# ALGEBRA II Billings Public Schools Correlation and Pacing Guide Math - McDougal Littell High School Math 2007

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1 ALGEBRA II Billings Public Schools Correlation and Guide Math - McDougal Littell High School Math 2007 (Chapter Order: 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 10)

2 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 1 Equations and Inequalities Lesson 1.1 (1 day) Real # Properties Real # Sets Lesson 1.2 (1 day) ic Expressions Lesson 1.3 (1 day) Solving Linear Equations Learning Objectives 1 st Semester review Apply the laws of exponents to simplify, evaluate expressions and to solve equations (E, A) review Emphasize unit analysis Emphasize: -2² (-2)² and calculator vs. non-calculator Emphasize solving fractions and decimal equations 15 days (Includes 1 day for classzone.com introduction and registration) Lesson 1.4 (2 days) Formulas Lesson 1.5 (2 days) Problem Solving review review Include p. 33 Consider using 1.4B worksheet in place of 1.4 text Consider Quiz on 2 nd day Lesson 1.6 (2 days) Linear Inequalities review Allow time to introduce Lesson 1.7 (2 days) Absolute Value Equations Solve and graph absolute value equations (D, E) Omit absolute value inequalities. Include p. 59 Review / Test (3 days) 2

3 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 2 Linear Equations and Lesson 2.1 (1 day) Domain & Range of Vertical Line Test Lesson 2.2 (2 days) Slope & Rate of Change Learning Objectives 1 st Semester review review 15 days Lesson 2.3 (1 day) Graphing y=mx+b Lesson 2.4 (2 days) Point-Slope Form Lesson 2.5 (1 day) Direct Variation Recognize and use the standard forms for functions (I, D, E) Determine the transformational effects of an equation and its graph from its parent function (I, D, E, A) Technology Determine the appropriate window on a graphing calculator for a given relation (I, D, E, A) Use graphing technology to graph linear and quadratic equations and systems of equations (I, D, E, A) review Identify and graph both direct and inverse situations, and fit the proper equation to data (I, D, E, A) Emphasize: 1. Calculator and no calculator with transformational effects 2. Appropriate viewing window with problem solving sections Emphasize applications on day 2. Include p

4 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 2 Linear Equations and Lesson 2.6 (2 days) Scatterplots & Best- Fitting Lines Lesson 2.7 (2 days) Absolute Value Intro (h,k) Transformations Learning Objectives 1 st Semester Identify and graph both direct and inverse situations, and fit the proper equation to data (I, D, E, A) Solve and graph absolute value equations (D, E) Determine the transformational effects of an equation and its graph from its parent function (I, D, E, A) Emphasize correlation coefficient and applications Include activity pp (continued) Lesson 2.8 (1 day) Graphing Linear Inequalities review Emphasize p. 137 applications Review / Test (3 days) 4

5 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Learning Objectives 1 st Semester Chapter 3 Linear Systems and Matrices 13 days Lesson 3.1 (1 days) Solving by Graphing Number and Type of Solutions Lesson 3.2 (1 days) Solving by Substitution Solving by Elimination Lesson 3.3 (3 days) Systems of Inequalities Linear Programming Lesson 3.4 Solve systems of equations and inequalities graphically, algebraically, and by using matrices (I, D) Solve systems of equations and inequalities graphically, algebraically, and by using matrices (I, D) Recognize and use the standard forms for functions (I, D, E) Solve systems of equations and inequalities graphically, algebraically, and by using matrices (I, D) Graph and interpret linear programming problems (I, D) Recognize and use the standard forms for functions (I, D, E) Technology Determine the appropriate window on a graphing calculator for a given relation (I, D, E, A) Use graphing technology to graph linear and quadratic equations and systems of equations (I, D, E, A) Emphasize calculator and no calculator methods Emphasize strategy After 3.3 Extension Linear Programming pp Day 1-Graphing systems of inequalities review Day 2-Linear programming Day 3-Mixed strategies for solving systems 5

6 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 3 Linear Systems and Matrices (continued) Lesson 3.5 (1 day) Add & Subtract Matrices Scalar Multiplication Lesson 3.6 (2 days) Multiplying Matrices Lesson 3.7 Learning Objectives 1 st Semester Geometry Find scalar multiples of matrices and perform transformations using matrix operations (D, E) Add, subtract, multiply, find the determinant and the inverse of a matrix (I, D, E) Technology Use graphing technology to perform matrix operations and solve matrix equations (I, D, E, A) Add, subtract, multiply, find the determinant and the inverse of a matrix (I, D, E) No calculator Day 1-Multiply matrices (no calculator) Day 2-Add, Subtract, multiply matrices with a calculator Lesson 3.8 (2 days) Solving Systems with Matrices (Calculator only) Add, subtract, multiply, find the determinant and the inverse of a matrix (I, D, E) Solve systems by matrices only using graphing calculator Review / Test (3 days) 6

