Algebra II Pacing and Curriculum Guide Greene County Public Schools

Transcription

1 Algebra II Pacing and Curriculum Guide Greene County Public Schools 1

2 Greene County Public Schools Algebra II Pacing and Curriculum Guide Course Outline Quarter 1 Quarter 2 Quarter 3 Quarter 4 AII.4a - Absolute Value Equations and AII.9 Curve of Best Fit AII.10 Variations AII.7a-h Graphing Functions Review Inequalities AII.6/AII.7 Polynomial Functions AII.6/AII.7 Rational Functions AII.5 Systems of Non-Linear Equations AII.6/AII.7 Absolute Value Functions AII.8 Solution/zero/x-intercept/factors AII.1a Rational Expressions AII.11 Normal Distributions and Z-scores AII.1d Factoring AII.1bc Radical Expressions and AII.4c Rational Equations AII.1-AII.12 SOL Review AII.3 Complex Numbers Rational Exponents AII.6/AII.7 Exponential and AII.4b Solve Quadratic Equations AII.4d Radical Equations Logarithmic Functions AII.6/AII.7 Quadratic Functions AII.7h Composite Functions AII.2 Sequences and Series AII.7g Inverse Functions AII.12 Permutations and Combinations Big Ideas 1. Equations and Inequalities 2. Factoring 3. Radicals & Complex Numbers 4. Quadratics & Systems 5. Function Families & 6. Rational Expressions 7. Sequences & Series 8. Normal Distribution & Z- scores Algebra II SOL Test Blueprint (50 questions total) Expressions and Operations 13 Questions 26% of the Test Equations and Inequalities 13 Questions 26% of the Test Functions and Statistics 24 Questions 48% of the Test Resources Transformations 9. Variation 10. Curve of Best Fit & Counting Principles Text: Algebra 2, 2004, McDougal Littell Virginia Department of Education Mathematics SOL Resources DOE Enhanced Scope and Sequence Lesson Plans VDOE Vertical Alignment Charts /opening_session/2009sol_vertical_articulation_by_topic_eoc_alg_ pdf HCPS Algebra 2 Online Module Homepage GCPS Math Instructional Strategies Guide GCPS SPBQ Review Document w/strategies 2

3 Greene County Public Schools Algebra II Curriculum & Pacing Guide Quarter 1 August 19, 2014 October 17, 2014 Time/Dates SOL/Strand Objective/Content/Essential Questions/Cognitive Level 8/19-8/27 AII.4a Absolute Value 1-7 The student will solve, algebraically and graphically, a) absolute value equations and inequalities Graphing calculators will be used for solving and for confirming the algebraic solutions. mathematical reasoning, connections, and representations to Solve absolute value equations and inequalities algebraically and graphically Blooms = Apply Vertical Alignment SOL 7.14 a) solve one and two step linear equations; b) solve practical problems in one variable SOL 8.15 a) solve multistep linear equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve SOL A.4 solve multistep linear/ quad equation (2 vars) Vocabulary Absolute value Absolute value equation Absolute value inequality Compound inequality Compound sentence Extraneous solution Intersection Union Cross-curricular Connections Biology range of normal body temperatures 54 #69) Sports weight range of balls 55 #72) 3

4 8/28-9/5 2-8 AII.6 Absolute Value Functions AII.7a-d Graphing The student will recognize the general shape of (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of s. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these s. mathematical reasoning, connections, and representations to Recognize graphs of parent s. Given a transformation of a parent, identify the graph of the transformed. Given the equation and using a transformational approach, graph a. Given the graph of a, identify the parent. SOL 7.12 represent relationships with tables, graphs, rules, and words SOL 7.15 a) solve one step inequalities; b) graph solutions on number line SOL 8.14 make connections between any two representations (tables, graphs, words, rules) SOL 8.15 b) solve two step linear inequalities and graph results on number line; c) ID properties of operations used to solve SOL 8.16 Graph linear equations in two variables SOL 8.17 ID domain, range, indep/dep variable SOL A.2 perform operations on Absolute value Dilation Family of s Intercepts (x and y) Parent Reflection Transformation of graphs Translation (vertical and horizontal) Vertex Domain Range Zeroes of s x and y- intercepts End behavior Increasing intervals Decreasing intervals Axis of symmetry Music Finding sound level of musical pieces ( 127 #44-45) 4

