Advanced Algebra 2 Pacing Guide Lynchburg City Schools

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1 Grading Period: 1 st Nine Weeks Days to Teach = 44 SOL & Enabling Objectives: Description Text Recommended Activities Time Frame Begin the school year with relationship building activities continue integrating relationship building throughout the school year Activity Ideas PRE-TEST (for Teacher Evaluation & School Improvement: Interactive Achievement) will be released by the division to be administered at a time TBA Begin teaching the 3 rd day of school. DO NOT FEEL BOUND TO THE TEXT BOOK! PLEASE USE ONLINE RESOURCES, APPLETS, & HANDS-ON ACTIVITIES CPM = Connections to Precalculus Masters (Prentice Hall) Properties of the Real Number System A113.b Determine which field properties apply to the complex number system. 1-1 ESS All3.a-h Complex Numbers unit = 5

2 All3.f Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole, & natural. 1-2 Operations with Complex numbers Ti 83 Lesson Field Properties Testing the field Properties and Density CPM p.1-2 Solving Absolute Value Equations & Inequalities A11.4a Solve absolute value equations & inequalities algebraically & graphically. 1-3, 1-4, 1-5 ESS All4.a Absolute Value Equations & Inequalities Compound inequality game for this unit = 5 Graphing Function Transformations Absolute Value Inequality Number Line Intro to Domain, Range, and Functions All.7a Identify the domain, range, zeros, & intercepts of a function presented algebraically & graphically. 2-1, 2-2, 2-3 Finding the Domain & Range of a Function from a graph Function Grapher for this unit = 3

3 Graph, Domain & Range of Common Functions Absolute Value Functions All.6a Recognize graphs of parent functions. All.6b Given a transformation of a parent function, identify the graph of the transformed function. 2-5, 2-6 Illuminations Lesson Rates & Taxes ESS A11.6a-f Transformational Graphing Transformation Activity for Exponential and Absolute Value Graphing Function Transformations for this unit = 5 All.6c Given the equation & using a transformation approach, graph a function. Function Grapher All.6d Given the graph of a function, identify the parent function. All.6e Given the graph of a function, identify the transformations that map the preimage to the image in order to determine the equation of the image. All.6f Using a transformational approach, write the equation of a function given its graph. Piecewise Functions Examples: Floor & Ceiling Functions for

4 Supports All.7 Floor and Ceiling Functions Graphing Piecewise Functions Writing Functions Given the Graph Identify Domain & Range of a Piecewise Function Properties of Quadratics All.6a Recognize graphs of parent functions All.6b Given a transformation of a parent function, identify the graph of the transformed function. All.6c Given the equation & using a transformation approach, graph a function CPM p Guided Discovery: Piecewise Functions PowerPoint Instruction Piecewise Functions Illuminations Activity Cell Phone Cost Per Minute Graphing Function Transformations Interactive Multi-Function Data Flyer Illuminations Lesson Hanging Chains Function Grapher this unit = 5 for this unit = 4 All.6d Given the graph of a function, identify the parent function. Matching parabola to equation All.6e Given the graph of a function, identify the transformations that map the pre-image to the image in order to determine the equation of the image. Graph, Domain, and Range of Common Functions All.6f Using a transformational approach, write the

5 equation of a function given its graph. Advanced Algebra 2 Pacing Guide All.7a Identify the domain, range, zeros, & intercepts of a function presented algebraically & graphically. Factoring Polynomials All.1h Factor polynomials by applying general patterns including difference of squares, sum & difference of cubes, & perfect square trinomials. All.1i Factor polynomials completely over the integers. 5-4, 6-4 ESS All.1hi Factoring for this unit = 4 All.1j Verify polynomial identities: difference of squares, sum & difference of cubes, & perfect square trinomials. Solving Quadratic Equations by Factoring All.7a Identify the domain, range, zero, & intercepts of a function presented algebraically & graphically. 5-5 ESS All.8abc Factors Zeros & Solutions Finding the Domain and Range of a Function from a graph for this unit = 3 All.8a Describe the relationship among solutions of an equation, zeros of a function, x-intercepts of a graph, & factors of a polynomial expression. Function Grapher