7 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 4 Quadratic and Factoring 19 days Lesson 4.1 (1 day) Quadratics in Standard Form Lesson 4.2 (2 days) Intercept Form Vertex Form Lesson 4.3 (2 days) Solving x 2 +bx+c=0 by Factoring Learning Objectives 1 st Semester Apply properties of and graph quadratic functions (I, D, E) Recognize and use the standard forms for functions (I, D, E) Apply properties of and graph quadratic functions (I, D, E) Recognize and use the standard forms for functions (I, D, E) Determine the transformational effects of an equation and its graph from its parent function (I, D, E, A) Apply properties to factor and solve polynomials (D, E, A) Emphasize location of vertex and symmetry with function table and graph Review vertex form and introduce intercept form Factor the expression worksheet included as a supplemental in binder Lesson 4.4 (2 days) Solving x 2 +bx+c=0 by Factoring Apply properties to factor and solve polynomials (D, E, A) Factor the expression worksheet included as a supplemental in binder Lesson 4.5 (2 days) Simplifying Radicals Solving Quadratics with Square Roots Lesson 4.6 (1 day) Complex Number Operations Solve equations involving radicals (D, E, A) Add, subtract, multiply, divide and simplify rational expressions (I, D, E) Estimate the number of real and complex roots from an equation and a graph (I, D) Identify and apply properties for complex number systems (I, D) Include p. 274 Omit graphing in complex plane and a+bi (magnitude) 7

8 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 4 Quadratic and Factoring (continued) Lesson 4.7 (2 days) Completing the Square Lesson 4.8 (2 days) Quadratic Formula Discriminant Lesson 4.9 Learning Objectives 1 st Semester Solve quadratic equations by completing the square and applying the quadratic formula (I, D) Estimate the number of real and complex roots from an equation and a graph (I, D) Use the discriminant to determine the nature of the roots of a quadratic equation (D, E) Solve quadratic equations by completing the square and applying the quadratic formula (I, D) Consider Tile Activity p. 283 Omit when a 1 Emphasize vertical motion formula p. 295 Use table in TE p. 294 (Differentiated Instruction) Lesson 4.10 (2 days) Writing Quadratic Models Review / Test (3 days) Apply properties of and graph quadratic functions (I, D, E) Determine the equation, graph and characteristics of quadratic relations (I, D) Use p

9 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 5 Polynomials and Polynomial Lesson 5.1 (2 days) Properties of Exponents Scientific Notation Learning Objectives 1 st Semester Apply the laws of exponents to simplify, evaluate expressions and to solve equations (E, A) Emphasize expanded (factored form) i.e. -2³=-2*2*2 15 days Lesson 5.2 (2 days) Polynomials End Behavior Lesson 5.3 (1 day) Add, Subtract, and Multiply Polynomials Lesson 5.4 (1 day) Solving Polynomial Equations by Factoring Lesson 5.5 (2 days) Dividing Polynomials Synthetic Division Lesson 5.6 (2 days) Zeroes of Polynomials Apply long division and synthetic substitution/division to simplify rational expressions (I, D, E) Apply properties to factor and solve polynomials (D, E, A) Apply properties to factor and solve polynomials (D, E, A) Apply the remainder and factor theorems for rational functions (I, D) Identify and apply properties for complex number systems (I, D) Solve and graph polynomial functions (I, D, E) Emphasize end behavior and sketching graphs with appropriate window Optional: Sum and difference of cubes Introduce factoring by grouping Begin 2 nd Semester 9

10 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 5 Polynomials and Polynomial (continued) Lesson 5.7 Lesson 5.8 (2 days) Finding Key Points on Polynomial Graphs Lesson 5.9 Learning Objectives 1 st Semester Identify and fit the proper equation to a data table (I, D) Technology Use technology to analyze and model data (I, D, E, A) Include box problem p. 389 Review / Test (3 days) 1 st Semester Final Exam (2-4 days) 10