5 Given the graph of a, identify the transformations that map the preimage to the image in order to determine the equation of the image. Using a transformational approach, write the equation of a given its graph. polynomials c) factor first /second degree binomials/ trinomials (1 or 2 vars) SOL A.6 graph linear equations/linear inequal (2 vars) The student will investigate and analyze s algebraically and graphically. Key concepts include a) domain and range, including limited and discontinuous domains and ranges; b) zeros; c) x- and y-intercepts; d) intervals in which a is increasing or decreasing; Graphing calculators will be used as a tool to assist in investigation of s. mathematical reasoning, connections, and representations to Identify the domain, range, zeros, and intercepts of a presented algebraically or graphically. SOL A.7 investigate/analyze (linear/quad) families and characteristics (alg/graph) a) determine relation is ; b) domain/range; c) zeros; d) x and y- intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic) SOL AFDA.1 investigate/analyze (linear/quad/exp/log) families/characteristics a) continuity; b) local/abs max/min; c) domain/range; 5

6 Given the graph of a, identify intervals on which the is increasing and decreasing. Blooms = Analyze d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes SOL AFDA.2 use transformations to write equations, given graph of (linear/quad/exp/log) SOL AFDA.4 transfer between/analyze mult representations of s 6

7 9/8-9/ AII.1d Factor The student, given rational, radical, or polynomial expressions, will d) factor polynomials completely. mathematical reasoning, connections, and representations to Factoring Polynomial Difference of squares Difference of cubes Sum of cubes Perfect square trinomial Factor polynomials by applying general patterns including difference of squares, sum and difference of cubes, and perfect square trinomials. Factor polynomials completely over the integers. Verify polynomial identities including the difference of squares, sum and difference of cubes, and perfect square trinomials Blooms = Evaluate 7

8 9/15-9/ AII.3 Complex Numbers The student will perform operations on complex numbers, express the results in simplest form using patterns of the powers of i, and identify field properties that are valid for the complex numbers. mathematical reasoning, connections, and representations to Recognize that the square root of 1 is represented as i. Determine which field properties apply to the complex number system. SOL 7.16 apply properties w/ real numbers: a) commutative and associative properties for add/mult; b) distrib property; c) add/mult identity properties; d) add/mult inverse properties; e) mult property of zero SOL 8.15 c) ID properties of operations used to solve equations Complex numbers Real numbers Imaginary numbers Pure imaginary numbers Rational numbers Irrational numbers Integers Whole numbers Natural numbers Conjugate Physics Finding the impedance of a series circuits 279 #95-96) Simplify radical expressions containing negative rational numbers and express in a+bi form. Simplify powers of i. Add, subtract, and multiply complex numbers. SOL A.2 perform operations on polynomials a) apply laws of exponents to perform ops on expressions; b) add/sub/ mult/div poly; Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole, and natural. Write a real number in a+bi form. Write a pure imaginary number in a+bi form. Blooms = Analyze 8

9 9/23-10/ AII.4b Quadratic Equations The student will 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. mathematical reasoning, connections, and representations to Solve a quadratic equation over the set of complex numbers using an appropriate strategy. Calculate the discriminant of a quadratic equation to determine the number of real and complex solutions. SOL 7.14 a) solve one and two step linear equations; b) solve practical problems in one variable SOL 8.15 a) solve multistep linear equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve SOL A.4 solve multistep linear/ quad equation (2 vars) c) solve quad equations (alg/graph); d) solve multistep linear equations (alg/graph) Roots Solutions Discriminant Factor Quadratic equation Standard form of a quadratic equation General form of a quadratic equation Completing the square Quadratic Formula Building Trades Area of a parking lot 261 #91) Fashion Design Quilting 261 #90) Urban Planning Landscaping 260 #22) Environmental Science Planning an ecology garden 262 #98) Apply an appropriate equation to solve a real-world problem. Recognize that the quadratic formula can be derived by applying the completion of squares to any quadratic equation in standard form. Blooms = Analyze Astronomy Height of a falling object 268 #71) Firefighting Horizontal and vertical water stream 298 #91) 9