6 All.8b Define a polynomial function, given its zeros. All.8c Determine a factored form of a polynomial expression from the x-intercepts of the graph of its corresponding function. Advanced Algebra 2 Pacing Guide All.8d For a function, identify zeros of multiplicity greater than 1 and describe the effect of those zeros on the graph of the function. Linear and Quadratic Regressions All.9a Collect & analyze data. All.9b Investigate scatterplots to determine if patterns exist & then identify the patterns All.9c Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, & logarithmic functions. 2-4, 5-1 Illuminations Activity: Exploring Linear Data Illuminations Activity: Making Predictions using Body Measurements Interactive: Regression Plotting Block Patterns to create curve of best fit Illuminations Activity Line of Best Fit for this unit = 3 All.9d Make predictions, using data, scatterplots, or the equation of the curve of best fit. Illuminations Lesson Barbie Bungee (Regression) All.9e Given a set of data, determine the model that

7 would best describe the data. Complex Number System All.1d Simplify radical expressions containing positive rational numbers & variables p. 262 ESS All.3a-h Complex Numbers for this unit = 3 All.3a Recognize that the square root of -1 is represented as i. 5-6 Operations with Complex Numbers Ti-83 All.3b Determine which field properties apply to the complex number system. Arithmetic operations with complex numbers from vectors All.3c Simplify radical expressions containing negative rational numbers & express in a + bi form All.3d Simplify powers of i. All.3e +, -, and x complex numbers. All.3f Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole, & natural. All.3g Write a real number in a + bi form

8 All.3h Write a pure imaginary number in a +bi form Flex /Remediation 3 Grading Period: 2 nd Nine Weeks Days to Teach = 45 SOL & Enabling Objective: Description Text Recommended Activities Time Frame Complex Number System All.1d Simplify radical expressions containing positive rational numbers & variables. p. 262 ESS All.3a-h Complex Numbers unit = 2 All.3a Recognize that the square root of -1 is represented as i. All.3b Determine which field properties apply to the complex number systems. All.3c Simplify radical expressions containing negative rational numbers & express in a + bi form 5-6 Operations with Complex Numbers Ti-83 Arithmetic operations with complex numbers from vectors

9 All.3d Simplify power of i. All.3e +, -, and x complex numbers. All.3f Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole, & natural. All.3g Write a real number in a + bi form. All.3h Write a pure imaginary number in a + bi form. More on Solving Quadratic Equations All.4b Solve a quadratic equation over the set of complex numbers using an appropriate strategy Finding the Domain and Range of a Function from a graph unit = 6 All.4c Calculate the discriminant of a quadratic equation to determine the number of real & complex solutions. All.7a Identify the domain, range, zeroes, & Function Grapher Illuminations Activity: Proof without words: completing the square

10 intercepts of a function presented algebraically & graphically. All.8a Describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, & factors of a polynomial expression. Solve quadratic equations graphically The discriminant calculator Discriminant and roots of quadratic All.8e Given a polynomial equation, determine the number of real solutions & non-real solutions. All.4h Recognize that the quadratic formula can be derived by applying the completion of squares to a quadratic equation in standard form.

11 Solving Non-Linear Systems All.5a Predict the numbers of solutions to a nonlinear system of 2 equations. p.577 ESS All.5abc Nonlinear Systems of Equations unit = 4 All.5b Solve a linear-quadratic system of 2 equations algebraically & graphically. Function Grapher All.5c Solve a quadratic-quadratic system of 2 equations algebraically & graphically. CPM p Illuminations Activity Pan Balance with expressions Higher Order Polynomials All.7e Describe the end behavior of a function. All.9e Given a set of data, determine the model that would best describe the data. p Illuminations Lesson Shrinking Candles ESS All.7abce Functions Domain Range End Behavior unit = 4 All.9c Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, & logarithmic functions. Activity: page 300 text Block Patterns to create curve of best fit

12 Solving Polynomial Functions All.7c Given the graph of a function, identify intervals on which the function is increasing & decreasing. All.8c Determine a factored form of a polynomial expression from the x-intercepts of the graph of its corresponding function. All.8d For a function, identify zeros of multiplicity greater that 1 and describe the effect of those zeros on the graph of the function ESS all. 8abc Factors Zeros & Solutions Using tangent line to show increasing and decreasing Include: Synthetic Division with Complex Zeros Fundamental Theorem of Algebra Descartes Rule of Signs unit =9 All.8e Given a polynomial equation, determine the number of real solutions & non-real solutions. Simplifying Radicals All.1d Simplify radical expressions containing positive rational numbers & variables unit = 4 All.1g x and radical expressions not requiring rationalizing the denominators. All.1f +, and radical expressions.

