mcps algebra ii pacing guide · mcps algebra ii pacing guide | 2016-2017 august 2016 ixl modules of...

MCPS Algebra II Pacing Guide | 2016-2017

August 2016

Units to be covered 1st Semester:

Units to be covered 2nd Semester:

Unit: Functions & Graphs

Vocabulary

Suggested Pacing Semester Class: 10 days Year Long: 20 days OR Include content with individual units

Standards of Learning SOL AII.6 Recognize the general shape of function families and convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions. SOL AII.7 Investigate and analyze functions algebraically and graphically. Key concepts include a) domain/range; b) zeros; c) x- and y-intercepts; d) intervals in which a function is increasing or decreasing; and h) compositions

Manipulatives

Calculator Skills

Resources

PH Chapter 2 (Lesson 2-6) iXL Modules


August 2016

Unit: Solving and Graphing Absolute Value Equations and Inequalities

Vocabulary Absolute Value Extraneous Solution Absolute Value Function Axis of Symmetry Vertex Vertical Stretch Vertical Compression Horizontal Shift Vertical Shift Reflection Translation Dilation

Suggested Pacing Semester Class: 7 days Year Long: 14 days

Standards of Learning SOL AII.4 Solve algebraically and graphically, a) absolute value equations and inequalities. Graphing calculators will be used for solving and for confirming the algebraic solutions. SOL AII.6 Recognize the general shape of function (absolute value) families and convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions. [You may choose to include this standard with Topic 1 on functions and graphs instead of this topic.]

Manipulatives

Calculator Skills I can graph both sides of an absolute

value equation to find its solution(s) using the point(s) of intersection.

I can graph an absolute value inequality in two variables.

I can confirm algebraic solutions of absolute value equations.

Resources

PH Chapter 1 (Lesson 1-6)

PH Chapter 2 (Lessons 2-7 & 2-8) Enhanced Scope and Sequence Lessons – VDOE ESS Absolute Value Equations and Inequalities - Solving absolute value equations and inequalities

iXL Modules

Solve absolute value equations (Algebra 2 - B.3)

Graph solutions to absolute value equations (Algebra 2 - B.4)

Solve absolute value inequalities (Algebra 2 - C.7)

Graph solutions to absolute value inequalities (Algebra 2 - C.8)

Graph solutions to two-variable absolute value inequalities (Algebra 2 - C.9)

http://www.pen.k12.va.us/testing/solsearch/sol/math/AII/m_ess_a2-4a.pdf


August 2016

Unit: Complex Numbers, Quadratic Functions, and Simplifying Radicals

Vocabulary Form Imaginary Function Parabola Quadratic Function Vertex Form Axis of Symmetry Vertex of the Parabola Minimum Value Maximum Value Standard Form Factoring Greatest Common Factor (GCF) of an expression Perfect Square Trinomial Difference of Two Squares Zero of a Function Zero-Product Property Completing the Square Quadratic Formula Discriminant Imaginary Unit Imaginary Number Complex Number Pure Imaginary Number Complex Plane Absolute Value of a Complex Number Complex Conjugates

Suggested Pacing Semester Class: 8 days Parts/Year Long: 16 days

Standards of Learning SOL AII.3 Perform operations on complex numbers, express the results in simplest form using patterns of the patterns of i, and identify field properties that are valid for complex numbers. SOL AII.4 Solve algebraically and graphically, b) quadratic equations over the set of complex numbers. Graphing calculators will be used for solving and for confirming the algebraic solutions. SOL AII.5 Solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, algebraically and graphically. Graphing calculators will be used as a tool to visualize graphs and predict the number of solutions. SOL AII.6 Recognize the general shape of function (quadratic) families and convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions. SOL AII.7 Investigate and analyze functions (quadratic) algebraically and graphically, including: a) domain/range; b) zeros; c) x- and y-intercepts; d) intervals in which a function is increasing or decreasing; and f) end behavior.