10 10/7-10/ AII.6 Quadratic Functions AII.7a-d,f Graphing The student will recognize the general shape of (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of s. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these s. mathematical reasoning, connections, and representations to Recognize graphs of parent s. Given a transformation of a parent, identify the graph of the transformed. Given the equation and using a transformational approach, graph a. Given the graph of a, identify the parent. Given the graph of a, identify the transformations that map the preimage to the image in order to determine the equation of the image. Using a transformational approach, write the equation of a given its graph. SOL 7.12 represent relationships with tables, graphs, rules, and words SOL 7.15 a) solve one step inequalities; b) graph solutions on number line SOL 8.14 make connections between any two representations (tables, graphs, words, rules) SOL 8.15 b) solve two step linear inequalities and graph results on number line; c) ID properties of operations used to solve SOL 8.16 Graph linear equations in two variables SOL 8.17 ID domain, range, indep/dep variable SOL A.6 graph linear equations/linear inequal (2 vars) Quadratic Dilation Family of s Intercepts (x and y) Parent Reflection Transformation of graphs Translation (vertical and horizontal) Vertex Domain Range Zeroes of s x and y- intercepts End behavior Increasing intervals Decreasing intervals Axis of symmetry Parabola Physics Maximizing torque 254 #51) Sports Surface of football field 254 #52) Physiology Energy consumed while walking 254 #53) 10

11 The student will investigate and analyze s algebraically and graphically. Key concepts include a) domain and range, including limited and discontinuous domains and ranges; b) zeros; c) x- and y-intercepts; d) intervals in which a is increasing or decreasing; f) end behavior; Graphing calculators will be used as a tool to assist in investigation of s. mathematical reasoning, connections, and representations to Identify the domain, range, zeros, and intercepts of a presented algebraically or graphically. Given the graph of a, identify intervals on which the is increasing and decreasing. Describe the end behavior of a. Blooms = Analyze SOL A.7 investigate/analyze (linear/quad) families and characteristics (alg/graph) a) determine relation is ; b) domain/range; c) zeros; d) x and y-intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic) SOL AFDA.1 investigate/analyze (linear/quad/exp/log) families/characteristics a) continuity; b) local/abs max/min; c) domain/range; d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes SOL AFDA.2 use transformations to write equations, given graph of (linear/quad/exp/log) SOL AFDA.4 transfer between/analyze mult representations of s 11

12 Greene County Public Schools Algebra II Curriculum & Pacing Guide Quarter 2 October 20, 2014 December 19, 2014 Time/Dates SOL/Strand Objective/Content/Essential Questions/Cognitive Level 10/20-10/22 AII.9 Curve of Best Fit 2-5 The student will 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, exponential, and logarithmic s. mathematical reasoning, connections, and representations to Collect and analyze data. Investigate scatterplots to determine if patterns exist and then identify the patterns. Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, and logarithmic s. Make predictions, using data, scatterplots, or the equation of the curve of best fit. Given a set of data, determine the model that would best describe the data. Vertical Alignment SOL 7.11 a) construct/analyze histograms; b) compare/contrast histograms SOL 8.13 a) make comparisons/predictions/ inferences, using information displayed in graphs; b) construct/ analyze scatterplots SOL A.10 compare/contrast mult univ data sets with box andwhisker plots SOL A.11 collect/analyze data/determine equation of curve best fit to make predictions/solve real world problems, using models (linear/quad) SOL AFDA.3 collect data/generate equ for curve (linear/quad/ exp/log) of best fit/use best fit equ to interpolate values/make decisions/justify conclusions (alg/graph models) Vocabulary Scatter plot Curve of best fit Regression equation Linear regression Quadratic regression Positive correlation Negative correlation No correlation Correlation coefficient Cross-curricular Connections Earth Science Find the correlation coefficient for interval time between eruptions 104 #23) Business Use data to predict future business investments 103 #6-7) 12

