Absolute Value Inequalities (Advanced Only)

Transcription

1 Unit 1: Linear Functions and Inequalities Time Frame: 5 weeks August 16 to September 20, 2011 Unit Description This unit focuses on the development of concepts of functions that was begun in Algebra I and that are essential to mathematical growth. This unit explores absolute value expressions and graphs of absolute value functions, step functions, and piecewise functions. It reviews linear functions and inequalities Student Understandings A major goal in mathematics today is for student understanding of functions, being comfortable using numerical, symbolic, graphical, and verbal representations, and being able to choose the best representation to solve problems. In this unit, students review finding the equation of a line in the various forms while developing the concepts of piecewise linear functions, absolute value equations, inequalities, and other functions. Students state their solutions in five forms number lines or coordinate graphs, roster, set notation, interval notation, and absolute value notation. 9 th 8 9 th 11 9 th 11 9 th 11 Use order of operations to simplify or rewrite variable expressions (A- 1-H) (A-2-H) Use equivalent forms of equations and inequalities to solve real- life problems (A- 1- H) Use equivalent forms of equations and inequalities to solve real- life problems (A- 1- H) Use equivalent forms of equations and inequalities to solve real- life problems (A- 1- H) Order of Operations Can students simplify and solve equations using the order of operations? Solve Linear Equations Can students solve linear equations and apply to real world problems? Solve Inequalities Can students solve linear inequalities and apply to real world problems? Solving Absolute Value Equations Absolute Value Inequalities Can students solve absolute value equations and inequalities and state their solutions in five forms when appropriate number lines or coordinate graphs, roster, set notation containing compound sentences using and or or, interval notation using and, and absolute value notation? Sect. 1.1 Review Order of Operations Sect. 1.3 Solving Equations Review Test Sect. 1.5 Solving Inequalities Sect. 1.4 Solving Absolute Value Equations Absolute Value Inequalities (Advanced Only) Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 1 2 day

2 Unit 1: Linear Functions and Inequalities Time Frame: 5 weeks August 16 to September 20, th 11 Use equivalent forms of equations and inequalities to solve real- life problems (A- 1- H) 25 Apply the concept of a function and function notation to represent and evaluate functions (P-1- H)(P-5-H) 25 Apply the concept of a function and function notation to represent and evaluate functions (P-1- H)(P-5-H) 9 th 13 Translate between the characteristics defining a line (i.e., slope, intercepts, points) and both its equation and graph (A-2-H) (G-3-H) Compound inequalities Can students solve compound inequalities and apply to real world problems? Linear Functions Domain Range Can students state the difference between a function and a relation in graphical, symbolic, and numerical representations? Can students determine the graphs, domains, ranges, intercepts, and global characteristics of functions? Can students verbalize the real world meanings of these? Identifying Linear Functions Can students identify and graph linear equations? Slope Can students use translations, reflections, and dilations to graph new absolute value functions and step functions from parent functions? Review Test Sect. 1.6 Solve Compound Inequalities Sect. 2.1 Relations and Functions Unit 1: Act. 1 and Act 3 Sect. 2.2 Linear Equations Review Test Sect. 2.3 Slope intercept and point slope form Unit 1: Act 5 Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 2

3 Unit 1: Linear Functions and Inequalities Time Frame: 5 weeks August 16 to September 20, th 6 Write the equation of a line parallel or perpendicular to a given line through a specific point (A- 3- H) (G- 3- H) 10 Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A-4-H) 9 th 14 Graph and interpret linear inequalities in one or two variables and systems of linear inequalities (A-2- H) (A-4-H) Slope intercept form, parallel and perpendicular lines Can students write linear equations in slope intercept form? Can students write the equations for parallel and perpendicular lines? Linear Piecewise function Absolute Value Functions Greatest Integer Functions Can students extend their explanation of the slope of a line to special linear equations such as absolute value, piecewise linear functions, and greatest integer functions? Can students determine the graphs, domains, ranges, intercepts, and global characteristics of absolute value functions, step functions, and piecewise linear functions both by hand and by using technology? Can they verbalize the real world meaning of these? Graph linear and absolute inequalities Can students solve absolute value equations and inequalities and state their solutions in five forms when appropriate number lines or coordinate graphs, roster, set notation containing compound sentences using and or or, interval notation using and, and absolute value notation? Sect. 2.4 Writing equations of lines (omit midpoint and distance) Review Test Only identify these functions, find domain and range, at this we are not writing equations for these functions. Sect. 2.7 Graphing Inequalities Review Unit 1: Act. 7, Act. 10 Unit 8:Act. 10 BLM Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 3