13 Radical Equations All.1e Convert from radical notation to exponential notation, & vice versa. Solve an equation containing a radical expression Rules of exponents game Function Grapher unit = 5 All.4e Algebraically & graphically Radical Functions All.6a Recognize graphs of parent functions. All.6b Given a transformation of a parent function, identify the graph of the transformed function. EXT Graphing Function Transformations Function Grapher Graph: Domain and Range of Common Functions unit = 5 All.6c Given the equation & using a transformation approach, graph a function. All.6d Given the graph of a function, identify the parent function. All.6e Given the graph of a function, identify the transformations that map the pre-image to the image in order to determine the equation of the image.

14 All.6f Using a transformational approach, write the equation of a function given its graph. Exam Review & Testing 4 Flex /Remediation 2 Grading Period: 3 rd Nine Weeks Days to Teach = 48 SOL & Enabling Objective: Description Text Recommended Activities Time Frame Direct, Inverse, & Joint Variation All.10a Translate y varies jointly as ax and z as y=kxz 2-3 Variation activity with Ti-83 unit = 5 All.10b Translate y is directly proportional to x as y= kx Illuminations Lesson Inverse Variation All.10c Translate y is inversely proportional to x as y = k/x.

15 All.10d Given a situation, determine the value of the constant of proportionality. All.10e Set up & solve problems, including realworld problems, involving inverse variation, joint variation, & a combination of direct & inverse variations. Rational Functions All.7a Identify the domain, range, zeros, & intercepts of a function presented algebraically & graphically. All.7b Describe restricted/discontinuous domains & ranges. 9-3 Finding the Domain and Range of a Function from a graph Function Grapher Rational Functions graphs, asymptotes, and holes unit = 5 All.7c Given the graph of a function, identify intervals on which the function is increasing & decreasing. All.7d Find the equations of vertical & horizontal asymptotes of functions. CPM p Graph, Domain, and Range of Common Functions Illuminations Lesson whelk Come to Math Illuminations Lesson Domain Representations

16 All.7e Describe the end behavior of a function Advanced Algebra 2 Pacing Guide Simplifying Rational Expressions All.1a +, -, x, rational algebraic expressions. All.1b Simplify a rational algebraic expression w/ c common monomial or binomial factors ESS All.1abc Rational Expressions Rational Expressions Review unit = 10 All.1c Recognize a complex algebraic fraction, & simplify it as a quotient or product of simple algebraic fractions. Solving Rational Equations All.4d Solve equations containing rational algebraic expressions w/ monomial or binomial denominators algebraically & graphically. 4-4 ESS All.4df Rational Equations Function Grapher unit = 5

17 More Regression Equations All.9c Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, & logarithmic functions Illuminations Lesson Determining f(x)s using regression Illuminations Lesson Paying for your wheels unit = 5 All.9d Make predictions, using data, scatterplots, or the equation of the curve of best fit. All.9e Given a set of data, determine the model that would best describe the data. All.6a Recognize graphs of parent functions Block Patterns to create curve of best fit Graphing Exponential Functions with asymptote, domain, and range Transformation activity for exponential and absolute value All.6b Given a transformation of a parent function, identify the graph of the transformed function. Graphing Function: Transformations Function Grapher All.6c Given the equation & using a transformation approach, graph a function. All.6d Given the graph of a function, identify the parent function. EggMath: Embryo exponential explanation Exponential penny growth word problem All.6e Given the graph of a function, identify the

