CL Algebra I Alignment to OAS CARNEGIE LEARNING TEXTBOOK

Transcription

1 CL Alignment to OAS A1.N.1 Extend the understanding of number and operations to include square roots and cube roots A1.A.1 Represent and solve mathematical and real-world problems using linear equations, absolute value equations, and systems of equations; interpret solutions in the original A1.A.2 Represent and solve real-world problems using linear inequalities, compound inequalities and systems of linear inequalities; interpret solutions in the original A1.N.1.1 A1.N.1.2 A1.A.1.1 A1.A.1.2 A1.A.1.3 A1.A.2.1 A1.A.2.2 A1.A.2.3 Write square roots and cube roots of monomial algebraic expressions in simplest radical form Add, subtract, multiply, and simplify square roots of monomial algebraic expressions and divide square roots of whole numbers, rationalizing the denominator when necessary. Use knowledge of solving equations with rational values to represent and solve mathematical and real-world problems (e.g., angle measures, geometric formulas, science, or statistics) and interpret the solutions Solve absolute value equations and interpret the solutions in the original Analyze and solve real-world and mathematical problems involving systems of linear equations with a maximum of two variables by graphing (may include graphing calculator or other appropriate technology), substitution, and elimination. Interpret the solutions in the original Represent relationships in various contexts with linear inequalities; Represent relationships in various contexts with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line. Solve systems of linear inequalities with a maximum of two variables; graph and interpret the solutions on a coordinate plane. 5.5 Radical! Because It's a Cliché! (337) 12.6 Could it Be Groovy to Be a Square? (761) 9: Radical 9.4 Keepin' It Real (693) 8: Radical Expressions 9: Radical 9.5 Time to Operate! (709) 8: Radical Expressions 3.1 Is it Getting Hot in Here? (163) 3.2 Tickets for Sale (173) 3.4 A Growing Business (195) 2.5 Play Ball! (123) 6: Systems of 6.1 Prepping for the Robot Challenge (367) 6.2 There's Another Way? (383) 6.3 What's for Lunch? (391) 6.4 Which is the Best Method? (399) 2.3 Scouting for Prizes (101) 7: Systems of Linear Inequalities 7.1 The Play Offs (411) 7: Systems of Linear Inequalities 2.4 We're Shipping Out (111) 2.5 Play Ball! (123) 7.2 Working the System (419) 7.3 Our Biggest Sale of the Season (431) 7.4 Take it to the Max or Min (439) 1: Simplification and Operations with 1: Simplification and Operations with 4: Absolute Value 5: Systems of Linear 4: Absolute Value 1: Simplifying 2: Adding and Subtracting 3: Multiplying 4: Dividing 1: Representing Systems of Linear 2: Solving Linear Systems Using Combinations 3: Solving Linear Systems Using Any Method 6: Linear Inequalities in 1: Graphing Linear Two Variables 3: Reasoning About Absolute Value Inequalities 6: Linear Inequalities in 2: Systems of Linear Two Variables 1: Graphing Simple Absolute Value using Number Lines 2: Solving Absolute Value Inequalities in Two Variables Inequalities A1.A.3.1 Solve equations involving several variables for one variable in terms of the others. 3.3 Cool as a Cucumber of Hot Like a Tamale (187) Page 1 of 5

