Carnegie Learning High School Math Solution Virginia Standards Alignment: Algebra II

Transcription

1 Virginia Standards Alignment: Virginia State Standard Textbook MATHia Std. Description Course Chapter Lesson Module Unit Workspace a. The student will add, subtract, multiply, divide, and simplify rational algebraic expressions; 4: and 4.1: Don t Take This Out of ConText: (p. 317) 4.2 The Great Divide (p. 325) and 1: Simplifying 2: Multiplying and Dividing 3: Adding and Subtracting AII.1 b. add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents; and 8: Solving 9: Radical 8.1: There Must Be a Explanation (p. 603) 8.2: Different Client, Same Deal (p. 613) 9.4: Keepin It Real (p. 693) 9.5: Time to Operate! (p. 709) Radical Radical Radical with Variables Radical with Variables 1: Simplifying Radicals with Variables 2: Adding and Subtracting Radicals with Variables 3 Multiplying Radicals with Variables 1: Simplifying Radicals with Variables 2: Adding and Subtracting Radicals with Variables 3: Multiplying Radicals with Variables c. factor polynomials completely in one or two variables. 4: and 4.3: The Factors of Life (p. 343) 4.4: Break It Down (p. 351) 4.5: Getting to the Root of It All (p. 363) 4.6: Identity Theft (p. 371) AII.2 The student will perform operations on complex numbers and express the results in simplest form using patterns of the powers of i. 2: 2.6: Now It Is Getting Complex But It Is Still Not Difficult (p. 165) Operations with Complex Numbers 1: Introduction to Complex Numbers 2: Simplifying Radicals with Negative Radicands 3: Simplifying Powers of i 4: Adding and Subtracting Complex Numbers 5: Multiplying Complex Numbers AII.3 The student will solve Forms of 1: Equation Solving 2: Solving with Complex Roots

2 and 1: Solving that Result in Linear 2: Solving that Result in 3: Solving with Extraneous Solutions 4: Modeling and Solving with a. absolute value linear equations and inequalities; Algebra I 2: Graphs,, and Inequalities 2.5: Play Ball! (p. 123) Relating Quantities and Reasoning with Absolute Value 1: Graphing Simple Absolute Value Using Number Lines 2: Solving Absolute Value 3: Reasoning About Absolute Value AII.3 b. quadratic equations over the set of complex numbers; 2: 2.7: You Can t Spell Fundamental Theorem of Algebra without F-U- N! (p. 179) c. equations containing rational algebraic expressions; and 7: 8: Solving 7.4: There s a Hole in my Function, Dear Liza (p. 569) 7.5: The Breaking Point (p. 583) 8.3: Things Are Not Always as They Appear (p. 621) 8.4: Get to Work, Mix It Up, Go the Distance, and Lower the Cost! (p. 641) d. equations containing radical expressions 9: Radical 9.6: Look to the Horizon (p. 721) AII.4 The student will solve systems of linear-quadratic and quadratic-quadratic equations, algebraically and graphically. Algebra I 2: 13: Solving and Inequalities 2.5 What s the Point (p. 147) 13.4 You Must Have a System (p. 789) 2

3 1.1: : They re Grrrrrowing! (p. 3) 1.2: Are They Saying the Same Thing? (p. 9) Function Overview Searching for 1: Exploring and Analyzing Student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first n terms, determining the n th term, and evaluating summation formulas. Notation will include and a n. 6: Sequences and Series 6.1: Sequence-Not Just Another Glittery Accessory (p. 465) 6.2: This is Series(ous) Business (p. 473) 6.4: These Series Just Go On And On And On (p. 499) 6.5: The Power of Interest (It s a Curious Thing) (p : A Series of Fortunate Events (p. 525) Sequences and Series Finite Geometric Series 1: Introduction to Finite Geometric Series 2: Problem Solving using Finite Geometric Series AII : Small Investments, Big Reward (p. 739) Exponential Models 1: Properties of Exponential Graphs 2: Introduction to Function Overview Graphs of 2: Transforming Inverse Inverses of 2: Graphing Square Root AII.6 For absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic functions, the student will Graphs of Solving s 3: Classifying 4: Comparing in Different Forms of 1: Examining the Shape and Structure of 4: Transformations and 1: Introduction to 2: Modeling Ratios as 3

4 For absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic functions, the student will and Models 3: Solving Work, Mixture, and Distance Problems 1: Search for 1.3: Are They Saying the Same Thing (p. 25) 1.4: Planting the Seeds (p. 49) 3: functions 3.4: DNA (p. 261) 7.1: A Existence (p. 541) a. recognize the general shape of function families; and 9: Radical 9.2 The Root of the Matter (p. 675) AII : Small Investment, Big Reward (p. 739) 10.5: More Than Meets 12.2: Paint by Numbers (p. 905) b. use knowledge of transformations to convert between equations and the corresponding graphs of functions 7: 7.2: A Shift in Behavior (p. 553) 7.3: A Approach (p. 563) 10.3: I Like to Move It (p. 763) 4

5 The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include 1.2: Are They Saying the Same Thing? (p. 9) 1.5: I ve Created a Monster (p. 57) Function Overview Searching for 2: Comparing Familiar Function Representations AII.7 2: 2.1: Shape and Structure (p. 89) 2.2: Function Sense (p. 109) 2.3: Up and Down (p. 119) 2.4: Side to Side (p. 133) 2.5: What s the Point (p.147) 2.7: You Can t Spell Fundamental Theorem of Algebra without F-U- N! (p. 179) Function Overview Graphs of 1: Identifying Key Characteristics of Graphs of 3: 3.1: Planting the Seeds (p. 207) 3.2: Power (p. 225) 3.3: Function Makeover (p. 239) 3.4: DNA (p. 261) 3.5: That Graphing Looks a Little Sketchy (p. 277) 3.6: Closing Time (p. 295) Forms of 2: Modeling 4: and 4.1: Don t Take This Out of ConText: (p. 317) Graphs of 4: Interpreting Key Features of Graphs in Terms of Quantities 5: Identifying Key Characteristics of 6: Identify Zeros of s 7: Using Zeros to Sketch a Graph of 5

