solving Non-Linear Equations and Inequalities Graphically Algebra I: A Common Core Program 1

2 3 3.1 Is it Getting Hot in Here? Linear Modeling Data Using Linear Regression This chapter focuses on linear functions, especially the mathematical and contextual meaning that can be determined from the form of a linear function. S.ID.6 S.ID.7 N.Q.2 A.REI.3 linear regression, line of best fit, linear regression equation, significant digits, correlation coefficient 3.2 Tickets For Sale Standard Form of Linear Equations A.SSE.1 A.CED.2 A.CED.3 A.CED.4 A.REI.3 standard form; slope-intercept form Linear in General Form Section 1: Modeling with Linear Inequalities Section 2: Modeling Linear Equations in General Form 3.3 Cool As a Cucumber or Hot Like a Tamale! Literal Equations in Standard and Slope-Intercept Form A.CED.2 A.CED.4 A.REI.1 literal equation Literal Equations Section 1: Solving Literal Equations with Variable Terms on the Same Side (No Type In) Section 2: Solving Literal Equations with Variable Terms on the Same Side (Type In) Section 3: Solving Literal Equations with Variable Terms on Opposite Sides (No Type In) Section 4: Solving Literal Equations with Variable Terms on Opposite Sides (Type In) Section 5: Solving Literal Equations (No Type In) Section 6: Solving Literal Equations (Type In) 3.4 A Growing Business Combining Linear Equations A.SSE.1 A.CED.2 A.CED.3 A.REI.3 Linear and the Distributive Property Equations of a Line Linear Function Operations and Composition Section 1: Modeling with Integer Rates of Change Section 2: Modeling with Fractional Rates of Change Section 3: Modeling using the Distributive Property over Division Section 4: Modeling More Complex Equations Section 1: Modeling Given Slope and a Point Section 2: Calculating Slopes Section 3: Modeling Given Two Points Section 4: Modeling Given an Initial Point Section 1: Evaluating Linear Section 2: Adding and Subtracting Linear Section 3: Modeling with Linear Function Composition Section 4: Composing Linear Algebra I: A Common Core Program 2

3 Unit 2: Linear and Exponential Relationships Chapter Lesson Title Key Math Objective Is There a Pattern Here? The Password Is Operations! Sequences Recognizing Patterns and Sequences Arithmetic and Geometric Sequences CCSS F.LE.1.b F.BF.1.a Key Terms sequence term of a sequence infinite sequence finite sequence arithmetic sequence common difference geometric sequence common ratio Worked Examples Peer Analysis Talk the Talk Sequences Sequences and This chapter sequences, and focuses on arithmetic and geometric sequences. Sequences are described using recursive and explicit formulas. The relationship between arithmetic and geometric sequences, and linear and exponential functions is developed. Section 1: Describing Patterns in Sequences Section 2: Writing Recursive Formulas Section 3: Writing Explicit Formulas Section 1: Writing Sequences as 4.3 The Power of Algebra is a Curious Thing Using Formulas to Determine Terms of a Sequence F.BF.1, F.BF.1.a F.BF.2, A.SSE.1 A.SSE.1.a index explicit formula recursive formula ` 4.4 Thank Goodness Descartes Didn't Drink Some Warm Milk! Graphs of Sequences F.IF.1 F.IF Well, Maybe It IS a Function! Sequences and Graphs of Linear and Exponential F.IF.1, F.IF.2, F.IF.3,F.BF.1, F.BF.2,F.LE.1, F.LE.1.a,F.LE.1.b, F.LE.1.c,, F.LE.5 This chapter examines the graphical behavior of exponential functions, including domain, range, increasing or decreasing, and asymptotes. Transformations of exponential functions are addressed. The relationship between rational exponents and radical form is introduced. Common bases are used to solve simple exponential equations algebraically. 