2 CL Alignment to OAS A1.A.3 Generate equivalent algebraic expressions and use algebraic properties to evaluate expressions and arithmetic and geometric sequences. A1.A.4 Analyze mathematical change involving linear equations in real-world A1.A.3.2 A1.A.3.3 A1.A.3.4 A1.A.3.5 A1.A.3.6 A1.A.4.1 A1.A.4.2 A1.A.4.3 Simplify polynomial expressions by adding, subtracting, or multiplying. Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1. Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as!! = 2! +!. Recognize that arithmetic sequences are linear using equations, tables, graphs, and verbal descriptions. Use the pattern, find the next term Recognize that geometric sequences are exponential using equations, tables, graphs and verbal descriptions. Given the formula f(x) = a(r)^x, find the next term and define the meaning of a and r within the context of the problem. Calculate and interpret slope and the x- and y-intercepts of a line using a graph, an equation, two points, or a set of data points to solve realworld Solve mathematical and real-world problems involving lines that are parallel, perpendicular, horizontal, or vertical Express linear equations in slopeintercept, point-slope, and standard forms and convert between these forms. Given sufficient information (slope and y-intercept, slope and one-point on the line, two points on Module 3, Topic 1: Algebraic Expressions 4: Sequences 4: Sequences 1: Tools of Geometry 12.1 Controlling the Population (703) 4: Quadratics 12.2 They're Multiplying - Like Polynomials (717) 12.3 What Factored Into It?(731) 12.4 Zeroing In (743) 4: Quadratics 12.5 What Makes You So Special? (751) 1.1 No Substitution for Hard Worked (M3-7) 4.1 Is There a Pattern Here? (213) 4.2 The Password is Optional (223) 4.3 The Power of Algebra is Curious (235) 4.4 Graphs of Sequences (251) 4.5 Well, Maybe it IS a Function! (275) 4.1 Is There a Pattern Here? (213) 4.2 The Password is Optional (223) 4.3 The Power of Algebra is Curious (235) 4.4 Graphs of Sequences (251) 4.5 Well, Maybe it IS a Function! (275) 1.5 Did You Find a Parking Spot? 1: Tools of Geometry (61) 3.2 Tickets for Sale 3.3 Cool As a Cucumber or Hot Like a Tamale! 1: Introduction to Polynomial Arithmetic 2: Adding Polynomials 4: Polynomial 3: Subtracting Polynomials Operations 4: Using a Factor Table to Multiply Polynomials 5: Multiplying Polynomials 1: Using a Factor Table to 5: Quadratic Multiply Binomials Expression Factoring 2: Multiplying Binomials 5: Quadratic 3: Factoring Trinomials with Expression Factoring Coefficients of One 1: Describing Patterns in Sequences 3: Sequences 2: Writing Recursive Formulas 3: Writing Explicit Formulas 4: Sequences and 1: Describing Patterns in Sequences 3: Sequences 2: Writing Recursive Formulas 3: Writing Explicit Formulas 4: Sequences and 1: Modeling with Rates of Change 2: Modeling Linear 2: Linear Given Two Points 3: Modeling Linear Using Multiple Representations 1: Introduction to Parallel and 3: Parallel and Perpendicular Lines Perpendicular Lines 2: Modeling Parallel and Perpendicular Lines 5: Comparing Linear 2: Linear in Different Forms Page 2 of 5

3 CL Alignment to OAS A1.F.1 Understand functions as descriptions of covariation (how related quantities vary together) in real-world A1.F.2 Recognize functions and understand that families of functions are characterized by their rate of change. A1.F.3 Represent functions in multiple ways and use the representation to interpret real-world A1.A.4.4 A1.F.1.1 A1.F.1.2 A1.F.1.3 A1.F.1.4 A1.F.2.1 A1.F.2.2 A1.F.3.1 A1.F.3.2 Translate between a graph and a situation described qualitatively. Distinguish between relations and functions. Identify the dependent and independent variables as well as the domain and range given a function, equation, or graph. Identify restrictions on the domain and range in real-world contexts. Write linear functions, using function notation, to model real-world and mathematical situations. Given a graph modeling a real-world situation, read and interpret the linear piecewise function (excluding Distinguish between linear and nonlinear (including exponential) functions arising from real-world situations that are Recognize the graph of the functions f(x) x and g(x) =! and predict the effects of transformations [!(! +!) and!(!) +!, where! is a positive or negative constant] algebraically and graphically using various methods Identify and generate equivalent representations of linear equations, graphs, tables, and real-world situations. Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of realworld 1.1 A Picture is Worth a Thousand Words (3) 1.2 A Sort of Sorts (17) Module 2, Topic 3: Introduction to 3.3 One or More Xs to One Y (M2-205) 1.1 A Picture is Worth a Thousand Words 1.2 Analyzing and Sorting Graphs 15: Other and Inverses 15.1 I Graph in Pieces (877) 11: Introduction to Quadratic 1.4 Function Families for 200, Alex (53) 5.1 Go for the Curve! (295) 5.2 Downtown and Uptown (305) 1.4 Function Families for 200, Alex (53) 5.3 Let the Transformations Begin! (313) 5.4 Take Some Time to Reflect (337) 3.1 Is it Getting Hot in Here? (163) 3.4 A Growing Business (195) 5.1 Go for the Curve! (295) 5.2 Downtown and Uptown (305) 11.1 Up and Down or Down and Up (617) 1: Exploring 2: Linear 2: Exploring Graphs of 1: Relations and 3: Classifying Relations and 1: Function Overview 1: Identifying Quantities 5: Compare Linear and 1: Recognizing Linear and Exponential Exponential Models 1: Introduction to 6: Linear and Exponential Transformations 1: Function Overview Transforming 2: Shifting Vertically 3: Reflecting and Dilating Using Graphs 4: Shifting Horizontally 4: Evaluating Liner Page 3 of 5