4 Unit 1: Linear Functions and Inequalities Time Frame: 5 weeks August 16 to September 20, 2011 Test Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 4

5 Unit 2: Polynomial Equations and Inequalities Time Frame: 6 weeks September 21 to November 3, 2011 Unit Description This unit reviews simplifying radicals and the laws of exponents. It covers adding, subtracting, and multiplying polynomials. It develops the procedures for factoring polynomial expressions in order to solve polynomial equations. Following the basic operations with polynomials, this unit covers operations on functions, composite and inverse functions. Student Understandings Even in this day of calculator solutions, symbolically manipulating algebraic expressions is still an integral skill for students to advance to higher mathematics. However, these operations should be tied to real-world applications so students understand the relevance of the skills. Students need to understand the reasons for factoring a polynomial and determining the correct strategy to use. 10 th 1 9 th 2 Simplify and determine the value of radical expressions (N- 2- H) (N- 7- H) Evaluate and write numerical expressions involving integer exponents (N- 2- H) Also 11 th grade 2 Simplify radicals Simplify Radical expressions Add, subtract, multiply & divide radical expressions Can students simplify radicals and radical expressions? Can students perform basic operations involving radicals? Sect. 5.5 Roots of real numbers Sect. 5.6 Radical Expressions Regular: Rationalize denominator with square root only Honors Only: 1) Rationalize denominators for roots other than square root 2) Do conjugates Refer to Algebra I textbook section 11.2 for additional resources Quiz Review Laws of Exponents Sect 5.1 Monomials Unit 3: Simplifying, multiplying, and dividing Act.1 monomials BLM Can students use the rules of exponents to multiply monomials? 3 days 9 th 8 Use order of operations to simplify or rewrite variable expressions (A-1-H) (A-2- H) Review Test Add, subtract polynomials,distributive Sect. 5.2 Polynomials property, multiply polynomials, Pascal s Triangle Can students add and subtract polynomials and apply to geometric problems? Can students multiply polynomials and Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 1

6 Unit 2: Polynomial Equations and Inequalities Time Frame: 6 weeks September 21 to November 3, th 5 11 th th 25 Factor simple quadratic expressions including general trinomials, perfect squares, difference of two squares, and polynomials with common factors (A-2- H) Also 2,10,24,27 Apply the concept of a function and function notation to represent and evaluate functions (P-1- H)(P-5-H) Also 24 Apply the concept of a function and function notation to represent and evaluate functions (P-1- identify special products? Can students apply multiplication of polynomials and factoring to geometric problems? Can students expand a binomial using Pascal s Triangle? Review Test Factor by GCF, Grouping, formulas involving squares and cubes Can students factor expressions using the greatest common factor, and can they factor binomials containing the difference in two perfect squares and the sum and difference in two perfect cubes? Can students factor perfect square trinomials and general trinomials? Can students factor polynomials by grouping? Can students select the appropriate technique for factoring? Can students apply multiplication of polynomials and factoring to geometric problems? Add, subtract, multiply, and divide functions Composition of functions Can students find the composition of two functions and decompose a composition into two functions? Find the inverse and determine if two functions are inverses of each other Can students define one-to-one Sect. 5.4 Factor Polynomials Unit 2: Act 2 Refer to Algebra I textbook Chapter 9 can use practice problems from book and workbook Sect. 7.7 Operations on functions Composite functions 1 (this includes tests and quizzes throughout) Unit 1: 11 BLM Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 2 3 days Sect. 7.8 Inverse functions and relations Unit 1: Act 12 BLM