Manipulatives

Calculator Skills I can graph quadratic functions. I can graph a system of

linear/quadratic or uadratic/quadratic equations and find the point of

Resources

PH Chapter 4

PH Lesson VA-1 Enhanced Scope and Sequence Lessons – VDOE ESS Complex Numbers - Performing complex number arithmetic

iXL Modules

Domain and range (Algebra 2 - D.1)

http://www.pen.k12.va.us/testing/solsearch/sol/math/AII/m_ess_a2-3.pdf


August 2016

Match quadratic functions and graphs (Algebra 2 - J.5)

Graph a linear function (Algebra 2 - D.7)

Characteristics of quadratic functions (Algebra 2 - J.1)

Graph a quadratic function (Algebra 2 - J.4)

Solve a quadratic equation using square roots (Algebra 2 - J.6)

Solve a non-linear system of equations (Algebra 2 - E.15)

Solve polynomial equations (Algebra 2 - K.7)


Find a quadratic function (Algebra 2 - J.3)

Introduction to complex numbers (Algebra 2 - H.1)

Add and subtract complex numbers (Algebra 2 - H.2)

Complex conjugates (Algebra 2 - H.3)

Multiply complex numbers (Algebra 2 - H.4)

Divide complex numbers (Algebra 2 - H.5)

Add, subtract, multiply, and divide complex numbers (Algebra 2 - H.6)

Absolute values of complex numbers (Algebra 2 - H.7)

Powers of i (Algebra 2 - H.8)

Complex conjugate theorem (Algebra 2 - K.11)

Conjugate root theorems (Algebra 2 -

intersection. I can perform operations with complex

numbers using the i key.

Quadratic Equations - Solving quadratic equations over the set of complex numbers Nonlinear Systems of Equations - Solving nonlinear systems of equations

http://www.pen.k12.va.us/testing/solsearch/sol/math/AII/m_ess_a2-4b.pdf



August 2016

K.12)

Unit: Polynomials and Polynomial Functions

Vocabulary Turning Point Relative Minimum Relative Minimum Expand Monomial Degree of a Monomial Polynomial Degree of a Polynomial Polynomial Function Standard Form of a Polynomial Function Turning Point End Behavior Factor Theorem Multiple Zero Multiplicity Sum of Cubes Difference of Cubes Synthetic Division Remainder Theorem Rational Root Theorem Conjugate Root Theorem Descartes’ Rule of Signs Fundamental Theorem of Algebra Expand Pascal’s Triangle Binomial Theorem


Standards of Learning SOL AII.1 Given rational, radical, or polynomial expressions, will d) factor polynomials completely. SOL AII.6 Recognize the general shape of function (polynomial) families and convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions. SOL AII.7 Investigate and analyze functions (polynomial) algebraically and graphically, including: a) domain/range; b) zeros; c) x- and y-intercepts; d) intervals in which a function is increasing or decreasing; and f) end behavior. SOL AII.8 Investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression. SOL AII.9 Collect and analyze data, determine the equation of the curve of best fit, make predictions, and solve real-world problems, using mathematical models. Mathematical models will include polynomial functions.

Manipulatives

Calculator Skills I can graph a polynomial function.

Resources


August 2016

iXL Modules

Graph a linear inequality in one variable (Algebra 2 – C.1)

Graph a linear inequality in the coordinate plane (Algebra 2 - C.2)

Write inequalities from graphs (Algebra 2 - C.3)

Graph solutions to linear inequalities (Algebra 2 - C.6)

Identify functions (Algebra 2 - D.2)

Evaluate functions (Algebra 2 - D.3)

Find the slope of a linear function (Algebra 2 - D.6)

Graph a linear function (Algebra 2 - D.7)

Write the equation of a linear function (Algebra 2 - D.8)


Complete a function table: quadratic functions (Algebra 2 - J.2)

Find a quadratic function (Algebra 2 - J.3)

Graph a quadratic function (Algebra 2 - J.4)

Match quadratic functions and graphs (Algebra 2 - J.5)

Match polynomials and graphs (Algebra 2 - K.14)

Write a polynomial from its roots (Algebra 2 - K.8)

Find the roots of factored polynomials (Algebra 2 - K.9)

Rational root theorem (Algebra 2 - K.10)

I can calculate the curve (polynomial) of best fit.

I can use the stored equation of the curve of best fit to make predictions.

