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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