7 Unit 2: Polynomial Equations and Inequalities Time Frame: 6 weeks September 21 to November 3, 2011 H)(P-5-H) Also 24 correspondence, find the inverse of a relation, and determine if it is a function? Review Test Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 3

8 Unit 3: Radicals and the Complex Number System Time Frame: 2 weeks November 4 to November 18, 2011 Unit Description This unit expands on the 9 th and 10 th grade GLEs regarding simplification of radicals with numerical radicands to include adding, subtracting, multiplying, dividing, and simplifying radical expressions with variables in the radicand. Students learn to solve equations containing radicals. The unit also includes the development of the complex number system in order to solve equations with imaginary roots. Student Understandings Students will simplify radicals containing variables and will solve equations containing radicals. Students will understand the makeup of the complex number system by identifying and classifying each subgroup of numbers. Students will connect the factoring skills developed in Unit 2 to finding complex roots. They will realize the roles of imaginary and irrational numbers in mathematics and determine when to use decimal approximations versus exact solutions. Upon investigation of the graphs of equations containing radicals and polynomials with imaginary roots, students should continue to develop the concepts of zeroes, domain, and range and use these to explain real and imaginary solutions and extraneous roots. Pre requisite skill: Estimating radicals and identifying approximate vs. exact 2 Evaluate and perform basic operations on expressions containing rational exponents (N- 2- H) 2 Evaluate and perform basic operations on expressions containing rational exponents (N- 2- H) Also 4,6,7,16,24,28 28 Represent and solve problems involving the translation of functions in the coordinate plane (P-4-H) Also 1,6,7,24,25 1 Read, write, and perform basic operations on complex numbers (N- 1- H) (N- 5- H) Rational exponents Can students simplify complex radicals having various indices and variables in the radicand? Solve radical equations Extraneous Roots Can students solve equations containing radicals and model real-world applications as a radical equation? Can students explain extraneous roots with and without technology? Graph & analyze square root functions Sect 5.7 Rational Exponents Unit 4 Act 2 (page 2) Sect 5.8 Radical equations and inequalities *Solve equations only* Sect. 7.9 Square root functions and Inequalities Can students classify numbers in the Regular: only rationalize denominators with i, no Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 1 Unit 4: Act. 4 BLM Refer to section 11.3 in the Algebra I textbook Can students explain extraneous roots with and without technology? Review Test +, -, x, divide complex numbers Sect 5.9 Complex number Unit 4: Act. 7 BLM

9 Unit 3: Radicals and the Complex Number System Time Frame: 2 weeks November 4 to November 18, 2011 complex numbers system as rational, irrational, or imaginary? Can students simplify expressions containing complex numbers? Can students simplify a complex rational expression? Can students solve equations containing imaginary solutions? conjugates Act 2 (page 1) Quiz Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 2

10 Unit 4: Quadratic Functions Time Frame: 7 weeks November 28, 2011 to February 3, 2012 Unit Description This unit covers solving quadratic equations and inequalities by graphing, factoring, using the Quadratic Formula, and modeling quadratic equations in real-world situations. Graphs of quadratic functions are explored with and without technology, using symbolic equations as well as using data plots. Student Understandings Students will understand the progression of their learning in Algebra II. They studied first-degree polynomials (lines) in Unit 1, and factored to find rational roots of higher order polynomials in Units 2, and were introduced to irrational and imaginary roots in Unit 3. Now they can solve real-world application problems that are best modeled with quadratic equations and higher order polynomials, alternating from equation to graph and graph to equation. They will understand the relevance of the zeroes, domain, range, and maximum/minimum values of the graph as it relates to the real-world situation they are analyzing. Students will distinguish between root of an equation and zero of a function, and they will learn why it is important to find the zeroes of an equation using the most appropriate method. They will also understand how imaginary and irrational roots affect the graphs of polynomial functions. 4 Translate and show the relationships among non-linear graphs, related tables of values, and algebraic symbolic representations (A-1-H) Also 6-10,19,24, Analyze functions based on zeros, asymptotes, and local and global characteristics of the function (A- 3- H) Also 9,10,24,28,29 Graphing functions, max & min of quadratic functions Can students graph a quadratic equation and find the zeroes, vertex, global characteristics, domain, and range with technology? Can students graph a quadratic function in standard form without technology? Can students determine the effects on the graph of factoring out a greatest common constant factor? Can students predict the end-behavior of a polynomial based on the degree and sign of the leading coefficient? Solve or estimate solutions of quadratic equations by graphing Curve of best fit Can students determine if a table of data is best modeled by a linear, quadratic, or higher order polynomial function and find the equation? Can students draw scatter plots using realworld data and create the quadratic Sect. 6.1 Graphing quadratic functions Unit 2: Act. 7 BLM (Page 1) Unit 5: Act 1 Sect. 6.2 Solving Quadratic Equations by graphing Unit 5: Act 7 Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 1