PH Chapter 5 Enhanced Scope and Sequence Lessons – VDOE ESS Factors, Zeros, and Solutions - Exploring relationships among factors, zeros, and solutions Factoring - Factoring polynomials


http://www.pen.k12.va.us/testing/solsearch/sol/math/AII/m_ess_a2-1d.pdf


August 2016

Descartes' Rule of Signs (Algebra 2 - K.13)

Factor monomials (Algebra 2 - I.1)

Factor quadratics (Algebra 2 - I.2)

Factor quadratics using algebra tiles (Algebra 2 - I.3)

Factor using a quadratic pattern (Algebra 2 - I.4)

Factor by grouping (Algebra 2 - I.5)

Factor sums and differences of cubes (Algebra 2 - I.6)

Factor polynomials (Algebra 2 - I.7)

Fundamental Theorem of Algebra (Algebra 2 - K.15)

Graph parabolas (Algebra 2 - T.9)

Solve polynomial equations (Algebra 2 - K.7)

Write equations of parabolas in vertex form from graphs (Algebra 2 - T.5)


August 2016

Unit: Rational Expressions, Solving Rational Equations, Graphing Rational Functions

Vocabulary Inverse Variation Combined Variation Joint Variation Reciprocal Function, Branch Rational Function Continuous Graph Discontinuous Graph, Point of Discontinuity, Removable Discontinuity, Non-Removable Discontinuity Rational Expression Simplest Form Complex Fraction Rational Equation Oblique Asymptote


Standards of Learning SOL AII.1 Given rational, radical, or polynomial expressions, will a) add, subtract, multiply, divide, and simplify rational algebraic expressions. SOL AII.4 Solve algebraically and graphically, c) equations containing rational algebraic expressions. Graphing calculators will be used for solving and for confirming the algebraic solutions. SOL AII.6 Recognize the general shape of function (rational) families and convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions. SOL AII.7 Investigate and analyze functions (rational) algebraically and graphically. Key concepts include a) domain and range, including limited and discontinuous domains and ranges; b) zeros; c) x- and y-intercepts; e) asymptotes; and f) end behavior. Graphing calculators will be used as a tool to assist in investigation of functions.

Manipulatives

Calculator Skills I can graph rational algebraic functions. I can graph both sides of a rational

equation to find its solution(s) using the point(s) of intersection.

Resources

PH Chapter 8

PH Standards Review: Functions (p. VA 10) after Lesson 8-2 Enhanced Scope and Sequence Lessons – VDOE ESS Rational Functions: Intercepts, Asymptotes, and Discontinuity – Exploring asymptotes and discontinuity Rational Expressions - Performing operations with rational expressions Rational Equations - Solving equations containing radical expressions

iXL Modules

Evaluate rational expressions I (Algebra 2 - N.2)

Evaluate rational expressions II (Algebra 2 - N.3)

Simplify rational expressions (Algebra 2 - N.4)

Multiply and divide rational expressions (Algebra 2 - N.5)

http://www.pen.k12.va.us/testing/solsearch/sol/math/AII/m_ess_a2-7abce.pdf

http://www.pen.k12.va.us/testing/solsearch/sol/math/AII/m_ess_a2-1a.pdf



August 2016

Add and subtract rational expressions (Algebra 2 - N.6)

Evaluate integers raised to rational exponents (Algebra 1 - V.10)

Evaluate rational exponents (Algebra 2 - M.1)

Multiplication with rational exponents (Algebra 2 - M.2)

Simplify expressions involving rational exponents I (Algebra 2 - M.5)

Solve rational equations (Algebra 2 - N.7)

Rational functions: asymptotes and excluded values (Algebra 2 - N.1)

Unit: Exponential and Logarithmic Functions

Vocabulary Exponential Function Exponential Growth Exponential Decay Asymptote Growth Factor Decay Factor Natural Base Exponential Function Continuously Compounded Interest Change of Base Formula Exponential Equation Logarithmic Equation Natural Logarithmic Function Asymptote Common Logarithm Logarithm Logarithmic Scale


Standards of Learning SOL AII.6 Recognize the general shape of function (exponential and logarithmic) families and convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions. SOL AII.7 Investigate and analyze functions (exponential and logarithmic) algebraically and graphically. Key concepts include a) domain/range; b) zeros; c) x- and y-intercepts; d) intervals in which a function is increasing or decreasing; e) asymptotes; f) end behavior; and g) inverse of a function. Graphing calculators will be used as a tool to assist in investigation of functions. SOL AII.9 Collect and analyze data, determine the equation of the


August 2016

curve of best fit, make predictions, and solve real-world problems, using mathematical models. Mathematical models will include exponential and logarithmic functions.

