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

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

2 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 1 The Real Number System Lesson 1.1 (1-2 days) Real Number System Ordering Numbers Absolute Value Number Sense Order and compare real numbers (D, Determining numbers belonging to various subsets of the real number system and recognizing the relationships among the subsets, e.g., whole numbers, rational numbers, real numbers (I, D, Approximately days Lesson 1.2 (1 day) Add and Subtract Integers Lesson 1.3 (2 days) Multiply and Divide Integers Prime and Composite Numbers Add, subtract, multiply and divide with real numbers and demonstrate an understanding of how mathematical operations effect real numbers including operations involving exponents and roots (D, Recognize and generate equivalent forms of real numbers (D, Add, subtract, multiply and divide with real numbers and demonstrate an understanding of how mathematical operations effect real numbers including operations involving exponents and roots (D, Use #122 p. 32 Sieve of Eratosthenes for prime/composite #1-100 Grid 2

3 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 1 The Real Number System continued Lesson 1.4 (3 days) Operations with Fractions and Decimals Lesson 1.5 (3 days) Exponents Order of Operations Properties Review/Test (4 days) Use mental math and number sense to compute with rational numbers (D, Add, subtract, multiply and divide with real numbers and demonstrate an understanding of how mathematical operations effect real numbers including operations involving exponents and roots (D, Apply order of operations and laws of exponents (D, Identify and apply associative, commutative, distributive, identity and inverse properties (D, E) 3

4 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 2 Fundamenta ls of Approximately days Lesson 2.1 (2 days) ic Expressions Lesson 2.2 (4-5 days) Simplifying ic Expressions Properties Lesson 2.3 (2-3 days) Verbal Models Lesson 2.4 (2 days) Checking Solutions of Equations Review/Test (3 days) Evaluate algebraic expressions for given a value(s) of the variable(s) (D, Add, subtract, multiply, divide and simplify rational expressions (I, D) Approximate square roots and memorize the perfect squares up to and including 225 ( Recognize and write equivalent expressions (D, Draw conclusions and make predictions based on mathematical patterns and relationships (I, D, E, A) Represent real life situations with algebraic expressions, equations, and inequalities (D, Recognize and write equivalent expressions (D, Represent real life situations with algebraic expressions, equations, and inequalities (D, Determine solutions to linear equations and systems of linear equations in two variables algebraically and graphically (D, Use technology to compute the value of an expression (I, D, Supplement with Rescue workbooks, if available Emphasize checking solutions algebraically and using technology (store x) 4

5 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 3A- Equations, Inequalities, and Problem Solving Approximately 14 days Lesson 3.1 (4 days) Solving 1 & 2 Step Equations Lesson 3.2 (3 days) Solving Multi-Step Equations Solving Equations with Fractions and Decimals Identify and apply associative, commutative, distributive, identity and inverse properties (D, E) Represent real life situations with algebraic expressions, equations, and inequalities (D, Determine solutions to linear equations and systems of linear equations in two variables algebraically and graphically (D, Number Sense Apply proportions and percents to real-world problems and develop an understanding of percent change (A) Add, subtract, multiply, divide and simplify rational expressions (I, D) Identify and apply associative, commutative, distributive, identity and inverse properties (D, E) Determine solutions to linear equations and systems of linear equations in two variables algebraically and graphically (D, Day 1-Solve ax=b, a+x=b, ax+b=c Rescue 3-1, 3-2 Day 2-Solve ax+b=cx, ax+b=cx+d Rescue 3-3 Day 3-Solve a(x+b)=(x+c) Day 4-Application problems 5

6 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 3A- Equations, Inequalities, and Problem Solving Continued Lesson 3.3 (3 days) Percent Problems Lesson 3.4 (3 days) Ratio and Proportion Unit Pricing Review/Test (3 days) Number Sense Apply proportions and percents to real-world problems and develop an understanding of percent change (A) Apply appropriate estimation strategies and recognize when estimation, approximation, or exact answers are appropriate and recognize errors (D, Represent real life situations with algebraic expressions, equations, and inequalities (D, Use technology to compute the value of an expression (I, D, Number Sense Apply proportions and percents to real-world problems and develop an understanding of percent change (A) Add, subtract, multiply and divide with real numbers and demonstrate an understanding of how mathematical operations effect real numbers including operations involving exponents and roots (D, Represent real life situations with algebraic expressions, equations, and inequalities (D, Elastic Band Percent Activity Unit Price Activity 6