11 Unit 4: Quadratic Functions Time Frame: 7 weeks November 28, 2011 to February 3, 2012 regression equations using calculators? Review Review 9 Solve quadratic equations by factoring, completing the square, using the quadratic formula, and graphing (A- 4- H) Also 5, 6, 9, 24, 29 9 Solve quadratic equations by factoring, completing the square, using the quadratic formula, and graphing (A- 4- H) Also 9, 24 9 Solve quadratic equations by factoring, completing the square, using the quadratic formula, and graphing (A- 4- H) Also 9, 24, 29 Zero product property Sect 6.3 Solving quadratic equations by factoring Unit 4: Act. 2 BLM Can students factor in order to solve polynomial equations using the Zero Product Property? Can students relate factoring a polynomial to the zeroes of the graph of a polynomial? Test Completing the square Sect. 6.4 Completing the Square 3 days Can students complete the square to solve a quadratic equation? Quiz Quadratic formula (include imaginary Sect 6.5 Quadratic formula and discriminant 3 days solutions) Discriminant Can students solve a quadratic equation by factoring and using the Quadratic Formula? Can students solve equations containing imaginary solutions? Quiz Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 2

12 Unit 4: Quadratic Functions Time Frame: 7 weeks November 28, 2011 to February 3, Analyze functions based on zeros, asymptotes, and local and global characteristics of the function (A-3-H) Also 4, 7, 8, 10, 19, 20, 24, 29 6 Analyze functions based on zeros, asymptotes, and local and global characteristics of the function (A-3-H) 5 Factor simple quadratic expressions including general trinomials, perfect squares, difference of two squares, and polynomials with common factors (A-2-H) Also 6 5 Factor simple quadratic expressions including general trinomials, perfect squares, difference of two squares, and polynomials with common factors (A- 2- H) Also 6 Graphing quadratic functions Can students determine if a table of data is best modeled by a linear, quadratic, or higher order polynomial function and find the equation? Can students determine the effects on the graph of factoring out a greatest common constant factor? Can students solve quadratic inequalities algebraically and graphing? Long division, synthetic division Sect. 6.6 Analyzing Graphs of Quadratic functions Unit 5: Act. 7 BLM The Changing Parabola Worksheet Transform APP on graphing calculator 3 days Review Test Graphing quadratic inequalities Sect. 6.7 Graphing and solving quadratic Unit 5: Act. 10 BLM inequalities Optional Can students use synthetic division to evaluate a polynomial for a given value and show that a given binomial is a factor of a given polynomial? Can students determine the possible rational roots of a polynomial and use these and synthetic division to find the irrational roots? Synthetic division Can students use synthetic division to evaluate a polynomial for a given value and show that a given binomial is a factor of a given polynomial? Can students determine the possible rational roots of a polynomial and use these and synthetic division to find the irrational roots? Sect. 5.3 Dividing polynomials Optional for Regular Sect 7.4 The remainder and factor theorem Optional for Regular Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 3 Unit 5: Act. 7 BLM Unit 5: Act 12 Test 6 Analyze functions based on Number and type of roots Sect. 7.5 Roots and zeros Unit 5: Act. 13 BLM