6 5: 5.5: The Choice is Yours (p. 445) 1: Introduction to 2: Modeling Ratios as AII.7 The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include 7: 9: Radical 7.1: A Existence (p. 541) 7.2: A Shift in Behavior (p. 553) 7.3: A Approach (p. 563) 7.4: There s a Hole in My Function, Dear Liza (p. 569) 7.5: The Breaking Point (p. 583) 9.1: With Great Power (p. 663) 9.2: The Root of the Matter (p. 675) 10.2: We Have Liftoff! (p. 749) 10.3: I Like to Move It (p. 763) 10.5 More Than Meets and Models 1: Modeling Ratios as 2: Using Models 4: Modeling and Solving with 11: 11.5 So When Will I Use This? (p. 863) 7: 7.4: There s a Hole in My Function, Dear Liza (p. 569) a. domain, range, and continuity; 10.2: We Have Liftoff! (p. 749) 6

7 b. intervals in which a function is increasing or decreasing; 10.2 We Have Liftoff! (p. 749) 10.3 I Like to Move It (p. 763) I Feel the Earth 10.5 More Than Meets c. extrema; 3: 3.4: DNA (p. 261) 3.5: That Graphing Looks a Little Sketchy (p. 277 d. zeros; 1.5: I ve Created a Monster (p. 57) 2.7: You Can t Spell Fundamental Theorem of Algebra without F-U- N! (p. 179) AII.7 e. intercepts; 10.2: We Have Liftoff! (p. 749) 10.3: I Like to Move It (p. 763) 10. 4: I Feel the Earth 10.5: More Than Meets f. values of a function for elements in its domain; 1.2: Are They Saying the Same Thing? (p.9) Relating Quantities and Reasoning with Function Overview 4: Evaluating Linear g. connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs; 1.2: Are They Saying the Same Thing? (p.9) 1.3: Are All Created Equal (p.25) 1.4: Water Under the Bridge (p. 49) This standard is not an isolated skill, but as a theme that runs throughout the curriculum, for all function types. h. end behavior; 3: 3.2: Power (p. 225) 7

8 h. end behavior; 10.2: We Have Liftoff! (p. 749) 10.3: I Like to Move It (p. 763) 10.5: More Than Meets i) vertical and horizontal asymptotes; 10.2: We Have Liftoff! (p. 749) 10.3: I Like to Move It (p. 763) 10.5: More Than Meets Inverse Inverses of 1: Investigating Inverses of 2: Graphing Square Root 3: Sketching Graphs of Inverses 4: Calculating Inverses of Linear AII.7 2: 2.1: Shape and Structure (p. 89) j) inverse of a function; and 9: Radical 9.1: With Great Power (p. 663) 9.2: The Root of the Matter (p. 675) 9.3: Making Waves (p. 685) k) composition of functions algebraically and graphically 9: Radical 9.1: With Great Power (p. 663) 9.2: The Root of the Matter (p. 675) 9.3: Making Waves (p. 685) AII.8 The student will investigate and describe relationships among solutions of an equation, zero of a function, x- intercepts of a graph, and factors of a polynomial expression. 1.5: I ve Created a Monster Graphs of 6: Use Zeros to Sketch a Graph of a 8

9 AII.8 The student will investigate and describe relationships among solutions of an equation, zero of a function, x- intercepts of a graph, and factors of a polynomial expression. 2: 3: 2.5: What s the Point (p.147) 2.7: You Can t Spell Fundamental Theorem of Algebra without F-U- N! (p. 179) 3.1: Planting Seeds (p. 207) 3.2: Power (p. 225) 3.4: DNA (p. 261) 3.5: That Graphing Looks a Little Sketchy (p : Closing Time (p. 295) AII.9 The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of quadratic and exponential functions. 2: 12: Modeling with 2.5: What s the Point (p.147) 12.6: Grab Bag (p. 941) AII.10 The student will represent and solve problems, including practical problems, involving inverse variations, joint variation, and a combination of direct and inverse variations. 7: 7.1 A Existence (p. 541) 7.2: A Shift in Behavior (p. 553) 7.3: A Approach (p. 563) 7.5: The Breaking Point (p. 583) AII.11 a. The student will identify and describe properties of a normal distribution; 15: Interpreting Data in Normal Distributions 15.1: Recharge it! (p. 1073) 15.2: I m Online (p. 1083) 9

10 b. interpret and compare z- scores for normally distributed data; and 15: Interpreting Data in Normal Distributions 15.1: Recharge it! (p. 1073) 15.2: I m Online (p. 1083) 15.3: Below the Line, Above the Line, and In Between the Lines (p. 1093) 15.4: You Make the Call (p. 1105) c. apply properties of normal distributions to determine probabilities associated with areas under the standard normal curve. 15: Interpreting Data in Normal Distributions 15.1: Recharge it! (p. 1073) 15.2: I m Online (p. 1083) 15.3: Below the Line, Above the Line, and In Between the Lines (p. 1093) 15.4: You Make the Call (p. 1105) AII.12 The student will compute and distinguish between permutations and combinations. Geometry 15: More Probability and Counting 15.1 Left, Left, Left, Right, Left (p. 1135) 15.3: Counting (p. 1167) 10