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1 Updated: Thursday, December 02, 2010 Mathematics Curricular Guide ALGEBRA 2 2010-2011 SCHOOL YEAR

ALGEBRA 2 - Pasco School Districtand inequalities. Graph quadratic inequalities in two 5.7 Graphing and Solving Quadratic Inequalities variables Solve quadratic inequalities in real

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  • 1 Updated: Thursday, December 02, 2010

    Mathematics Curricular Guide

    ALGEBRA 2

    2010-2011 SCHOOL YEAR

  • Pasco School District Algebra 2 2010 – 2011 School Year

    2 Updated: Thursday, December 02, 2010

    MATHEMATICS SCOPE & SEQUENCE

    Unit Title Dates Page 1. Chapter 1 – Equations and Inequalities .................................................................................................................................... 3

    2. Chapter 2- Linear Equations and Functions .............................................................................................................................. 5

    3. Chapter 5 – Quadratic Functions.............................................................................................................................................. 7

    4. Chapter 3 – Systems of Linear Equations and Inequalities ..................................................................................................... 10

    5. Chapter 6 – Polynomials and Polynomial Functions ............................................................................................................... 12

    6. Chapter 12 – Probability and Statistics................................................................................................................................... 14

    7. Chapter 7 – Powers, Roots, and Radicals ............................................................................................................................... 17

    8. Chapter 8 – Exponential and Logarithmic Functions .............................................................................................................. 19

    9. Chapter 9 – Rational Equations and Functions ....................................................................................................................... 21

    10. Chapter 11 – Sequences and Series ....................................................................................................................................... 22

    11. Chapter 13 – Trigonometric Ratios and Functions ................................................................................................................. 23

  • Pasco School District Algebra 2 2010 – 2011 School Year

    3 Updated: Thursday, December 02, 2010

    Unit Name: Chapter 1 Equations and Inequalities

    [Starting Date] [Ending Date]

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.2.A Explain how whole, integer, rational, real, and complex numbers are related, and identify the number system(s) within which a given algebraic equation can be solved.

    1.1 Real Numbers and Number Operations

    Identify properties of and use operations with real numbers.

    Recognize and explain the relationship amongst different number systems.

    2 This standard is briefly mentioned, but a typical student would not be able to achieve mastery with the available content. A relationship between number systems if not identified. Locate materials to use for instruction and reinforcement.

    A2.2.B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents.

    1.2 Algebraic Expressions and Models

    Evaluate algebraic expressions.

    Simplify algebraic expressions by combining like terms.

    2 The laws of rational exponents occur in section 7.2 which will be addressed later in the curriculum.

    A2.1.A Select and justify functions and equations to model and solve problems.

    1.3 Solving Linear Equations

    Solve linear equations.

    Use linear equations to model and solve real-life problems.

    2 While solving linear equations is not addressed specifically in the PEs, a review of this skill is needed prior to completion of the rest of the curriculum. Refer to 1.3 Practice B and 1.3 Practice C worksheets to find additional application problems.

    1.4 Rewriting Equations and Formulas

    Rewrite equations with more than one variable.

    2 This section is included in anticipation for the unit on solving systems of equations.

  • Pasco School District Algebra 2 2010 – 2011 School Year

    4 Updated: Thursday, December 02, 2010

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.1.A Select and justify functions and equations to model and solve problems.

    1.5 Problem Solving Using Algebraic Models

    Use a general problem-solving plan to solve real-life problems.

    Have students write a verbal model, assign labels, write an algebraic model, then solve the algebraic model to solve the problem.

    2

    In anticipation of A2.1.B Solve problems that can be represented by systems of equations and inequalities.

    1.6 Solving Linear Inequalities

    Solve simple inequalities.

    2

    3 Add three days for review, reteaching, and assessment.

    Process Standards Addressed: A2.8.A Analyze a problem situation and represent it mathematically.

    Assessment: Chapter 1 common assessment

  • Pasco School District Algebra 2 2010 – 2011 School Year

    5 Updated: Thursday, December 02, 2010

    Unit Name: Chapter 2 Linear Equations and Functions

    [Starting Date] [Ending Date]

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.1.A Select and justify functions and equations to model and solve problems.

    2.1 Functions and their graphs

    Distinguish between relations and functions.