13 Unit 4: Quadratic Functions Time Frame: 7 weeks November 28, 2011 to February 3, 2012 zeros, asymptotes, and local and global characteristics of the function (A-3-H) Also 1,4,25 20 Interpret and explain, with the use of technology, the regression coefficient and the correlation coefficient for a set of data (D- 2- H) Also 4, 10, 20, 21, 24, 28, 29 Discriminant Can students determine the number and nature of roots using the discriminant? Can students explain the difference in a root of an equation and zero of the function? Can students look at the graph of a quadratic equation and determine the nature and type of roots? Word problems Quadratic Regressions Unit 2: Act. 7 ( s 4-7) Unit 5: Act days Can students draw scatter plots using realworld data and create the quadratic regression equations using calculators? Review Test Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 4

14 Unit 5: Rational Equations and Inequalities Time Frame: 3 weeks February 6 to February 29, 2012 Unit Description The study of rational equations reinforces the students abilities to multiply polynomials and factor algebraic expressions. This unit develops the process for simplifying rational expressions, adding, multiplying, and dividing rational expressions, and solving rational equations and inequalities. Student Understandings Students symbolically manipulate rational expressions in order to solve rational equations. They determine the domain restrictions that drive the solutions of rational functions. They relate the domain restrictions to vertical asymptotes on a graph of the rational function but realize that the calculator does not give an easily readable graph of rational functions. Students also solve application problems involving rational functions. 10 Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A- 4- H) Also 5 10 Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A- 4- H) Also 5 10 Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A-4-H) Also 4,5,6,9 Simplifying, multiplying, dividing rational expressions, complex fractions Can students add, subtract, multiply, and divide rational expressions? Can students simplify a complex rational expression? LCD and add, subtract rational expressions Can students add, subtract, multiply, and divide rational expressions? Sect 9.1 Multiplying and dividing rational expressions Unit 3: Act 1 Sect 9.2 Adding and subtracting rational expressions Optional for Regular Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 1 Unit 3: Act. 3 BLM Review Test Solving rational equations and Sect 9.6 Solving rational equations and inequalities Unit 3: Act. 6,7,9 BLM inequalities, Least common denominator Inequalities optional for Regular 3 days Extraneous roots Can students solve rational equations? Can students solve rational inequalities? Can students solve real world problems involving rational functions? Can students simplify rational expressions in order to solve rational equations? Can students explain extraneous roots with

15 Unit 5: Rational Equations and Inequalities Time Frame: 3 weeks February 6 to February 29, 2012 and without technology? 10 Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A- 4- H) Also 4, 5, 6, 9 10 Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A- 4- H) Also 4, 5, 6, 9, 24, 29 Review Test Graphing Rational Functions Sect 9.3 Graph Rational Functions Asymptotes Can students identify the domain and vertical asymptotes of rational functions? Real world problems with rational functions Can students solve real world problems involving rational functions? Review Test Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 2

16 Unit 6: Exponential and Logarithmic Functions Time Frame: 4 weeks March 1 to March 28, 2012 Unit Description In this unit, students explore exponential and logarithmic functions, their graphs, and applications. Student Understandings Students solve exponential and logarithmic equations and graph exponential and logarithmic functions by hand and by using technology. They will compare the speed at which the exponential function increases to that of linear or polynomial functions and determine which type of function best models data. They will comprehend the meaning of a logarithm of a number and know when to use logarithms to solve exponential functions. Students will recognize the inverse relationship between exponential and logarithmic functions. 10 Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A-4-H) Also 2,3,4 3 Describe the relationship between exponential and logarithmic equations (N-2-H) Also 2,4,6,7,8,10,19,25,28 10 Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A-4-H) Also 2, 3 graph exponential function, solve exponential equations Can students solve exponential equations with variables in the exponents and having a common base? Can students solve exponential equations not having the same base by using logarithms with and without technology? Can students graph and transform exponential functions? exponential and logarithmic functions graph Sect Exponential functions Use graphing calculator to find exponential and log function of best fit Unit 6: Act. 2, 3 BLM Extra Research Project Unit 6: Act 4 Sect Logarithms and logarithmic functions Unit 6: Act. 7 Can student write exponential functions in logarithmic form and vice versa? Can students graph and transform logarithmic functions? Review Test simplify and evaluate expressions Sect Properties of logarithmic functions 3 days Can students use the properties of logarithms to solve equations that contain logarithms? Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 1 3 day 2 day