7 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 3B- Equations, Inequalities, and Problem Solving Approximately 11 days Lesson 3.5 (3 days) Formulas Lesson 3.6 (4 days) Linear Inequalities Compound Inequalities Lesson 3.7 (2 days) Absolute Value Equations Review/Test (2 days) Measurement Solve problems involving rates and formulas (I, D, Solve simple and compound interest problems (excluding continuous) (I, D) Represent real life situations with algebraic expressions, equations, and inequalities (D, Use technology to compute the value of an expression (I, D, Represent real life situations with algebraic expressions, equations, and inequalities (D, Determine solutions to linear inequalities and systems of linear inequalities in two variables graphically (D, E) Graph linear equations and linear inequalities (D, Solve absolute value equations (I, D) De-emphasize rewriting formulas requiring factoring and multiples Include transforming linear equations in standard form to slopeintercept form (See supplemental worksheet) Include formula problems Mixture, work rate problems optional (#55-78) OMIT absolute value inequalities and equations with absolute value on both sides 7

8 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 4A- Graphs and Functions 13 days Lesson 4.1 (4 days) Coordinate Graphing Solutions to 2-Variable Equations Recognize functions represented by verbal descriptions, equations, tables, or graphs as linear, quadratic or neither (I, D, Represent real life situations with algebraic expressions, equations, and inequalities (D, Determine solutions to linear equations and systems of linear equations in two variables algebraically and graphically (D, Represent, analyze and generalize patterns relating to linear and quadratic functions through multiple representations (e. g. words, charts, algebraic expressions or equations and graphical representations) (I, D, Use technology to compute the value of an expression (I, D, Day 1-Plotting Points Day 2-Worksheet Solving for y Day 3-Determining Solutions Day 4-Problem Solving 8

9 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 4A- Graphs and Functions Continued Lesson 4.2 (3 days) Graphing Functions using Tables and Intercepts Lesson 4.3 (3 days) Function Notation Review/Test (3 days) Use mental math and number sense to compute with rational numbers (D, Recognize functions represented by verbal descriptions, equations, tables, or graphs as linear, quadratic or neither (I, D, Determine solutions to linear equations and systems of linear equations in two variables algebraically and graphically (D, Determine the slope and intercepts of a linear equation represented by a graph or an equation and interpret the meaning of those values relative to the context of the problem (D, Graph linear equations and linear inequalities (D, Use technology to graph linear and quadratic functions with an appropriate window (D,E) Use technology to compute the value of an expression (I, D, Use function notation to evaluate functions using numerical and variable inputs (I, D, E) Determine the domain and range of a function (D) Evaluate algebraic expressions for given a value(s) of the variable(s) (D, Emphasize Graphing Calculator Appropriate viewing window Table of values Finding intercepts 9

10 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 4B- Graphs and Functions days Lesson 4.4 (3-4 days) Slope y=mx+b Parallel and Perpendicular Lines Lesson 4.5 (5 days) Point-Slope Form General Form Geometry Determine lengths of segments using the distance formula, find midpoints, and determine whether lines are parallel or perpendicular using slopes (D, Determine the slope and intercepts of a linear equation represented by a graph or an equation and interpret the meaning of those values relative to the context of the problem (D, Graph linear equations and linear inequalities (D, Write equations to represent a given linear graph in slope-intercept form and standard form using two points and using a point and slope (D, Determine in a relationship (function) how a change in one variable affects the other variable (D, Use technology to graph linear and quadratic functions with an appropriate window (D,E) Graph linear equations and linear inequalities (D, Write equations to represent a given linear graph in slope-intercept form and standard form using two points and using a point and slope (D, Use technology to graph linear and quadratic functions with an appropriate window (D,E) Consider using Green Globs game and Shoot for the Stars game Application of Lines Through 2 Points Worksheet Parallel and Perpendicular Lines Worksheet OMIT General Form Use Standard Form (minimal emphasis) Strong emphasis on Point- Slope Form 10

11 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 4B- Graphs and Functions Continued Lesson 4.6 (2 days) Linear Inequalities Review/Test (3 days) Represent real life situations with algebraic expressions, equations, and inequalities (D, Determine solutions to linear equations and systems of linear equations in two variables algebraically and graphically (D, Graph linear equations and linear inequalities (D, 11