13 Blooms = Evaluate 10/23-10/ AII.6 Polynomial Functions AII.7 Polynomial Functions AII.8 Solution/Zero/ X-intercept/ Factors The student will recognize the general shape of (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of s. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these s. mathematical reasoning, connections, and representations to Recognize graphs of parent s. Given a transformation of a parent, identify the graph of the transformed. Given the equation and using a transformational approach, graph a. Given the graph of a, identify the parent. Given the graph of a, identify the transformations that map the preimage to the image in order to determine the equation of the image. SOL 7.12 represent relationships with tables, graphs, rules, and words SOL 7.15 a) solve one step inequalities; b) graph solutions on number line SOL 8.14 make connections between any two representations (tables, graphs, words, rules) SOL 8.15 b) solve two step linear inequalities and graph results on number line; c) ID properties of operations used to solve SOL 8.16 Graph linear equations in two variables SOL 8.17 ID domain, range, indep/dep variable Polynomial Multiplicity Degree of Linear Quadratic Cubic Quartic Intercepts (x and y) Domain Range Zeroes of s End behavior Increasing intervals Decreasing intervals Solutions Roots Factors Nursing Nursing graduate population 335 #83-84) Science Waterfalls 317 #36) Architecture Arch of Sydney Harbor Bridge in Sydney, Australia 303 #13) 13

14 Using a transformational approach, write the equation of a given its graph. The student will investigate and analyze s algebraically and graphically. Key concepts include a) domain and range, including limited and discontinuous domains and ranges; b) zeros; c) x- and y-intercepts; d) intervals in which a is increasing or decreasing; f) end behavior; Graphing calculators will be used as a tool to assist in investigation of s. mathematical reasoning, connections, and representations to Identify the domain, range, zeros, and intercepts of a presented algebraically or graphically. Given the graph of a, identify intervals on which the is increasing and decreasing. Describe the end behavior of a. The student will investigate and describe the relationships among solutions of an equation, zeros of a, x-intercepts of a graph, and factors of a polynomial expression. SOL A.6 graph linear equations/linear inequal (2 vars) SOL A.7 investigate/analyze (linear/quad) families and characteristics (alg/graph) a) determine relation is ; b) domain/range; c) zeros; d) x and y- intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic) SOL AFDA.1 investigate/analyze (linear/quad/exp/log) families/characteristics a) continuity; b) local/abs max/min; c) domain/range; 14

15 mathematical reasoning, connections, and representations to Describe the relationships among solutions of an equation, zeros of a, x-intercepts of a graph, and factors of a polynomial expression. d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes SOL AFDA.2 use transformations to write equations, given graph of (linear/quad/exp/log) Define a polynomial, given its zeros. Determine a factored form of a polynomial expression from the x- intercepts of the graph of its corresponding. For a, identify zeros of multiplicity greater than 1 and describe the effect of those zeros on the graph of the. Given a polynomial equation, determine the number of real solutions and nonreal solutions. SOL AFDA.4 transfer between/analyze mult representations of s (alg formulas/graphs/tables/ words) Blooms = Analyze 15

16 10/31-11/ AII.1b,c Radical Expressions The student, 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; c) write radical expressions as expressions containing rational exponents and vice versa mathematical reasoning, connections, and representations to Convert from radical notation to exponential notation, and vice versa. Add and subtract radical expressions. SOL 7.13 b) evaluate algebraic expressions SOL 8.1 a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, properties; SOL 8.4 evaluate algebraic expressions using order of operations SOL A.1 represent verbal quantitative situations algebraically/evaluate expressions for given replacement values of variables Square root Cube root n th root indices radical radicand rational exponent Biology Comparing surface areas of lynx 411 example #9) Business Inflation rates 405 #64) Multiply and divide radical expressions not requiring rationalizing the denominators. Simplify radical expressions containing positive rational numbers and variables. Blooms = Apply 16

17 11/14-11/ AII.4d Radical Equations The student will solve, algebraically and graphically, d) equations containing radical expressions. Graphing calculators will be used for solving and for confirming the algebraic solutions. mathematical reasoning, connections, and representations to Solve an equation containing a radical expression algebraically and graphically. Verify possible solutions to an equation containing rational or radical expressions. Blooms = Evaluate SOL 7.14 a) solve one and two step linear equations; b) solve practical problems in one variable SOL 8.15 a) solve multistep linear equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve SOL A.4 solve multistep linear/quad equation (2 vars) a) solve literal equation; b) justify steps used in simplifying expressions and solving equations; c) solve quad equations (alg/graph); d) solve multistep linear equations (alg/graph); f) solve real world problems involving equations and systems of equations Extraneous roots Radical Solution Root Sports Minimum requirements for America s Cup 443 #68) Business Manufacturing plumb bobs 442 #66) Medicine Population of women doctors 442 #65) 17