17 Unit 6: Exponential and Logarithmic Functions Time Frame: 4 weeks March 1 to March 28, Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A-4-H) Also 2,3 10 Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A-4-H) Also 2,3,27 10 Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A-4-H) Also 2-4,8,19,24,29 Review Test change of base formula Sect Common logarithms. Can students solve common logarithms and use the change of base formula? evaluate expressions, solve exponential equations using natural log. Can students find natural logarithms and anti-natural logarithms? Sect Base and natural log Review Test use logarithms to solve problems Sect Exponential growth and decay Unit 6: Act. 10 involving exponential growth and If time permits decay Can students use logarithms to solve problems involving exponential growth and decay? Unit 6: Act 13 Research Project 3 days Test or alternate assessment Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 2

18 Unit 7: Advanced Functions and Higher Order Functions Time Frame: 4 weeks March 29 to April 26, 2012 Unit Description This unit ties together all the functions studied throughout the year. It categorizes them, graphs them, translates them, and models data with them Student Understandings The students will demonstrate how the rules affecting change of degree, coefficient, and constants apply to all functions. They will be able to quickly graph the basic functions and make connections between the graphical representation of a function and the mathematical description of change. They will be able to translate easily among the equation of a function, its graph, its verbal representation, and its numerical representation. 7 Explain, using technology, how the graph of a function is affected by change of degree, coefficient, and constants in polynomial, rational, radical, exponential, and logarithmic functions (A- 3- H) Also 6, 8, 10, 27, 29 Definition Degrees and leading coefficients End behavior Can students relate multiplicity to the effects on the graph of a polynomial? Can students predict the end-behavior of a polynomial based on the degree and sign of the leading coefficient? Can students sketch a graph of a polynomial in factored form using end behavior and zeroes? Sect 7.1 Polynomial Functions From Unit 2 of the LA CC Unit 2 Act 7 graphing polynomial equations Act 9 graphing polynomial inequalities Advanced Math Textbook Section 3.2 p.195 Section 3.3 p Explain, using technology, how the graph of a function is affected by change of degree, coefficient, and constants in polynomial, rational, radical, exponential, and logarithmic functions (A- 3- H) Also 6, 8, 10, 27, 29 Graph Locate zeroes Max and min Can students relate multiplicity to the effects on the graph of a polynomial? Can students predict the end-behavior of a polynomial based on the degree and sign of the leading coefficient? Can students sketch a graph of a polynomial in factored form using end behavior and zeroes? Sect 7.2 Graphing Polynomial Functions (incorporate extra resources such as the Advanced Math Textbook and Statistics Textbook) From Unit 2 of the LA CC Unit 2 Act 7 graphing polynomial equations Act 9 graphing polynomial inequalities Advanced Math Textbook Section 3.2 p.195 Section 3.3 p.201 Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 1

19 Unit 7: Advanced Functions and Higher Order Functions Time Frame: 4 weeks March 29 to April 26, Explain, using technology, how the graph of a function is affected by change of degree, coefficient, and constants in polynomial, rational, radical, exponential, and logarithmic functions (A- 3- H) Also 6, 8, 10, 27, 29 Can students relate multiplicity to the effects on the graph of a polynomial? Can students predict the end-behavior of a polynomial based on the degree and sign of the leading coefficient? Can students sketch a graph of a polynomial in factored form using end behavior and zeroes? Sect 7.3 Solving Equations Using Quadratic Techniques (incorporate extra resources such as the Advanced Math Textbook and Statistics Textbook) From Unit 2 of the LA CC Unit 2 Act 7 graphing polynomial equations Act 9 graphing polynomial inequalities Advanced Math Textbook Section 3.2 p.195 Section 3.3 p Explain, using technology, how the graph of a function is affected by change of degree, coefficient, and constants in polynomial, rational, radical, exponential, and logarithmic functions (A- 3- H) Also 6, 8, 10, 27, 29 Number and types of roots Finding the zeros Use the zeros to write the polynomial Can students relate multiplicity to the effects on the graph of a polynomial? Sect 7.5 Roots and Zeros (incorporate extra resources such as the Advanced Math Textbook and Statistics Textbook) From Unit 2 of the LA CC Unit 2 Act 7 graphing polynomial equations Act 9 graphing polynomial inequalities Unit 5: Act 13 and 15 Advanced Math Textbook Section 3.2 p.195 Section 3.3 p.201 (incorporate extra resources such as the Advanced Math Textbook and Statistics Textbook) Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 2