12 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 5- Exponents and Polynomials 20 days Lesson 5.1 (7 days) Integer Exponents Scientific Notation Lesson 5.2 (3 days) Add and Subtract Polynomials Lesson 5.3 (4 days) Multiply Polynomials Number Sense Interpret integral and rational exponents and square roots ( Apply the laws of exponents to simplify and evaluate expressions (D, E) Translating between standard and scientific notation with positive and negative exponents (A) Apply order of operations and laws of exponents (D, Add, subtract, multiply and divide with real numbers and demonstrate an understanding of how mathematical operations effect real numbers including operations involving exponents and roots (D, Use technology to compute the value of an expression (I, D, Add, subtract, multiply and factor polynomials (D, Add, subtract, multiply and factor polynomials (D, Day 1-Supplemental Worksheet Rules of Exponents Product and Quotient Rules (p. 296) Day 2-Supplemental Worksheet Power Rules (p. 296) Day 3-Supplemental Worksheet Zero and Negative Exponent Rules (p. 296) Day 4-Supplemental Worksheet Combination of Power Rules Day 5-Scientific Notation from text Day 1-Multiply by Monomials Day 2-Multiply Binomials (Show FOIL, Box, and Distributive Methods) Day 3-Squaring Binomials and Multiplying Polynomials 12

13 BILLINGS PUBLIC SCHOOLS Intermediate Chapter 5- Exponents and Polynomials Lesson 5.4 (2 days) Dividing Polynomials Review/Test (4 days) Add, subtract, multiply, divide and simplify rational expressions (I, D) Add, subtract, multiply and factor polynomials (D, OMIT Synthetic Division Continued 13

14 BILLINGS PUBLIC SCHOOLS Intermediate Time/Pacing Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 6- Factoring and Solving Equations 17 days Lesson 6.1 (2 days) Greatest Monomial Factor Lesson 6.2 (2 days) Factor x²+bx+c Lesson 6.3 (3 days) Factor ax²+bx+c Add, subtract, multiply and factor polynomials (D, Add, subtract, multiply and factor polynomials (D, Add, subtract, multiply and factor polynomials (D, Day 1-Monomial Factoring Day 2-Emphasize Box Method for # Day 3-Supplemental Worksheet on Combination Factoring Lesson 6.4 (2 days) Factor Perfect Square Factor Difference of Squares Lesson 6.5 (4 days) Zero Product Property Review/Test (4 days) Add, subtract, multiply and factor polynomials (D, Determine solutions to quadratic functions through factoring, quadratic formula, square roots and graphically (I, D, Use technology to graph linear and quadratic functions with an appropriate window (D,E) OMIT Sum and Difference of Cubes Falling Object Activity or Problem Solving Worksheet 14

15 BILLINGS PUBLIC SCHOOLS Intermediate Time/Pacing Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 8- Systems of Equations and Inequalities days Lesson 8.1 (4 days) Solving by Graphing Solving by Substitution Lesson 8.2 (3-4 days) Solving by Elimination Lesson 8.3 (3 days) Solving 3 x 3 Systems (optional) Solving with Matrices Determine solutions to linear equations and systems of linear equations in two variables algebraically and graphically (D, Determine the slope and intercepts of a linear equation represented by a graph or an equation and interpret the meaning of those values relative to the context of the problem (D, Graph linear equations and linear inequalities (D, Use technology to solve systems graphically and with matrices (I, D) Determine solutions to linear equations and systems of linear equations in two variables algebraically and graphically (D, Use technology to compute the value of an expression (I, D, Use technology to solve systems graphically and with matrices (I, D) Day 1-Solve by graphing (no calculator) and number of solutions Day 2-Solve by graphing with technology and type of solution Day 3 & 4-Substitution Include application problems Day 1-Determinant and Inverse of a 2x2 Matrix (no calculator) Determinant and Inverse of a 3x3 Matrix with technology Day 2-Solving systems with inverse matrix (technology only and 3x3 systems are optional) Day 3-Mixed methods and applications (Use problem set from 8.2 for solving with matrix) 15

16 BILLINGS PUBLIC SCHOOLS Intermediate Time/Pacing Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 8- Systems of Equations and Inequalities Continued Lesson 8.4 & 8.5 OMIT Lesson 8.6 (2 days) Systems of Inequalities Review/Test (4 days) Determine solutions to linear inequalities and systems of linear inequalities in two variables graphically (D, E) De-emphasize application problems 16