    Graph and evaluate linear functions.

    2 Be sure to emphasize the definitions of relation and function. The second objective is included in anticipation of the section on graphing lines which follows.

    A2.1.A Select and justify functions and equations to model and solve problems.

    2.2 Slope and Rate of Change

    Use slope to solve real-life problems.

    2 A basic review of calculating slope may be necessary before students are ready to solve problems with rate of change. This section is included to address problem solving with rates of change, to meet the PE.

    In anticipation of A2.1.B Solve problems that can be represented by systems of equations and inequalities.

    2.3 Quick Graphs of Linear Equations

    Graph linear equations in slope-intercept form.

    2

    A2.1.A Select and justify functions and equations to model and solve problems.

    2.4 Writing Equations of Lines

    Model functions by writing linear equations.

    2

    2.7 Piecewise Functions

    Represent piecewise functions.

    Use piecewise functions to model real-life situations.

    2 Sections 2.7 and 2.8 do not match PEs. They are included so students will be prepared for the Compass test at CBC.

    2.8 Absolute Value Functions

    Represent absolute value functions.

    Use absolute value functions to model real-life situations.

    2

  • Pasco School District Algebra 2 2010 – 2011 School Year

    6 Updated: Thursday, December 02, 2010

    3 Add three days for review, reteaching, and assessment.

    Process Standards Addressed: A2.8.A Analyze a problem situation and represent it mathematically.

    Assessment: Chapter 2 common assessment

  • Pasco School District Algebra 2 2010 – 2011 School Year

    7 Updated: Thursday, December 02, 2010

    Unit Name: Chapter 5 Quadratic Functions [Starting Date] [Ending Date]

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. A2.3.A Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.

    5.1 Graphing Quadratic Functions

    Graph quadratic functions.

    Use quadratic functions to solve real-life problems.

    2

    A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. A2.3.A Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.

    5.2 Solving Quadratic Equation by Factoring

    Factor quadratic expressions

    Solve quadratic equations by factoring

    Find solutions (zeros) of quadratic functions.

    2

    A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities.

    5.3 Solving Quadratic Equations by Finding Square Roots

    Solve quadratic equations by finding square roots.

    Use quadratic equations to solve real-life problems.

    2

    A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities.

    5.4 Complex Numbers

    Solve quadratic equations with complex solutions.

    2

    A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities.

    5.5 Completing the Square

    Solve quadratic equations by completing the square.

    2

  • Pasco School District Algebra 2 2010 – 2011 School Year

    8 Updated: Thursday, December 02, 2010

    A2.3.A Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.

    Use completing the square to write quadratic functions in vertex form.

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities.

    5.6 The Quadratic Formula and the Discriminant

    Solve quadratic equations using the quadratic formula.

    Use the quadratic formula in real-life situations.

    Use the discriminant to determine the number and type of solutions of a quadratic equation.

    2

    A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities.

    5.7 Graphing and Solving Quadratic Inequalities

    Graph quadratic inequalities in two variables

    Solve quadratic inequalities in real-life situations.

    2

    A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities.

    5.8 Modeling with Quadratic Functions

    Write quadratic functions given characteristics of their graphs.

    2

    3 Add three days for review, reteaching, and assessment.

  • Pasco School District Algebra 2 2010 – 2011 School Year

    9 Updated: Thursday, December 02, 2010

    Process Standards Addressed: A2.8.A Analyze a problem situation and represent it mathematically.

    Assessment: Chapter 5 common assessment

  • Pasco School District Algebra 2 2010 – 2011 School Year

    10 Updated: Thursday, December 02, 2010

    Unit Name: Chapter 3 Systems of Linear Equations and Inequalities

    [Starting Date] [Ending Date]

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.1.B Solve problems that can be represented by systems of equations and inequalities.

    3.1 Solving Linear Systems by Graphing

    Graph and solve systems of linear equations.

    Use linear systems to solve real-life problems.

    2

    A2.1.B Solve problems that can be represented by systems of equations and inequalities.

    3.2 Solve Linear Systems Algebraically

    Use algebraic methods to solve linear systems.

    Use linear systems to model real-life situations.

    2

    A2.1.B Solve problems that can be represented by systems of equations and inequalities.