11 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 6 Rational Exponents and Radical 15 days Lesson 6.1 (2 days) Rational Exponents Lesson 6.2 (2 days) Properties of Radicals Lesson 6.3 (2 days) Operations with Composition of Lesson 6.4 (2 days) Inverse Learning Objectives 2 nd Semester Demonstrate the meaning of rational and real-number exponents (D, E) Use the properties of radicals to simplify expressions (D, E) Demonstrate the meaning of rational and real-number exponents (D, E) Determine the composite of two functions (I, D, E) Determine and graph the inverse of a function (I, D, E) Emphasize negative powers vs. negative bases A Level questions only Include activity p. 437 Lesson 6.5 (1 day) Graphing Square Root and Cube Determine the transformational effects of an equation and its graph from its parent function (I, D, E, A) Lesson 6.6 (2 days) Solve Radical Equations Review/Test (3 days) Use the properties of radicals to simplify expressions (D, E) Solve equations involving radicals (D, E, A) Emphasize checking for extraneous solutions 11

12 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 7 Exponential and Logarithmic days Lesson 7.1 (1-2 days) Exponential Growth Lesson 7.2 (2 days) Exponential Decay Lesson 7.3 (1 day) Natural Base e Lesson 7.4 (2 days) Logarithms Lesson 7.5 (2 days) Logarithm Properties Learning Objectives 2 nd Semester Solve all types of compound interest problems (I, D) Solve and graph exponential and logarithmic functions (I, D) Solve and graph exponential and logarithmic functions (I, D) Solve all types of compound interest problems (I, D) Solve and graph exponential and logarithmic functions (I, D) Convert equations between exponential and logarithmic forms (I, D, E) Evaluate common and natural logarithms (I, D, E) Apply the laws of logarithms (I, D, E) Determine and graph the inverse of a function (I, D, E) Solve and graph exponential and logarithmic functions (I, D) Determine the transformational effects of an equation and its graph from its parent function (I, D, E, A) Apply the laws of logarithms (I, D, E) Day 1- Textbook Day 2- Use IEFA Lesson MT Native American Population (Only do #1-5. Exclude negative residuals) Find the lesson at urrsearch/index.html click on Mathematics. Use Log Properties activity (Included as a supplemental activity in binder) 12

13 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 7 Exponential and Logarithmic (continued) Lesson 7.6 (2 days) Solving Exponential and Logarithmic Equations Lesson 7.7 Learning Objectives 2 nd Semester Solve and graph exponential and logarithmic functions (I, D) Review / Test (3 days) 13

14 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 8 Rational Lesson 8.1 (1 day) Inverse Variation Joint Variation Learning Objectives 2 nd Semester Identify and graph both direct and inverse situations, and fit the proper equation to data (I, D, E, A) 13 days Lesson 8.2 (1 day) Graphing Hyperbolas Lesson 8.3 (2 days) Graphing Rationals Solve and graph rational functions (I, D, E) Identify and graph both direct and inverse situations, and fit the proper equation to data (I, D, E, A) Determine the transformational effects of an equation and its graph from its parent function (I, D, E, A) Solve and graph rational functions (I, D, E) Include p. 564 Recommend worksheet 8.3B Emphasize technology Lesson 8.4 (2 days) Multiply and divide Rational Expressions Add, subtract, multiply, divide and simplify rational expressions (I, D, E) May need to review factoring before beginning this section Lesson 8.5 (2 days) Add and Subtract Rational Expressions Add, subtract, multiply, divide and simplify rational expressions (I, D, E) Terminology: use cross products not cross multiply Lesson 8.6 (2 days) Solving Rational Equations Solve and graph rational functions (I, D, E) Question #16 requires the quadratic formula to solve Review / Test (3 days) 14

15 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 9 Quadratic Relations Lesson 9.1 (1 day) Distance Formula Midpoint Formula Lesson 9.2 (2 days) Focus and Directrix of Parabolas Learning Objectives 2 nd Semester Review Analyze conic sections and apply translation properties to them (I, D) Distance formula and Midpoint formula and review topics Focus on questions Include hands-on activity i.e. Activity Generator days (Check for GeoGebra applets throughout the chapter at bra.org) Lesson 9.3 (1 day) Circles Lesson 9.4 (1 day) Ellipses Lesson 9.5 (2 days) Hyperbolas Lesson 9.6 (1 day) Translate (h,k) Conic Sections Lesson 9.7 Analyze conic sections and apply translation properties to them (I, D) Analyze conic sections and apply translation properties to them (I, D) Analyze conic sections and apply translation properties to them (I, D) Determine the equation, graph and characteristics of quadratic relations (I, D, E) Analyze conic sections and apply translation properties to them (I, D) Determine the transformational effects of an equation and its graph from its parent function (I, D, E, A) Day 2: Mixed ellipse and hyperbola questions A Level questions only Review / Test (3 days) 15