5.1 Go for the Curve! Comparing Linear and Exponental A.SSE.1.a, A.SSE.1.b, A.CED.1, F.IF.3, F.IF.6, F.IF.7.e, F.BF.1.a, F.BF.2, F.LE.1.a, F.LE.1.b, F.LE.1.c,, F.LE.3,F.LE.5 simple interest, compound interest Exponential Section 1: Modeling Equations with Starting Points of One Section 2: Modeling Equations with Starting Points Other Than One 5.2 Downtown and Uptown Graphs of Exponential A.SSE.1.a, A.SSE.1.b, A.CED.1, A.REI.11, F.IF.4, F.IF.7.e, F.LE.5 horizontal asymptote Graphs of Exponential Section 1: Identifying Key Characteristics of Exponential Let the Transformations Begin! Take Some Time to Reflect Translations of Linear and Exponential Reflections of Linear and Exponential F.BF.3 A.REI.10 F.IF.4 A.REI.10 basic function, transformation, vertical translation, horizontal translation, argument of a function reflection, line of reflection Linear and Exponential Transformations Section 1: Shifting Vertically Section 2: Reflecting and Dilating using Graphs Section 3: Shifting Horizontally Section 4: Transforming using Tables of Values Section 5: Using Multiple Transformations Algebra I: A Common Core Program 3

4 5.5 Radical! Because It's Cliché! Properties of Rational Exponents 5.6 Checkmate! Solving Exponential 6 Systems of Equations N.RN.1 N.RN.2 A.REI.3, A.CED.1, A.CED.2, N.Q.2, A.REI.10, A.REI.11 cube root, index, nth root, radicand, rational exponent Properties of Exponents This chapter focuses on solving systems of linear equations graphically and algebraically using the substitution method or the linear combinations method. Section 1: Using the Product Rule Section 2: Using the Quotient Rule Section 3: Using the Power to a Power Rule Section 4: Using the Product to a Power Rule Section 5: Using the Quotient to a Power Rule Section 6: Using Properties of Exponents with Whole Number Powers Section 7: Simplifying Expressions with Negative Exponents Section 8: Using Properties of Exponents with Integer Powers 6.1 Prepping for the Robot Challenge Solving Linear Systems Grpahically and Algebraically A.REI.5 A.REI.6 A.REI.10 A.REI.11 system of linear equations; break-even point; substituion method; consistent systems; inconsistent systems Systems of Linear Equations Modeling Section 1: Solving Linear Systems using Integers Section 2: Solving Linear Systems using Decimals 6.2 There's Another Way? Using Linear Combinations to Solve a Linear System A.REI.5 A.REI.6 A.REI.10 A.REI.11 linear combinations method Linear System Solving using Substitution Section 1: Solving Linear Systems using Substitution 6.3 What's For Lunch? Solving More Systems A.REI.5 A.REI.6 A.REI.10 A.REI.11 Linear System Solving using Linear Combinations Section 1: Solving Linear Systems using Linear Combinations Section 2: Solving Linear Systems using Student's Choice 6.4 Which is the Best Method? Using Graphing, Substitution, and Linear Combinations A.REI.6 A.REI.10 A.REI The Playoffs Graphing Inequalities A.REI.12 half-plane 7.2 Working the System Systems of Linear Inequalities A.REI.12 contraints; solution of a linear inequality Our Biggest Sale of the Season! Take it to the Max or Min Systems of Inequalities Systems with More than Two Linear Inequalities This chapter introduces linear inequalities in two variables and then extends to systems of linear inequalities. System of inequalities are used to represent constraints and a maximizing or minimizing function is determined. A.REI.12 Linear Programming A.REI.12 linear programming Graphs of Linear Inequalities in Two Variables Systems of Linear Inequalities Section 1: Graphing Linear Inequalities in Two Variables Section 1: Systems of Linear Inequalities Algebra I: A Common Core Program 4

5 Unit 3: Descriptive Statistics Chapter Lesson Title Key Math Objective CCSS Key Terms 8 Analyzing Data Sets for One Variable Worked Examples Peer Analysis Talk the Talk This chapter focuses on data in one variable through the use of visual displays and summarizing statistics. Emphasis is placed on interpreting data and using appropriate techniques to describe data. 8.1 Start Your Day the Right Way Graphically Representing Data S.ID.1, S.ID.3 dot plot, discrete data, distribution of data symmetric, skewed right, skewed left, box plot, five number summary, histogram, continuous data Measures of Central Tendency Section 1: Calculating Mean, Median, Mode, and Range Section 2: Determining Appropriate Measures Section 3: Measuring the Effects of Changing Data Sets Section 4: Calculating a Data Value Given a Mean 8.2 Which Measure Is Better? Determining the Best Measure of Center for a Data Set S.ID.1 S.ID.2, S.ID.3 statistic, measure of central tendency, mean, median Categorical Data Display Comaprisons Section 1: Comparing Displays of Categorical Data 8.3 Whose Scores Are Better? 