    3.3 Graphing and Solving Systems of Linear Inequalities

    Graph a system of linear inequalities to find the solutions of the system.

    Use systems of linear inequalities to solve real-life problems

    2

    A2.7.A Solve systems of three equations with three variables.

    3.6 Solving Systems of Linear Equations in Three Variables

    Solve systems of linear equations in three variables.

    2

  • Pasco School District Algebra 2 2010 – 2011 School Year

    11 Updated: Thursday, December 02, 2010

    Use linear systems in three variables to solve real-life problems.

    3 Add three days for review, reteaching, and assessment.

    Process Standards Addressed: A2.8.A Analyze a problem situation and represent it mathematically.

    Assessment: Chapter 3 common assessment

  • Pasco School District Algebra 2 2010 – 2011 School Year

    12 Updated: Thursday, December 02, 2010

    Unit Name: Chapter 6 Polynomials and Polynomial Functions

    [Starting Date] [Ending Date]

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.2.B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents.

    6.1 Using Properties of Exponents

    Use properties of exponents to evaluate and simplify expressions involving powers.

    Use exponents to solve real-life problems.

    2

    A2.2.B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents. A2.5.D Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax3 + d as an example of higher order polynomials and solve related equations.

    6.2 Evaluating and Graphing Polynomial Functions

    Evaluate a polynomial function.

    Graph a polynomial function.

    2 In order to meet the PE, be sure to emphasize the description of the graphs.

    A2.2.C Add, subtract, multiply, divide, and simplify rational and more general algebraic expressions.

    6.3 Adding, Subtracting and Multiplying Polynomials

    Add, subtract, and multiply polynomials.

    Use polynomial operations in real-life problems.

    2

    A2.5.D Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax3 + d as an example of higher order polynomials and solve related equations.

    6.4 Factoring and Solving Polynomial Equations

    Factor polynomial expressions.

    Use factoring to solve polynomial equations.

    Use polynomial equations to solve real-life problems.

    2

  • Pasco School District Algebra 2 2010 – 2011 School Year

    13 Updated: Thursday, December 02, 2010

    3 Add three days for review, reteaching, and assessment.

    Process Standards Addressed: A2.8.A Analyze a problem situation and represent it mathematically.

    Assessment: Chapter 6 common assessment

  • Pasco School District Algebra 2 2010 – 2011 School Year

    14 Updated: Thursday, December 02, 2010

    Unit Name: Chapter 12 Probability and Statistics

    [Starting Date] [Ending Date]

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.1.F Solve problems involving combinations and permutations.

    12.1 The Fundamental Counting Principle and Permutations

    Use the fundamental counting principle to count the number of ways an event can happen

    Use permutations to count the number of ways an event can happen

    12.2 Combinations and the Binomial Theorem

    Use combinations to count the number of ways and event can happen.

    3

    A2.6.A Apply the fundamental counting principle and the ideas of order and replacement to calculate probabilities in situations arising from two-stage experiments (compound events).

    12.3 An Introduction to Probability

    Find theoretical and experimental probabilities.

    12.4 Probability of Compound Events

    Find probabilities of unions and intersections of two events.

    Use complements to

    3

  • Pasco School District Algebra 2 2010 – 2011 School Year

    15 Updated: Thursday, December 02, 2010

    find the probability of an event.

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.6.B Given a finite sample space consisting of equally likely outcomes and containing events A and B, determine whether A and B are independent or dependent, and find the conditional probability of A given B. A2.6.C Compute permutations and combinations, and use the results to calculate probabilities.

    12.5 Probability of Independent and Dependent Events

    Find the probability of independent events

    Find the probability of dependent events.

    2

    A.2.6.D Apply the binomial theorem to solve problems using probability.

    12.6 Binomial Distributions

    Find binomial probabilities and analyze binomial distributions.

    2

    A2.6.F Calculate and interpret measures of variability and standard deviation and use these measures and the characteristics of the normal distribution to describe and compare data sets.

    7.7 Statistics and Statistical Graphs

    Use measures of central tendency and measures of dispersion to describe data sets.

    12.7 Normal Distributions

    Calculate probabilities using normal distributions.

    Use normal distributions to approximate binomial distributions.