Manipulatives

Calculator Skills I can graph exponential functions. I can graph logarithmic functions. I can calculate the curve (exponential

or logarithmic) of best fit. I can use the stored equation of the

curve of best fit to make predictions.

Resources

PH Chapter 7

PH Standards Review: Internal Behavior (p. VA 12) and Scatterplots (p. VA 14) after Lesson 7-3

Enhanced Scope and Sequence Lessons – VDOE ESS Curve of Best Fit - Collecting and analyzing data, using curve of best fit Transformational Graphing - Exploring transformational graphing

iXL Modules

Domain and range of exponential and logarithmic functions (Algebra 2 – S.1)

Match exponential functions and graphs (Algebra 2 – S.3)

Identify inverse functions (Algebra 2 – O.6)

Evaluate exponential functions (Algebra 2 – S.2)

Identify linear and exponential functions (Algebra 2 – S.9)

Find values of inverse functions from tables (Algebra 2 – O.7)

Find values of inverse functions from graphs (Algebra 2 – O.8)

Find inverse functions and relations (Algebra 2 – O.9)




August 2016

Unit: Radicals

Vocabulary nth Root Principal Root Radicand Index Simplest Form of a Radical Like Radicals Rational Exponent Composite Function Radical Function Square Root Function Cube Root Function One to One Function Inverse Function Radical Equation Square Root Equation Cube Root Equation


Standards of Learning SOL AII.1 Given rational, radical, or polynomial expressions, will b) add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents; and c) write radical expressions as expressions containing rational exponents & vice versa. SOL AII.4 Solve algebraically and graphically, d) equations containing radical expressions. Graphing calculators will be used for solving and for confirming algebraic solutions. SOL AII.7 Investigate & analyze functions (radical) algebraically & graphically. Key concepts include: a) domain/range; b) zeros; c) x- and y-intercepts; d) intervals in which a function is increasing or decreasing; f) end behavior; g) inverse of a function; and h) composition of multiple functions. Graphing calculators will be used as a tool to assist in investigation of functions.

Manipulatives

Calculator Skills I can graph radical functions. I can graph radical functions. I can graph both sides of a radical

equation to find its solution(s) using the point(s) of intersection.

I can graph the composition of two functions.

I can use stored functions to find the result of a composition given a value.

I can graph an inverse function of the form 𝑥 = 𝑔(𝑦) using the text tool.

Resources

PH Chapter 6

PH Lesson VA-2 after Lesson 6-6 Enhanced Scope and Sequence Lessons – VDOE ESS Exponents and Radicals - Performing operations with and writing radical expressions containing rational exponents Radical Equations - Solving equations containing radical expressions Inverse Functions - Exploring inverse functions Composition of Functions - Exploring composition of functions

iXL Modules

Roots of integers (Algebra 2 – L.1)

Roots of rational numbers (Algebra 2 – L.2)

Find roots using a calculator (Algebra 2 – L.3)

Domain and range of radical functions (Algebra 2 – L.12)

Solve radical equations (Algebra 2 – L.13)

Simplify radical expressions with variables I (Algebra 2 – L.5)

Simplify radical expressions with variables II (Algebra 2 – L.6)

Multiply radical expressions (Algebra 2

http://www.pen.k12.va.us/testing/solsearch/sol/math/AII/m_ess_a2-1bc.pdf


http://www.pen.k12.va.us/testing/solsearch/sol/math/AII/m_ess_a2-7g.pdf

http://www.pen.k12.va.us/testing/solsearch/sol/math/AII/m_ess_a2-7h.pdf


August 2016

– L.7)

Divide radical expressions (Algebra 2 – L.8)

Simplify radical expressions using the distributive property (Algebra 2 – L.10)

Simplify radical expressions using conjugates (Algebra 2 – L.11)

Evaluate rational exponents (Algebra 2 – M.1)

Multiplication with rational exponents (Algebra 2 – M.2)

Division with rational exponents (Algebra 2 – M.3)

Power rule (Algebra 2 – M.4)

Simplify expressions involving rational exponents I (Algebra 2 – M.5)

Simplify expressions involving rational exponents II (Algebra 2 – M.6)

Rational functions: asymptotes and excluded values (Algebra 2 – N.1)

Function transformation rules (Algebra 2 – P.5)

Describe function transformations (Algebra 2 – P.6)

Composition of linear functions (Algebra 2 – O.4)

Composition of linear and quadratic functions (Algebra 2 – O.5)


August 2016

Unit: Non-linear Systems

Vocabulary


Standards of Learning SOL AII.5 Solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, algebraically and graphically. Graphing calculators will be used as a tool to visualize graphs and predict the number of solutions.