18 11/20-12/2 7-3 AII.7h Composite Functions The student will investigate and analyze s algebraically and graphically. Key concepts include h) composition of multiple s. SOL A.7 e) find values of s for elements in domain Composition of s Personal Finance Sale price of clothing 419 #54-55) mathematical reasoning, connections, and representations to Find the composition of two s. Paleontology Relationship between height and footprint length of a dinosaur 419 #56) Use composition of s to verify two s are inverses. Blooms = Analyze 18

19 12/3-12/ AII.7g Inverse Functions The student will investigate and analyze s algebraically and graphically. Key concepts include g) inverse of a mathematical reasoning, connections, and representations to Find the inverse of a. Graph the inverse of a as a reflection across the line y = x. Blooms = Apply 19 SOL 7.12 represent relationships with tables, graphs, rules, and words SOL 8.14 make connections between any two representations (tables, graphs, words, rules) SOL 8.17 ID domain, range, indep/dep variable SOL A.7 investigate/analyze (linear/quad) families and characteristics (alg/graph) a) determine relation is ; b) domain/range; d) x and yintercepts; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic) SOL AFDA.1 investigate/analyze (linear/quad/exp/log) families/characteristics a) continuity; c) domain/ range; e) intercepts; h) asymptotes SOL AFDA.4 transfer between/analyze mult representations of s (alg formulas/ graphs/tables/words) Inverse of a Cube root Square root Physics Using Hooke s Law and inverse s 423 example #3) Astronomy Inverse model to find age of nebula as a of its volume 425 example #6) Business Using inverse of the to find the value of a US dollar in terms of Canadian dollars 427 #57) Science Using inverse to convert from Celsius to degree Fahrenheit 427 #58) Biology Using inverse to determine length of a hake fish 428 #61)

20 Greene County Public Schools Algebra II Curriculum & Pacing Guide Quarter 3 January 5, 2015 March 13, 2015 Time/Dates SOL/Strand Objective/Content/Essential Questions/Cognitive Level 1/5-1/8 AII.10 Variations 9-1 The student will identify, create, and solve real-world problems involving inverse variation, joint variation, and a combination of direct and inverse variations. mathematical reasoning, connections, and representations to Translate y varies jointly as x and z as y = kxz. Vertical Alignment SOL A.8 given real world context, analyze relation to determine direct/inverse variation/represent direct variation (alg/graph)/inverse variation (alg) Vocabulary Direct Variation Inverse Variation Joint Variation Proportional Constant of Variation Constant of Proportionality Cross-curricular Connections Physics Law of Universal Gravitation. ( 536, Example #6.) Astronomy Stars diameter vs luminosity. ( 538, #s 51-53) Translate y is directly proportional to x as y = kx. Translate y is inversely proportional to x as y = k x. Given a situation, determine the value of the constant of proportionality. Set up and solve problems, including real-world problems, involving inverse variation, joint variation, and a combination of direct and inverse variations. Blooms = Analyze 20

21 1/9-1/ AII.6 Rational Functions AII.7 Rational Functions The student will recognize the general shape of (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of s. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these s. mathematical reasoning, connections, and representations to Recognize graphs of parent s. Given a transformation of a parent, identify the graph of the transformed. Given the equation and using a transformational approach, graph a. SOL 7.12 represent relationships with tables, graphs, rules, and words SOL 7.15 a) solve one step inequalities; b) graph solutions on number line SOL 8.14 make connections between any two representations (tables, graphs, words, rules) SOL 8.15 b) solve two step linear inequalities and graph results on number line; c) ID properties of operations used to solve SOL 8.16 Graph linear equations in two variables Rational Intercepts (x and y Domain Range Zeroes of s End behavior Increasing intervals Decreasing intervals Multipicities Degree of Function Economics Laffer s Theory 544, #s 45 & 46) Physics Doppler Effect ( Page 545, #s 47 & 48) Earth Science Mean Temperature between given latitudes. 551, #40.) Physics Acceleration due to gravity of a falling object. 552, #s ) Given the graph of a, identify the parent. Given the graph of a, identify the transformations that map the preimage to the image in order to determine the equation of the image. SOL 8.17 ID domain, range, indep/dep variable SOL A.6 graph linear equations/linear inequal (2 vars) Using a transformational approach, write the equation of a given its graph. 21 SOL A.7 investigate/analyze (linear/quad) families and characteristics