18 transformations that map the pre-image to the image in order to determine the equation of the image. Advanced Algebra 2 Pacing Guide All.6f Using a transformational approach, write the equation of a function given its graph. Functions and Their Inverses All.7f Find the inverse of a function. All.7g Graph the inverse of a function as a reflection across the line y = x All.7h Investigate exponential & logarithmic functions, using the graphing calculator. Solving Logarithmic Equations All.7i Convert between logarithmic & exponential forms of an equation w/ bases consisting of natural numbers CPM p Drawing an Inverse Illuminations Lesson Counting the Trains Graph, Domain, and Range of Common Functions EggMath: Embryo Exponential explanation Frogger game with log expressions unit = 8 unit = 5 optional EXT: 8-6 Flex /Remediation 5

19 Grading Period: 4 th Nine Weeks Days to Teach = 43 SOL & Enabling Objective: Description Text Recommended Activities Time Frame Sequences and Series All.2a Distinguish between a sequence & a series 11-2 ESS All.2abcde Arith & Geo Sequence & Series unit = 8 All.2b Generalize patterns in a sequence using explicit & recursive formulas Function Machine for explicit and recursive definitions All.2c Use & interpret the notations All.2d Given the formula, find (the nth term) for an arithmetic or geometric sequence. All.2e Given formulas, write the first n terms and find the sum, of the first n terms of an arithmetic or a geometric sequence. All.2f Given the formula, find the sum of a Use limits to show sums of infinite series Geometric Series and sum calculations Visualizing An Infinite Series

20 convergent infinite series. The Normal Curve All.11a Identify the properties of a normal probability distribution. All.11b Describe how the standard deviation & mean affect the graph of the normal distribution Interactive Activity Fitted Normal distribution Data grapher with box, scatter, and histogram Illuminations activity sampling distribution Illuminations lesson mow whole thing unit = 8 All.11c Compare 2 sets of normally distributed data using a standard normal distribution & z- scores. Illuminations activity histogram tool Properties of the normal distribution curve All.11d Represent probability as area under the curve of a standard normal probability distribution. Interactive activity normal distribution All.11e Use the graphing calculator or a standard normal probability table to determine probabilities or percentiles based on z- scores Permutations and Combinations

21 All.12a Compare & contrast permutations & combinations. All.12b Calculate the number of permutations of n objects taken r at a time. All.12c Calculate the number of combinations of n objects taken r at a time. All.12d Use permutations & combinations as counting techniques to solve real-world problems. 6-7 EXT. 6-8 Permutation braid unit = 4 OPTIONAL CONIC SECTIONS Concrete on h,k form of a conic section Graph using translations of parent Interactive: Cross Section Grapher Interactiveate: Conic Flyer Activity: Exploring Conic Sections unit = 4 Illuminations Lesson Cutting Conics POST-TEST (for Teacher Evaluation & School Improvement use same test as PRE-TEST 1 day

22 SOL Review & Testing: 13 Days Final Exam Review & Testing 5 RECOMMENDED WEBSITES for additional lesson plans, activities, virtual manipulatives, and applets: Illuminatinos_NCTM Henrico Algebra Resources Algebra Bits Project interactive Suffolk Resources Texas Instruments Activities National Library of Virtual Manipulatives NVLM Jefferson Lab Sol Review Algebra 2: Math Cross Walk 2001 and 2009 SOLs Changes to the reporting categories for Algebra 1 s2l test: Now there are 3 reporting categories instead of 5. Relations & functions has become Functions & Statistics; Analytical Geometry and Systems of Equations/Inequalities strands have been removed. The 3 reporting categories for Algebra 2 now coincide with the Algebra 1 categories/strands.

23 Notice that the Functions & Statistics reporting category contains nearly all of the new/revised content of the 2009 Algebra 2 standards (All. 6, All.7sde & f, All.9, All.10, All.11, and All.12). See the VDOE s SOL crosswalk for additional details. Now the Functions & Statistics strand will encompass nearly 50% of the new math SOL test!!! Reporting Category 2009 SOL # items % of test # of items % of test Expressions & All.1a-d, All % 13 26% Operations Equations & All.4a-d, All % 13 26% Inequalities Functions & Statistics All.2, All.6, All.7a-h, All.8, All.9, All.10, All.11, All % 24 48%

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