8.4 You Are Too Far Away! Putting the Pieces Together Calculating and Interpreting Standard Deviation Calculating IQR and Identifying Outliers S.ID.1 S.ID.2, S.ID.3 standard deviation S.ID.1 S.ID.2, S.ID.3 interquartile range (IQR), outlier, lower fence, upper fence Analyzing and Interpreting Data S.ID.1, S.ID.2, S.ID.3 stem-and-leaf plot side-by-side stem-and-leaf plot Analyzing Data Sets for Two Quantitative Variables 9.1 Like a Glove Least Squares Regression S.ID.6a, S.ID.6.c, S.ID.7 interpolation, extrapolation, least squares regression line Numerical Data Display Comparisons Mean Absolute Deviation Variance and Standard Deviation Lines of Best Fit Section 1: Comparing Histograms, Dot Plots, and Stem and Leaf Plots Section 2: Comparing Box and Whisker Plots Section 1: Calculating Mean Absolute Deviation Section 2: Using Mean Absolute Deviation Section 1: Computing Variants and Standard Deviation This chapter focuses on data in two variables through the scatter plots and regression equations. Emphasis is placed on determining the appropriate function to model a set of data and analyzing how well the regression equation fits the data. Section 1: Estimating Lines of Best Fit Section 2: Using Lines of Best Fit 9.2 Gotta Keep It Correlatin' Correlation S.ID.7, S.ID.8, S.ID.6a, S.ID.6c correlation, correlation coefficient, causation Line of Best Fit Analysis Section 1: Interpreting Lines of Best Fit Section 2: Analyzing Residuals of Lines of Best Fit 9.3 The Residual Effect Creating Residual Plots S.ID.6.a, S.ID.6.b, S.ID.7, S.ID.8 residual, residual plot 9.4 To Fit or Not To Fit? That Is The Question! Using Residual Plots S.ID.6.a, S.ID.6.b. S.ID.7, S.ID Who Are You? Who? Who? Could You Participate in Our Survey? Causation Vs. Correlation Analyzing Data Sets for Two Categorical Variables Represent and interpret categorical data on two variables using a two-way frequency table S.ID.9 S.ID.5 causation This chapter focuses on categorical data in two variables through the use of visual displays and summarizing statistics. Emphasis is placed on interpreting data and using appropriate techniques to describe data. categorical data, two-way frequency table, frequency distribution, joint frequency, marginal frequency distribution 10.2 It's So Hot Outside! 10.3 She Blinded Me with Science! Construct relative frequency tables Interpret relative frequency table using a marginal distribution S.ID.5 S.ID.5 relative frequency distribution, relative frequency marginal distribution relative frequency, conditional distribution Frequency and Relative Frequency Section 1: Reading Visual Displays of Frequency Tables 10.4 Oh! Switch the Station! Interpret relative frequency tables using conditional distributions S.ID.5 Algebra I: A Common Core Program 5

6 Unit 4: Expressions and Equations Chapter Lesson Title Key Math Objective CCSS Key Terms Curve Ball Exploring Quadratic 11.2 Just U and I 11.3 Walking the Curve? Are You Afraid of Ghosts? Just Watch that Pumpkin Fly! 11.6 The Form is "Key" Comparing Linear and Quadratic Domain, Range, Zeros, and Intercepts Factored Form of a Quadratic Function Investigating the Vertex of a Quadratic Function Vertex Form of a Quadratic Function More Than Meets the Transformations of Quadratic Eye Polynomial Expressions Controlling the Population They're Multiplying-- Like Polynomials! Graphs of Quadratic Adding and Subtracting A.SSE.1, A.CED.1, A.CED.2, F.IF.4, F.IF.7a A.SSE.1, A.CED.1, A.CED.2, F.IF.4, F.IF.7a A.SSE.1, A.CED.1, A.CED.2, F.IF.4, F.IF.7a A.SSE.1, A.SSE.3.a, A.CED.1, A.CED.2, F.IF.4, F.IF.5 F.IF.4 F.IF.5 F.IF.7.a standard form parabola second differences Worked Examples Peer Analysis Talk the Talk roots, zeros factor an expression, factored form vertical motion model, vertex, axis of symmetry vertex form Quadratic in Factored Form Equivalent Forms of Quadratic and Graphs Linear and Quadratic Transformations vertical dilation F.BF.3 dilation factor This chapter