22 The student will investigate and analyze s algebraically and graphically. Key concepts include a) domain and range, including limited and discontinuous domains and ranges; b) zeros; c) x- and y-intercepts; d) intervals in which a is increasing or decreasing; f) end behavior; Graphing calculators will be used as a tool to assist in investigation of s. mathematical reasoning, connections, and representations to Identify the domain, range, zeros, and intercepts of a presented algebraically or graphically. Given the graph of a, identify intervals on which the is increasing and decreasing. Describe the end behavior of a. Blooms = Analyze (alg/graph) a) determine relation is ; b) domain/range; c) zeros; d) x and y-intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic) SOL AFDA.1 investigate/analyze (linear/quad/exp/log) families/characteristics a) continuity; b) local/abs max/min; c) domain/range; d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes SOL AFDA.2 use transformations to write equations, given graph of (linear/quad/exp/log) SOL AFDA.4 transfer between/analyze mult representations of s 22

23 1/20-1/ AII.1a Rational Expressions The student, given rational, radical, or polynomial expressions, will a) add, subtract, multiply, divide, and simplify rational algebraic expressions; mathematical reasoning, connections, and representations to Add, subtract, multiply, and divide rational algebraic expressions. SOL 8.1 a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, properties. SOL A.1 represent verbal quantitative situations algebraically/evaluate expressions for given replacement values of variables Rational Expressions Complex Fractions Business Finance Monthly payment of a loan. 565, # 11.) Physics Resistance of parallel circuits. 567, #s 52 & 53.) Simplify a rational algebraic expression with common monomial or binomial factors. Recognize a complex algebraic fraction, and simplify it as a quotient or product of simple algebraic fractions. Blooms = Apply 23

24 1/28-1/ AII.4c Rational Equations The student will solve, algebraically and graphically, c) equations containing rational algebraic expressions; and SOL 7.14 a) solve one and two step linear equations; b) solve practical problems in one variable Rational Equation Restricted variable Extraneous Roots Nursing Drug Absorption Amount ( page 566, #s ) mathematical reasoning, connections, and representations to Solve equations containing rational algebraic expressions with monomial or binomial denominators algebraically and graphically. Verify possible solutions to an equation containing rational or radical expressions. Blooms = Evaluate SOL 8.15 a) solve multistep linear equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve SOL A.4 solve multistep linear/ quad equation (2 vars) a) solve literal equation; b) justify steps used in simplifying expresessions and solving equations; c) solve quad equations (alg/graph); d) solve multistep linear equations (alg/graph); f) solve realworld problems involving equations. 24

25 2/2-2/ AII.6 Exponential Logarithmic Functions AII.7 Exponential Logarithmic Functions The student will recognize the general shape of (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of s. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these s. mathematical reasoning, connections, and representations to Recognize graphs of parent s. Given a transformation of a parent, identify the graph of the transformed. Given the equation and using a transformational approach, graph a. Given the graph of a, identify the parent. SOL 7.12 represent relationships with tables, graphs, rules, and words SOL 7.15 a) solve one step inequalities; b) graph solutions on number line SOL 8.14 make connections between any two representations (tables, graphs, words, rules) SOL 8.15 b) solve two step linear inequalities and graph results on number line; c) ID properties of operations used to solve SOL 8.16 Graph linear equations in two variables SOL 8.17 ID domain, range, indep/dep variable Exponential Logarithmic Intercepts (x and y) Domain Range Zeroes of s End behavior Increasing intervals Decreasing intervals Asymptotes Inverse of Translation (vertical/horizontal) Biology Exponential Decay model for amount of air left in lungs. 479, # 56) Government Exponential Growth model for Federal Debt 470, #s 52-54) Physics Radioactive Decay 478, # 46) Chemistry ph of a solution 491, # 77) Earth Science Richter Scale 491, #s 79-80) 25