Manipulatives

Calculator Skills

Resources

PH Chapter 4 (Lesson 4-9) Enhanced Scope and Sequence Lessons – VDOE ESS Nonlinear Systems of Equations - Solving nonlinear systems of equations

iXL Modules



August 2016

Unit: Variation

Vocabulary Direct Variation Joint Variation Inverse Variation Constant of Proportionality


Standards of Learning SOL AII.10 Identify, create, and solve real-world problems involving inverse variation, joint variation, and a combination of direct and inverse variations.

Manipulatives

Calculator Skills

Resources

PH Chapter 8 (Lesson 8-1) Enhanced Scope and Sequence Lessons – VDOE ESS Types of Variations - Exploring variations

iXL Modules

Write and solve direct variation equations (Algebra 2 – Q.1)

Write and solve inverse variation equations (Algebra 2 – Q.2)

Classify variation (Algebra 2 – Q.3)

Write joint and combined variation equations I (Algebra 2 – Q.4)

Find the constant of variation (Algebra 2 – Q.5)

Write joint and combined variation equations II (Algebra 2 – Q.6)

Solve variation equations (Algebra 2 – Q.7)



August 2016

Unit: Sequences & Series

Vocabulary Sequence Term of a Sequence Explicit Formula Recursive Formula Arithmetic Sequence Common Difference Arithmetic Mean Geometric Sequence Common Ratio Geometric Mean Series Infinite Series Finite Series Arithmetic Series Limits Geometric Series Diverge


Standards of Learning SOL AII.2 Investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include ∑ and an.

Manipulatives

Calculator Skills

I can use as needed.

Resources

PH Chapter 9 Enhanced Scope and Sequence Lessons – VDOE ESS Arithmetic and Geometric Sequences and Series - Exploring sequences and series

iXL Modules

nth roots (Algebra 2 – L.4)

Classify formulas and sequences (Algebra 2- BB.1)

Find terms of an arithmetic sequence (Algebra 2 – BB.2)

Find terms of a geometric sequence (Algebra 2 – BB.3)

Evaluate formulas for sequences (Algebra 2 – BB.5)

Write a formula for an arithmetic sequence (Algebra 2 – BB.6)

Write a formula for a geometric sequence (Algebra 2 – BB.7)

Sequences: mixed review (Algebra 2 –



August 2016

BB.9)

Identify a sequence as explicit or recursive (Precalculus – W.3)

Find recursive and explicit formulas (Precalculus – W.5)

Convert a recursive formula to an explicit formula (Precalculus – W.6)

Convert an explicit formula to a recursive formula (Precalculus – W.7)

Convert between explicit and recursive formulas (Precalculus – W.8)


August 2016

Unit: Probability

Vocabulary Simulation Conditional Probability Measure of Central Tendency Permutation Fundamental Counting Principle n factorial Combination Experimental Probability Simulation Sample Space Theoretical Probability Dependent Events Independent Events Mutually Exclusive Events Measure of Variation Variance Standard Deviation


Standards of Learning SOL AII.11 Identify properties of a normal distribution and apply those properties to determine probabilities associated with areas under the standard normal curve. SOL AII.12 Compute and distinguish between permutations and combinations and use technology for applications.

Manipulatives

Calculator Skills I can use the Normal Cdf Distribution

Function to find probabilities.

I can use the nCr and nPr functions to calculate combinations and permutations.

Resources

PH Lessons 11-1 and 11-9

PH Concept Byte p. 740

PH Lesson VA-3

VDOE Technical Assistance Document for 2009 Standard AII.11

Enhanced Scope and Sequence Lessons – VDOE ESS Permutations and Combinations - Counting using permutations and combinations Normal Distributions - Analyzing and using the standard normal curve

iXL Modules

Find probabilities using the normal distribution (Algebra 2 – CC.21)

Variance and standard deviation (Algebra 2 – D.2)

Combinations and permutations (Algebra 2 – CC.4)

Find probabilities using combinations and permutations (Algebra 2 – CC.5)



mcps algebra ii pacing guide · mcps algebra ii pacing guide | 2016-2017 august 2016 ixl modules of...

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