17 BILLINGS PUBLIC SCHOOLS Intermediate Time/Pacing Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 9- Radicals and Complex Numbers 14 days Lesson 9.1 (3 days) Radical Notation Rational Exponents Lesson 9.2 (2 days) Simplifying Radicals Lesson 9.3 (1 day) Add and Subtract Radicals Approximate square roots and memorize the perfect squares up to and including 225 ( Recognize and generate equivalent forms of real numbers (D, Apply order of operations and laws of exponents (D, Apply appropriate estimation strategies and recognize when estimation, approximation, or exact answers are appropriate and recognize errors (D, E, A) Use technology to compute the value of an expression (I, D, Approximate square roots and memorize the perfect squares up to and including 225 ( Apply appropriate estimation strategies and recognize when estimation, approximation, or exact answers are appropriate and recognize errors (D, E, A) Measurement Solve problems involving the Pythagorean Theorem ( Recognize and generate equivalent forms of real numbers (D, Determining numbers belonging to various subsets of the real number system and recognizing the relationships among the subsets, e.g., whole numbers, rational numbers, real numbers (I, D, E, A) Day 1- Perfect squares and square roots, perfect cubes and cube roots Day 2-Convert radical to rational exponent form Day 3-Evaluate exponents using technology (# ) Day 1-Simplify radicals (square root only) Day 2-Rationaize denominator/pythagorean Theorem 17

18 BILLINGS PUBLIC SCHOOLS Intermediate Time/Pacing Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 9- Radicals and Complex Numbers Continued Lesson 9.4 (3 days) Multiplying Radicals Triangles Triangles Lesson 9.5 (2 days) Solving Radical Equations Pythagorean Theorem Lesson 9.6 OMIT Review/Test (3 days) Determining numbers belonging to various subsets of the real number system and recognizing the relationships among the subsets, e.g., whole numbers, rational numbers, real numbers (I, D, E, A) Measurement Memorize the relationships between the sides of and triangles (D, Measurement Solve problems involving the Pythagorean Theorem ( Represent real life situations with algebraic expressions, equations, and inequalities (D, Day 1-Multiply radical expressions Day 2 & / Triangle relationships Day 1-Solving radical equations (#1-46) Day 2-Pythagorean Theorem applications 18

19 BILLINGS PUBLIC SCHOOLS Intermediate Time/Pacing Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 10- Quadratic Equations, Functions, and Inequalities 13 days Lesson 10.1 (2 days) Lesson 10.2 OMIT Lesson 10.3 (4 days) Quadratic Formula Discriminant Lesson 10.4 (2 days) Graphing Quadratics Lesson 10.5 (2 days) Quadratic Applications Lesson 10.6 OMIT Review/Test (3 days) Determine solutions to quadratic functions through factoring, quadratic formula, square roots and graphically (I, D, Use technology to graph linear and quadratic functions with an appropriate window (D, E) Determine solutions to quadratic functions through factoring, quadratic formula, square roots and graphically (I, D, Determine solutions to quadratic functions through factoring, quadratic formula, square roots and graphically (I, D, Use technology to graph linear and quadratic functions with an appropriate window (D, E) Represent real life situations with algebraic expressions, equations, and inequalities (D, Determine solutions to quadratic functions through factoring, quadratic formula, square roots and graphically (I, D, Use technology to graph linear and quadratic functions with an appropriate window (D, E) 19 Day 1 -Solve by factoring (exclude complex # solutions) Day 2-Solve by Square Root Property (find the x-intercepts with technology, optional) Exclude complex number solutions, use no real solution Day 1-Graphing (no calculator) Day 2-Graphing with technology

20 BILLINGS PUBLIC SCHOOLS Intermediate Time/Pacing Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 7- Rational Expressions, Equations, and Functions 20 days (If Time Allows) Lesson 7.1 (4 days) Domain & Range of Rational Functions Simplify Rational Expressions Lesson 7.2 (3 days) Multiply & Divide Rational Expressions Lesson 7.3 (5 days) Add & Subtract Rational Expressions Lesson 7.4 (2 days) Complex Fractions Lesson 7.5 (2 days) Solving Rational Equations Lesson 7.6 OMIT Review/Test (4 days) Add, subtract, multiply, divide and simplify rational expressions (I, D) Determine the domain and range of a function (D) Evaluate algebraic expressions for given a value(s) of the variable(s) (D, Add, subtract, multiply, divide and simplify rational expressions (I, D) Add, subtract, multiply, divide and simplify rational expressions (I, D) Add, subtract, multiply, divide and simplify rational expressions (I, D) Determine solutions to linear equations and systems of linear equations in two variables algebraically and graphically (D, Day 1-Domain and evaluate Day 2-Simplify Monomials Day 3 & 4-Simplify all Rational Expressions Day 1-Multiply Day 2-Division Day 3-Mixed Problems Day 1-Find LCM, rewrite with common denominators Day 2 & 3-Adding Rational Expressions Day 4-Subtracting Rational Expressions Day 5-Mixed Adding and Subtracting 20

Beginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions

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