26 Given the graph of a, identify the transformations that map the preimage to the image in order to determine the equation of the image. SOL A.6 graph linear equations/linear inequal (2 vars) Using a transformational approach, write the equation of a given its graph. The student will investigate and analyze s algebraically and graphically. Key concepts include a) domain and range, including limited and discontinuous domains and ranges; b) zeros; c) x- and y-intercepts; d) intervals in which a is increasing or decreasing; e) asymptotes; f) end behavior; Graphing calculators will be used as a tool to assist in investigation of s. mathematical reasoning, connections, and representations to Identify the domain, range, zeros, and intercepts of a presented algebraically or graphically. SOL A.7 investigate/analyze (linear/quad) families and characteristics (alg/graph) a) determine relation is ; b) domain/range; c) zeros; d) x and y- intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic) SOL AFDA.1 investigate/analyze (linear/quad/exp/log) families/characteristics a) continuity; b) local/abs max/min; c) domain/range; d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes 26

27 Describe restricted/discontinuous domains and ranges. Given the graph of a, identify intervals on which the is increasing and decreasing. Find the equations of vertical and horizontal asymptotes of s. Describe the end behavior of a. Investigate exponential and logarithmic s, using the graphing calculator. Convert between logarithmic and exponential forms of an equation with bases consisting of natural numbers. Blooms = Analyze SOL AFDA.2 use transformations to write equations, given graph of (linear/quad/exp/log) SOL AFDA.4 transfer between/analyze mult representations of s 27

28 2/11-2/ AII.2 Sequences and Series The student will 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 n th term, and evaluating summation formulas. Notation will include and a n. mathematical reasoning, connections, and representations to Distinguish between a sequence and a series. Generalize patterns in a sequence using explicit and recursive formulas. SOL 7.2 describe/represent arithmetic/geometric sequences using variable expressions Arithmetic sequence Arithmetic series Common difference Geometric sequence Geometric series Common ratio Infinite Explicit formula Recursive formula Sigma notation Summation Carpentry Vertical supports for a roof 656, #s 65-66) Building Design vineyard design 662, # 6) Computer Science Binary search 671, #s 72-73) Use and interpret the notations, n, n th term, and a n. Given the formula, find a n (the n th term) for an arithmetic or a geometric sequence. Genealogy Family Trees 491, #s 79-80) Given formulas, write the first n terms and find the sum, S n, of the first n terms of an arithmetic or geometric series. Given the formula, find the sum of a convergent infinite series. Model real-world situations using sequences and series. Blooms = Analyze 28

29 2/25-3/ AII.12 Permutations and Combinations The student will compute and distinguish between permutations and combinations and use technology for applications. mathematical reasoning, connections, and representations to Compare and contrast permutations and combinations. Calculate the number of permutations of n objects taken r at a time. Calculate the number of combinations of n objects taken r at a time. Use permutations and combinations as counting techniques to solve realworld problems. SOL 7.9 investigate/describe the difference between the experimental/theoretical probability SOL 7.10 determine the probability of compound events, Basic Counting Principle SOL 8.12 determine probability of indep/dep events with and without replacement SOL AFDA.6 calculate probabilities a) conditional prob; b) dep/indep events; c) add/mult rules; d) counting techniques (permutations & combinations); Law of Large Numbers Permutation Combination Factorial Computer Science Passwords 706, #57) Drama Assigning roles to a play 706, #61) Science Probability of tree damage 728, #46) Blooms = Analyze 29