introduces operations with polynomials, including factoring quadratic trinomials. Quadratic equations are solved graphically, by factoring, and by completing the square. A.SSE.1.a, A.APR.1, A.CED.1, A.CED.2 polynomials, term, coeffiecient, monomial, binomial, trinomials, degree of the term, degree of the polynomial, standard form Polynomial Operations Multiplying and Factoring A.APR.1 Like Terms and Order of Operations This chapter examines the graphical behavior of quadratic functions, including domain, range, increasing and decreasing, maximum and minimum, and symmetry. Transformations of exponential functions are addressed. The relationship between the form of a quadratic function and the graph of a quadratic function is discussed, especially the graphical characteristics that can be determined from the form of a quadratic function. Section 1: Modeling Area as Product of Monomial and Binomial Section 2: Modeling Area as Product of Two Binomials Section 3: Maximizing Area Section 1: - Identifying Key Characteristics of a Parabola Section 2: - Using Graphs to Write Equivalent Forms of Quadratic Section 1: Shifting Vertically Section 2: Reflecting and Dilating using Graphs Section 3: Shifting Horizontally Section 4: Transformations using Tables of Values Section 5: Using Multiple Transformations Section 1: Adding Polynomials Section 2: Adding Polynomials with Higher Orders Section 3: Subtracting Polynomials Section 4: Using a Factor Table to Multiply Binomials Section 5: Multiplying Polynomials using a Factor Table Section 1: Combining Like Terms Section 2: Combining Like Terms with Multiple Variables Section 3: Simplifying Variable Expressions (No Type In) Section 4: Simplifying Variable Expressions (Type In) 12.3 What Factored Into It? Factoring Polynomials and Factoring to Solve Quadratic Equations A.SSE.3.a A.APR.1 Symmetric Property of Equality Quadratic Expression Factoring Section 1: Using a Factor Table to Multiply Binomials Section 2: Multiplying Binomials Section 3: Factoring Trinomials with Positive Constants and Coefficients of One Section 4: Factoring Trinomials with Negative Constants and Coefficients of One Section 5: Factoring Trinomials with Positive Constants and Coefficients Other Than One Section 6: Factoring Trinomials with Negative Constants and Coefficients Other Than One Section 7: Factoring using Difference of Squares Section 8: Factoring Quadratic Expressions 12.4 The Power of Zero Solving Quadratics by Factoring A.REI.4.b Zero Product Property What Makes You So A.SSE.2 perfect square trinomial, difference of two Quadratic Equation 12.5 Special Products Section 1: Solving Quadratic Equations by Factoring Special? A.APR.1 squares, sum of two cubes, difference of two cubes Solving Using Factoring Algebra I: A Common Core Program 6

7 12.6 Could It Be Groovy to be a Square? 12.7 Another Method 13 Simplifying and Simplifying Roots Solving by Completing the Square Solving Quadratic Equations A.SSE.3 A.REI.4 A.SSE.3.a, A.SSE.3.b, A.REI.4.a square root, positive square root, principal square root, negative square root, extract the square root, radical expression, radicand Simplification and Operations with Radicals completing the square Forms of Quadratics Section 1: Simplifying Radicals Section 2: Adding and Subtracting Radicals Section 3: Multiplying Radicals Section 4: Dividing Radicals Section 1: Converting Quadratics to General Form Section 2: Converting Quadratics to Factored Form Section 3: Converting Quadratics to Factored Form This chapter introduces the quadratic formula and emphasizes choosing an appropriate method to solve quadratic equations. Quadratic inequalities are solved graphically and algebraically. Systems of equations involving one or more quadratic equations are solved Ladies and Gentlemen: Please Welcome the Quadratic Formula! The Quadratic Formula A.REI.4.a A.REI.4.b A.SSE.3.a Quadratic Formula, discriminant It's Got Its Eye On You-- Or Your Ball! They're A Lot More Than Just Sparklers! You Must Have a System Using a Calculator-Based Ranger to Model Quadratic Movement A.REI.4.b quadratic regression, coefficient of