High School Math Solution A1.N.1 Extend the understanding of number and operations to include square roots and cube roots A1.A.1 Represent and solve and real-world problems using linear equations, absolute value equations, and systems of equations; interpret solutions in the original context. A1.A.2 Represent and solve real-world and problems using linear inequalities, compound inequalities and systems of linear inequalities; interpret solutions in the original context. 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 and real-world problems (e.g., angle measures, geometric formulas, science, or statistics) and interpret the solutions in the original context. Solve absolute value equations and interpret the solutions in the original context. Analyze and solve real-world and 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 context. Represent relationships in various contexts with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions. 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: 9: Radical 9: Radical & & 6: Systems of & 7: Systems & 7: Systems 5.5 Radical! Because It s a Cliché! (337) 12.6 Could it Be Groovy to Be a Square? (761) 9.4 Keepin It Real (693) 9.5 Time to Operate! (709) 3.1 Is it Getting Hot in Here? (163) 3.2 Tickets for Sale (173) 2.5 Play Ball! (123) 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) 7.1 The Play Offs (411) 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) 8: Radical 8: Radical 1: Simplification and Operations with Radicals 1: Simplification and Operations with Radicals 4: Absolute Value 5: Systems 6: Linear in 4: Absolute Value 6: Linear in 1: Simplifying Radicals 2: Adding and Subtracting Radicals 3: Multiplying Radicals 4: Dividing Radicals 1: Graphing Simple Absolute Value using Number Lines 2: Solving Absolute Value 1: Representing Systems 2: Solving Linear Systems Using Combinations 3: Solving Linear Systems Using Any Method 1: Graphing Linear in 3: Reasoning About Absolute Value 2: Systems See supplemental materials on Carnegie Learning s microsite at: http://www.carnegielearning.com/okalgebra1 High School Math Solution: Alignment to OAS 1
High School Math Solution A1.A.3 Generate equivalent algebraic expressions and use algebraic properties to evaluate expressions and arithmetic and geometric sequences. A1.A.3.1 A1.A.3.2 A1.A.3.3 A1.A.3.4 A1.A.3.5 A1.A.3.6 Solve equations involving several variables for one variable in terms of the others. 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. Module 3, Topic 1: Algebraic 4: Sequences 4: Sequences 3.3 Cool as a Cucumber of Hot Like a Tamale (187) 12.1 Controlling the Population (703) 12.2 They re Multiplying - Like Polynomials (717) 12.3 What Factored Into It?(731) 12.4 Zeroing In (743) 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) 4: Quadratics 4: Quadratics 4: Polynomial Operations 5: Quadratic Expression Factoring 5: Quadratic Expression Factoring 3: Sequences 3: Sequences 1: Introduction to Polynomial Arithmetic 2: Adding Polynomials 3: Subtracting Polynomials 4: Using a Factor Table to Multiply Polynomials 5: Multiplying Polynomials 1: Using a Factor Table to Multiply Binomials 2: Multiplying Binomials 3: Factoring Trinomials with Coefficients of One 1: Describing Patterns in Sequences 2: Writing Recursive Formulas 3: Writing Explicit Formulas 4: Sequences and 1: Describing Patterns in Sequences 2: Writing Recursive Formulas 3: Writing Explicit Formulas 4: Sequences and See supplemental materials on Carnegie Learning s microsite at: http://www.carnegielearning.com/okalgebra1 High School Math Solution: Alignment to OAS 2
High School Math Solution A1.A.4 Analyze change involving linear equations in real-world and A1.F.1 Understand functions as descriptions of covariation (how related quantities vary together) in real-world and A1.A.4.1 A1.A.4.2 A1.A.4.3 A1.A.4.4 A1.F.1.1 A1.F.1.2 A1.F.1.3 A1.F.1.4 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 real-world and Solve 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 the line, x- and y-intercept, or a set of data points), write the equation of a line. 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 situations. Given a graph modeling a real-world situation, read and interpret the linear piecewise function (excluding step functions) & 1: Tools of Geometry & Module 2, Topic 3: Introduction to & 15: Other and Inverses 1.5 Did You Find a Parking Spot? (61) 3.2 Tickets for Sale 3.3 Cool As a Cucumber or Hot Like a Tamale! 1.1 A Picture is Worth a Thousand Words (3) Represent (35) 1.2 A Sort of Sorts (17) 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 Represent (35) Represent (35) 15.1 I Graph in Pieces (877) 1: Tools of Geometry 3: Parallel and Perpendicular Lines 1: Relations and 1: Function Overview 1: Modeling with Rates of Change 2: Modeling Linear Given Two Points 3: Modeling Linear Using Multiple Representations 1: Introduction to Parallel and Perpendicular Lines 2: Modeling Parallel and Perpendicular Lines 5: Comparing Linear in Different Forms 1: Exploring 2: Exploring Graphs of 3: Classifying Relations and 1: Identifying Quantities See supplemental materials on Carnegie Learning s microsite at: http://www.carnegielearning.com/okalgebra1 High School Math Solution: Alignment to OAS 3
High School Math Solution A1.F.2 Recognize functions and understand that families of functions are characterized by their rate of change. A1.F.2.1 A1.F.2.2 Distinguish between linear and nonlinear (including exponential) functions arising from real-world and situations that are represented in tables, graphs, and equations. Understand that linear functions grow by equal intervals and that exponential functions grow by equal factors over equal intervals 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 and tools that may include graphing calculators. 5: 5: 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) 5: Compare Linear and 6: Linear and Transformations 1: Recognizing Linear and Models 1: Introduction to Transforming 2: Shifting Vertically 3: Reflecting and Dilating Using Graphs 4: Shifting Horizontally 5: Transforming Using Tables of Values 6: Using Multiple Transformations A1.F.3.1 Identify and generate equivalent representations of linear equations, graphs, tables, and real-world situations. & Represent (35) A1.F.3 Represent functions in multiple ways and use the representation to interpret real-world and A1.F.3.2 Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of real-world and & 5: Represent (35) 3.1 Is it Getting Hot in Here? (163) 5.1 Go for the Curve! (295) 5.2 Downtown and Uptown (305) 1: Function Overview 4: Evaluating Liner 11: Introduction to Quadratic 11.1 Up and Down or Down and Up (617) A1.F.3.3 Add, subtract, and multiply functions using function notation See supplemental materials on Carnegie Learning s microsite at: http://www.carnegielearning.com/okalgebra1 High School Math Solution: Alignment to OAS 4
High School Math Solution 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.D.1.1 A1.D.1.2 A1.D.1.3 A1.D.2.1 A1.D.2.2 A1.D.2.3 A1.D.2.4 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. Apply probability concepts to realworld situations to make informed decisions. 8: Analyzing Data Sets for One Variable 9: Correlation and Residuals 14: Probability 14: Probability 14: Probability 15: More Probability and Counting 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 3: Descriptive 9: Probability 15.5 To Spin or Not to Spin (1207) 9: Probability 1: Numerical Summary 2: Lines of Best Fit 1: Sample Spaces 2: Independence and Conditional Probability 2: Independence and Conditional Probability 1: Determining Appropriate Measures 2: Measuring the Effects of 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 4: Recognizing Concepts of Conditional Probability 5: Calculating Concepts of Conditional Probability 6: Calculating Compound Probabilities See supplemental materials on Carnegie Learning s microsite at: http://www.carnegielearning.com/okalgebra1 High School Math Solution: Alignment to OAS 5