30 Greene County Public Schools Algebra II Curriculum & Pacing Guide Quarter 4 March 16, 2015 June 2, 2015 Time/Dates SOL/Strand Objective/Content/Essential Questions/Cognitive Level 3/16-3/20 AII.5 Non-Linear Systems 10-7 The student will solve nonlinear systems of equations, including linear-quadratic and quadraticquadratic, algebraically and graphically. Graphing calculators will be used as a tool to visualize graphs and predict the number of solutions. mathematical reasoning, connections, and representations to Predict the number of solutions to a nonlinear system of two equations. Solve a linear-quadratic system of two equations algebraically and graphically. Vertical Alignment SOL 7.15 a) solve one step inequalities; b) graph solutions on number line SOL 8.15 b) solve two step linear inequalities and graph results on number line; c) ID properties of operations used to solve SOL A.5 solve multistep linear inequ (2 vars) a) solve multistep linear inequal (alg/graph); b) justify steps used in solving inequal; c) solve real world problems involving inequal; d) solve systems of inequal Vocabulary Solution Root Nonlinear systems of equations Linear-quadratic system Quadratic-quadratic system Cross-curricular Connections Communications Range of radio station 636, #59) Earth Science Using a seismograph and system of equation to locate epicenter 634, example 4) Solve a quadratic-quadratic system of two equations algebraically and graphically. Blooms = Apply SOL AFDA.5 determine opt values in problem situations by identifying constraints/using linear programming techniques 30

31 3/23-4/ AII.11 Normal Distribution and Z-Scores The student will identify properties of a normal distribution and apply those properties to determine probabilities associated with areas under the standard normal curve. mathematical reasoning, connections, and representations to Identify the properties of a normal probability distribution. Describe how the standard deviation and the mean affect the graph of the normal distribution. Compare two sets of normally distributed data using a standard normal distribution and z-scores. SOL 5.16 a) describe mean/median/mode; b) describe mean as fair share; c) find the mean/median/mode/range; d) describe range as measure of variation SOL 6.15 a) describe mean as balance point; b) decide which measure of center is appropriate SOL A.9 given a set of data, interpret variation in realworld contexts/calculate/interpret mean absolute deviation/stand dev/zscores Normal distribution curve Mean Area under a curve Normal probability distribution Percentile Population Standard deviation Z-score Biology Heights of adult women 750, #44-46) Manufacturing Life expectancy of light bulb 750, #41-43) Business Wait time 750, #38-40) Represent probability as area under the curve of a standard normal probability distribution. Use the graphing calculator or a standard normal probability table to determine probabilities or percentiles based on z-scores. Blooms = Evaluate SOL AFDA.7 analyze norm distrib a) characteristics of normally distrib data; b) percentiles; c) normalizing data, using z scores; d) area under std norm curve/probability 31

32 4/13-4/17 AII.7a-f Graphing Functions Review The student will investigate and analyze s algebraically and graphically. Key concepts include a) domain and range, including limited and discontinuous domains and ranges; b) zeros; c) x- and y-intercepts; d) intervals in which a is increasing or decreasing; e) asymptotes; f) end behavior; Graphing calculators will be used as a tool to assist in investigation of s. mathematical reasoning, connections, and representations to Identify the domain, range, zeros, and intercepts of a presented algebraically or graphically. Describe restricted/discontinuous domains and ranges. Given the graph of a, identify intervals on which the is increasing and decreasing. SOL 7.12 represent relationships with tables, graphs, rules, and words SOL 8.14 make connections between any two representations (tables, graphs, words, rules) SOL 8.17 ID domain, range, indep/dep variable SOL A.7 investigate/analyze (linear/quad) families and characteristics (alg/graph) a) determine relation is ; b) domain/range; c) zeros; d) x and y- intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic) Parent Function Family of Functions Absolute value Quadratic Function Square Root Function Cubic Function Cube Root Function Radical Function Rational Function Exponential Function Logarithmic Function Transformation of Functions Dilation Refection Translation(vertical and horizontal) Vertex Domain Range Zeroes of s x and y-intercepts End behavior Increasing intervals Decreasing intervals Axis of symmetry Asymptote 32

33 Find the equations of vertical and horizontal asymptotes of s. Describe the end behavior of a. Investigate exponential and logarithmic s, using the graphing calculator. Blooms = Analyze SOL AFDA.1 investigate/analyze (linear/quad/exp/log) families/characteristics a) continuity; b) local/abs max/min; c) domain/range; d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes Discontinuity Continuous Discontinuous SOL AFDA.4 transfer between/analyze mult representations of s (alg formulas/graphs/tables/ words) 4/20-5/8 AII.1-AII.12 Review of all SOL concepts. 33