determination Solving Quadratics Inequalities A.CED.1 Systems of Quadratic Equations A.REI.7 Real Number Systems Quadratic Equation Solving Quadratic in General Form Systems of Linear Quadratic Equations Section 1: Solving Quadratic Equations Section 1: Using Regression Section 2: Modeling Projectile Motion from Ground Section 4: Modeling Projectile Motion Section 1: Modeling Systems of Linear and Quadratic Equations Section 2: Modeling Systems of Two Quadratic Equations This chapter introduces the set of complex numbers which consists of real numbers and imaginary numbers. Properties of the complex number system are discussed. Quadratic equations with imaginary solutions are solved The Real Numbers For Realsies! The Numbers of the Real Number System N.RN.3 natural numbers, whole numbers, closed (closure), counterexample, integers, rational numbers, irrational numbers, real numbers, Venn diagram 14.2 Getting Real, and Knowing How Properties of the Real Number System N.RN.3 Include in Glossary: commutative, associative, distributive, additive identity, multiplicative identity, additive inverse, multiplicative inverse Rational and Irrational Numbers Section 1: Creating Number Line Section 2: Ordering Rational and Irrational Numbers Imagine the Possibilities It's Not Complex--Just Its Solutions are Complex! Imaginary and Complex Numbers Solving Quadratics with Complex Solutions N.RN.2 exponentiation, the number i, imaginary numbers, pure imaginary number, complex numbers, real part of a complex number, imaginary part of a complex number A.REI.4.b imaginary roots, imaginary zeros Operations with Complex Numbers Quadratic Equation Solving with Comlex Roots Section 1: Simplifying Radicals with Negative Radicands Section 2: Simplifying Powers of I Section 3: Adding and Subtracting Complex Numbers Section 4: Multiplying Complex Numbers Section 5: Multiplying Complex Conjugates Section 6: Dividing Complex Numbers Section 1: Solving Quadratic Equations with Complex Roots Algebra I: A Common Core Program 7

8 Unit 5: Quadratic and Modeling Chapter 15 Lesson Title Key Math Objective CCSS Key Terms Worked Peer Talk the Examples Analysis Talk Other and Inverses This chapter focuses on piecewise functions, absolute value functions, and step functions. Inverses of linear functions are introduced graphically, numerically, and algebraically, which is then extended to include non-linear functions I Graph In Pieces Piecewise 15.2 Step By Step Step 15.3 The Inverse Undoes what a Function Does Inverses of Linear 15.4 Inverses of Non-Linear People, Tea, and Carbon Dioxide Stop! What Is Your Reaction? Modeling Data Helps Us Make Predictions 16.4 BAC is BAD News 16.5 Gas Prices and Single Family Homes Mathematical Modeling Modeling Using Exponential Modeling Stopping Distances and Reaction Times Using Quadratic to Model Data Choosing the Best Function to Model Data Modeling with Piecewise N.Q.2, F.IF.4, F.IF.5, F.IF.7b N.Q.2, F.IF.4, F.IF.5, F.IF.7b A.CED.1, A.CED.4, F.IF.1, F.IF.2, F.BF.1.a, F.BF.4.a A.CED.4, F.IF.1, F.IF.2, F.IF.5, F.IF.7, F.BF.4.a F.IF.7, F.BF.1, F.BF.4 F.LE.1, F.IF.7, F.BF.1, F.BF.4, F.LE.1, F.IF.7,F.BF.1, F.BF.4, F.LE.1, F.IF.7, F.BF.1, F.BF.4 F.LE.1, F.IF.7, F.BF.1, F.BF.4, F.LE.1, piecewise functions step function, greatest integer function floor functions, least integer function ceiling function inverse operation, inverse function, composition of functions Linear Piecewise one-to-one function, restrict the domain Inverses of Curve of Best Fit Analysis Linear and Non-Linear Regression Analysis Section 1: Graphing Piecewise Linear Section 2: Using Piecewise Linear Section 1: Sketching Graphs of Inverses Section 2: Recognizing Graphs of Inverses Section 3: Calculating Inverses of Linear This chapter presents opportunities to model real-world data using linear, exponential, quadratic, and piecewise functions. The focus is on determining the appropriate function or functions for a given data set. Section 1: Interpreting Curves of Best Fit Section 2:Analyzing Residuals of Curves of Best Fit Section 1: Analyzing Lines and Curves of Best Fit Algebra I: A Common Core Program 8