    2

    A2.6.G and A2.7.C Calculate and interpret margin of error and confidence intervals for

    ***MISSING!

  • Pasco School District Algebra 2 2010 – 2011 School Year

    16 Updated: Thursday, December 02, 2010

    population proportions.

    3 Add three days for review, reteaching, and assessment.

    Process Standards Addressed: A2.8.A Analyze a problem situation and represent it mathematically.

    Assessment: Chapter 12 common assessment

  • Pasco School District Algebra 2 2010 – 2011 School Year

    17 Updated: Thursday, December 02, 2010

    Unit Name: Chapter 7 Powers, Roots, and Radicals

    [Starting Date] [Ending Date]

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.2.B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents.

    7.2 Properties of Rational Exponents

    Use properties of rational exponents to evaluate and simplify expressions.

    Use properties of rational exponents to solve real-life problems.

    2

    A2.5.A Construct new functions using the transformations f(x – h), f(x) + k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s). ***The construction of new functions using transformations is missing for this PE.

    7.3 Power Functions and Function Operations

    Perform operations with functions including power functions.

    Use power functions and function operations.

    2 ***The construction of new functions using transformations is missing for this PE. While composition of functions is not a PE, this skill is needed for the Compass test at CBC.

    In anticipation of A2.4.A Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.

    7.4 Inverse Functions

    Find inverses of linear functions.

    Find inverses of non-linear functions.

    2

    A2.5.B Plot points, sketch, and describe the

    graphs of functions of the form f(x) = a (x − c) + d , and solve related equations.

    7.5 Graphing Square Root and Cube Root Functions

    Graph square root and cube root functions.

    Use square root and cube root functions to find real-life quantities.

    2

  • Pasco School District Algebra 2 2010 – 2011 School Year

    18 Updated: Thursday, December 02, 2010

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.5.B Plot points, sketch, and describe the

    graphs of functions of the form f(x) = a (x − c) + d , and solve related equations.

    7.6 Solving Radical Equations

    Solve equations that contain radicals or rational exponents.

    Use radical equations to solve real-life problems.

    2

    A2.6.F Calculate and interpret measures of variability and standard deviation and use these measures and the characteristics of the normal distribution to describe and compare data sets.

    7.7 Statistics and Statistical Graphs

    Use measures of dispersion to describe data sets.

    2

    3 Add three days for review, reteaching, and assessment.

    Process Standards Addressed: A2.8.A Analyze a problem situation and represent it mathematically.

    Assessment: Chapter 7 common assessment

  • Pasco School District Algebra 2 2010 – 2011 School Year

    19 Updated: Thursday, December 02, 2010

    Unit Name: Chapter 8 Exponential and Logarithmic Functions

    [Starting Date] [Ending Date]

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.4.C Solve exponential and logarithmic equations.

    8.1 Exponential Growth

    Graph exponential growth functions

    Use exponential growth functions to model real-life situations

    2

    A2.4.C Solve exponential and logarithmic equations.

    8.2 Exponential Decay

    Graph exponential decay functions

    Use exponential decay functions to model real-life situations

    2

    A2.1.D Solve problems that can be represented by exponential and logarithmic functions and equations.

    8.3 Using the Number e

    Use the number e as the base of exponential functions.

    Use the natural base e in real-life situations.

    2

    A2.1.D Solve problems that can be represented by exponential and logarithmic functions and equations.

    8.4 Logarithmic Functions

    Evaluate logarithmic functions.

    Graph logarithmic functions.

    Use logarithmic functions to model real-life situations.

    2

    A2.1.D Solve problems that can be represented by exponential and logarithmic functions and equations.

    8.5 Properties of Logarithms

    Use properties of logarithms.

    Use properties of logarithms to solve real-life problems.

    2

  • Pasco School District Algebra 2 2010 – 2011 School Year

    20 Updated: Thursday, December 02, 2010

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.1.D Solve problems that can be represented by exponential and logarithmic functions and equations.

    8.6 Solving Exponential and Logarithmic Equations

    Solve exponential equations in real-life situations

    Solve logarithmic equations in real-life situations

    2

    A2.1.D Solve problems that can be represented by exponential and logarithmic functions and equations.

    8.7 Modeling with Exponential and Power Functions

    Model data with exponential functions.