16 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 13 Trigonometric Ratios and 13 days (Check for GeoGebra applets throughout chapter at bra.org) Lesson 13.1 (1 day) Sine, Cosine, Tangent Ratios Trigonometric Values of Special Angles Lesson 13.2 (2 days) Radian Measure Lesson 13.3 (2 days) Unit Circle Lesson 13.4 (1 day) Inverse Trigonometric Learning Objectives 2 nd Semester Memorize exact values for sine, cosine, and tangent for the unit circle and their decimal approximations (I, D, E) Geometry State the properties of the trigonometric functions and their graphs (including domain, range and period) (I, D) Memorize exact values for sine, cosine, and tangent for the unit circle and their decimal approximations (I, D, E) Geometry Convert between degree and radian measure (I, D, E) Geometry Define, graph, and determine values of the circular trigonometric functions (I, D, E) Technology Use appropriate technology to evaluate measures involving trigonometric ratios (I, D, E, A) Geometry State the properties of the trigonometric functions and their graphs (including domain, range and period) (I,D) Technology Use appropriate technology to evaluate measures involving trigonometric ratios (I, D, E, A) SOH-CAH-TOA review Omit secant, cosecant, and cotangent Day 1: Emphasize degree/radian conversion (Use GeoGebra applet) Day 2: Emphasize degree/radian measures of special angles (Worksheet included in binder) Omit secant, cosecant, and cotangent Emphasize exact values Emphasize approximate vs. exact values 16

17 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 13 Trigonometric Ratios and (continued) Lesson 13.5 (2 days) Law of Sines Lesson 13.6 (2 days) Law of Cosines Review / Test (3 days) Learning Objectives 2 nd Semester Geometry State the properties of the trigonometric functions and their graphs (including domain, range and period) (I,D) Technology Use appropriate technology to evaluate measures involving trigonometric ratios (I, D, E, A) Geometry State the properties of the trigonometric functions and their graphs (including domain, range and period) (I,D) Technology Use appropriate technology to evaluate measures involving trigonometric ratios (I, D, E, A) 17

18 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 14 Trigonometric Graphs, Identities, and Equations 5-6 days Lesson 14.1 (2-3 days) Lesson 14.2 (2 days) Lesson 14.3 Lesson 14.4 Lesson 14.5 Lesson 14.6 Lesson 14.7 Review/Test (1 day) Learning Objectives 2 nd Semester Geometry Define, graph, and determine values of the circular trigonometric functions (I, D, E) State the properties of the trigonometric functions and their graphs (including domain, range and period) (I,D) Technology Use appropriate technology to evaluate measures involving trigonometric ratios (I, D, E, A) Geometry Define, graph, and determine values of the circular trigonometric functions (I, D, E) State the properties of the trigonometric functions and their graphs (including domain, range and period) (I,D) Technology Use appropriate technology to evaluate measures involving trigonometric ratios (I, D, E, A) Sine, Cosine and Tangent worksheet included in binder GeoGebra applet included in binder 18

19 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 10 Counting Methods and Probability 10 days Lesson 10.1 (1 day) Lesson 10.2 (2 days) Lesson 10.3 (1 day) Learning Objectives 2 nd Semester Probability Determine probabilities using counting procedures, tables, trees, area models, and formulas for permutations and combinations (I, D) Probability Determine probabilities using counting procedures, tables, trees, area models, and formulas for permutations and combinations (I, D) Probability Determine probabilities using counting procedures, tables, trees, area models, and formulas for permutations and combinations (I, D) Lesson 10.4 (1 day) Lesson 10.5 (2 days) Probability Explain and use the concepts of independent and dependent events and their relationship to compound events and conditional probability (I, D) Probability Explain and use the concepts of independent and dependent events and their relationship to compound events and conditional probability (I, D) Lesson 10.6 Optional if time allows Review / Test (3 days) 19

20 BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal Littell II 2007 Correlation/ Draft Chapter 11 Data Analysis and Statistics 0 days Lesson 11.1 Optional if time allows Lesson 11.2 Optional if time allows Lesson 11.3 Optional if time allows Lesson 11.4 Optional if time allows Lesson 11.5 Optional if time allows Review / Test Learning Objectives 2 nd Semester Chapter 12 Sequences and Series 0 days Lesson 12.1 Optional if time allows Lesson 12.2 Optional if time allows Lesson 12.3 Optional if time allows Lesson 12.4 Optional if time allows Review / Test Learning Objectives 2 nd Semester 20

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