4 CL Alignment to OAS A1.D.1 Display, describe, and compare data. For linear relationships, make predictions and assess the reliability of those predictions. A1.D.2 Calculate probabilities and apply probability concepts. A1.F.3.3 A1.D.1.1 A1.D.1.2 A1.D.1.3 A1.D.2.1 A1.D.2.2 A1.D.2.3 Add, subtract, and multiply functions using function notation Describe a data set using data displays, describe and compare data sets using summary statistics, including measures of central tendency, location, and spread. Know how to use calculators, spreadsheets, or other appropriate technology to display data and calculate summary statistics. Collect data and use scatterplots to analyze patterns and describe linear relationships between two variables. Using graphing technology, determine regression lines and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions. Interpret graphs as being discrete or continuous Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities. Describe the concepts of intersections, unions, and complements using Venn diagrams to evaluate probabilities. Understand the relationships between these concepts and the words AND, OR, and NOT. Calculate experimental probabilities by performing simulations or experiments involving a probability model and using relative frequencies of outcomes. 3.4 A Growing Business (195) 8: Analyzing Data Sets for One Variable 9: Correlation and Residuals 8.1 Start Your Day Out Right (455) 8.2 Which Measure is Better? (469) 8.3 You Are Too Far Away!(479) 8.4 Whose Scores are Better?(489) 8.5 Putting the Pieces Together (505) 9.1 Like a Glove (523) 9.2 Gotta Keep It Correlatin' (533) 9.3 The Residual Effect (541) 9.4 To Fit or Not To Fit? That is the Question! (553) 9.5 Who Are You? Who? Who? (563) 1.2 A Sort of Sorts (17) 14.1 These Are a Few of My Favorite Things (1037) 14.2 It's In the Cards (1045) 14.3 And? (1069) 14.4 Or? (1085) 14.5 And, Or, and More! (1099) 14.6 Do You Have a Better Chance of Winning the Lottery or Getting Struck by Lightening? (1111) 14.3 And? (1069) 14.4 Or? (1085) 14.5 And, Or, and More! (1099) 14.6 Do You Have a Better Chance of Winning the Lottery or Getting Struck by Lightening? (1111) 3: Descriptive Statistics 1: Numerical Summary 2: Measuring the Effects of Statistics 3: Descriptive Statistics 2: Lines of Best Fit 9: Probability 1: Sample Spaces 2: Independence and 1: Determining Appropriate Measures Changing Data Sets 3: Calculating and Interpreting Measures of Center 1: Estimating Lines of Best Fit 2: Using Lines of Best Fit 3: Interpreting Lines of Best Fit 4: Analyzing Residuals of Lines of Best Fit 1: Analyzing Sample Spaces with Visual Representations 2: Analyzing Sample Spaces 3: Calculating the Sample Space for Independent and Dependent Actions 1: Independent Events 2: Conditional Probability 3: Understanding Frequency Tables Conditional Probability 4: Recognizing Concepts of Conditional Probability 5: Calculating Concepts of Conditional Probability Page 4 of 5

5 CL Alignment to OAS Apply probability concepts to realworld situations to make informed 15: More Probability and Counting 15.5 To Spin or Not to Spin (1207) 9: Probability 2: Independence and 6: Calculating Compound A1.D.2.4 Conditional Probability Probabilities decisions. Page 5 of 5