    Model data with power functions.

    2

    3 Add three days for review, reteaching, and assessment.

    Process Standards Addressed: A2.8.A Analyze a problem situation and represent it mathematically.

    Assessment: Chapter 8 common assessment

  • Pasco School District Algebra 2 2010 – 2011 School Year

    21 Updated: Thursday, December 02, 2010

    Unit Name: Chapter 9 Rational Equations and Functions

    [Starting Date] [Ending Date]

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.1.E Solve problems that can be represented by inverse variations of the forms f(x) = (a/x) + b, f(x) = (a/x2) + b, and f(x) = a/(bx+c).

    9.1 Inverse and Joint Variation

    Write and use inverse variation models.

    2

    A2.2.C Add, subtract, multiply, divide, and simplify rational and more general algebraic expressions.

    9.4 Multiplying and Dividing Rational Expressions

    Multiply and divide rational expressions

    Use rational expressions to model real-life quantities.

    2

    A2.2.C Add, subtract, multiply, divide, and simplify rational and more general algebraic expressions.

    9.5 Addition, Subtraction, and Complex Fractions

    Add and subtract rational expressions.

    2 Complex fractions are not part of the PE.

    A2.5.C Plot points, sketch, and describe the graphs of functions of the form f(x) = (a/x) + b, f(x) = (a/x2) + b, and f(x) = a/(bx+c), and solve related equations.

    9.6 Solving Rational Equations

    Solve rational equations.

    Use rational equations to solve real-life problems.

    2

    3 Add three days for review, reteaching, and assessment.

    Process Standards Addressed: A2.8.A Analyze a problem situation and represent it mathematically.

    Assessment: Chapter 9 common assessment

  • Pasco School District Algebra 2 2010 – 2011 School Year

    22 Updated: Thursday, December 02, 2010

    Unit Name: Chapter 11 Sequences and Series

    [Starting Date] [Ending Date]

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    A2.7.B Find the terms and partial sums of arithmetic and geometric series and the infinite sum for geometric series.

    11.1 An Introduction to Sequences and Series

    Use and write sequences.

    Use summation notation to write series and find sums of series.

    11.2 Arithmetic Sequences and Series

    Write rules for arithmetic sequences and find sums of arithmetic series.

    11.3 Geometric Sequences and Series

    Write rules for geometric sequences and find sums of geometric series.

    11.4 Infinite Geometric Series

    Find sums of geometric series.

    8

    3 Add three days for review, reteaching, and assessment.

    Process Standards Addressed: A2.8.A Analyze a problem situation and represent it mathematically.

    Assessment: Chapter 11 common assessment

  • Pasco School District Algebra 2 2010 – 2011 School Year

    23 Updated: Thursday, December 02, 2010

    Unit Name: Trigonometric Ratios and Functions

    [Starting Date] [Ending Date]

    Standard Lesson & objective Days Formative Assessments/

    Assignments Alignment Notes

    ***NOTE: While this chapter does not meet any State PE’s, the committee felt it needed to be included in preparation for Pre-Calculus.

    13.1 Right Triangle Trigonometry

    Use trigonometric relationships to evaluate trigonometric functions of acute angles.

    Use trigonometric functions to solve real-life problems.

    2

    13.2 General Angles and Radian Measure

    Measure angles in standard position using degree measure and radian measure.

    Calculate arc lengths and areas of sectors.

    2

    13.3 Trigonometric Functions of Any Angle

    Evaluate trigonometric functions of any angle.

    Use trigonometric functions to solve real-life problems.

    2

    13.4 Inverse Trigonometric Functions

    2

  • Pasco School District Algebra 2 2010 – 2011 School Year

    24 Updated: Thursday, December 02, 2010

    Evaluate inverse trigonometric functions.

    Use inverse trigonometric functions to solve real-life problems.

    13.5 The Law of Sines

    Use the law of sines to find the sides and angles of a triangle.

    Find the area of any triangle.

    2

    13.6 The Law of Cosines

    Use the law of cosines to find the sides and angles of a triangle.

    Use Heron’s formula to find the area of a triangle.

    2

    3 Add three days for review, reteaching, and assessment.

    Process Standards Addressed:

    Assessment: Chapter 13 common assessment