20 Unit 7: Advanced Functions and Higher Order Functions Time Frame: 4 weeks March 29 to April 26, Explain, using technology, how the graph of a function is affected by change of degree, coefficient, and constants in polynomial, rational, radical, exponential, and logarithmic functions (A- 3- H) Also 6, 8, 10, 27, 29 Can students relate multiplicity to the effects on the graph of a polynomial? Can students predict the end-behavior of a polynomial based on the degree and sign of the leading coefficient? Can students sketch a graph of a polynomial in factored form using end behavior and zeroes? Sect 7.6 Rational Zero Theorem (optional) From Unit 2 of the LA CC Unit 2 Act 7 graphing polynomial equations Act 9 graphing polynomial inequalities Unit 5: Act 14 Advanced Math Textbook Section 3.2 p.195 Section 3.3 p Explain, using technology, how the graph of a function is affected by change of degree, coefficient, and constants in polynomial, rational, radical, exponential, and logarithmic functions (A- 3- H) Also 6, 8, 10, 27, 29 Polynomial inequalities Quadratic inequalities Sign chart Can students solve polynomial inequalities by the factor/sign chart method? Can students solve polynomial inequalities by examining the graph of a polynomial using technology? Can students determine if a table of data is best modeled by a linear, quadratic, or higher order polynomial function and find the equation? Can students draw scatter plots using real-world data and create the quadratic regression equations using calculators? Can students solve quadratic inequalities using a sign chart and a graph? Can students graph a higher order polynomial with real zeroes? Refer to Unit 6 blackline masters (incorporate extra resources such as the Advanced Math Textbook and Statistics Textbook) 24 Model a given set of real- life Exponential Regression equation From Unit 6 of the LA CC Unit 6: Act 3 Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 3

21 Unit 7: Advanced Functions and Higher Order Functions Time Frame: 4 weeks March 29 to April 26, 2012 data with a non- linear function (P- 1- H) (P- 5- H) Also 4, 10, 19, 29 8 Categorize non-linear graphs and their equations as quadratic, cubic, exponential, logarithmic, step function, rational, trigonometric, or absolute value (A-3-H)(P-5-H) Also 4,6,25,27 Can students look at a table of data and determine what type of function best models that data and create the regression equation? identify graphs and equations as different types of functions piecewise functions transformation graphing Can students determine the domains, ranges, zeroes, asymptotes, and global characteristics of these functions? Can students use translations, reflections, and dilations to graph new functions from parent functions? Can students determine domain and range changes for translated and dilated abstract functions? Can students graph piecewise defined functions, which are composed of several types of functions? Can students identify the symmetry of these functions and define even and odd functions? Can students analyze a set of data and match the data set to the best function graph? Can students quickly graph lines, power functions, radicals, logarithmic, exponential, step, rational, and absolute value functions? Can students determine the intervals on which a function is continuous, increasing, decreasing, or constant? (incorporate extra resources such as the Advanced Math Textbook and Statistics Textbook) REFER to Unit 7 blackline masters of the LA CC for better understanding of content (incorporate extra resources such as the Advanced Math Textbook) Sect. 9.5 Classes of Functions Statistics Book Section 4.1, 4.2 (refer to tech note) Unit 7: Act 2 BLM Act 3 BLM (1 st page) Act 7 and 8 Unit 1 Act 7 graphing absolute value functions Act 10 greatest integer discovery worksheet Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 4

22 Unit 8: Conic Sections Time Frame: Focus lessons May 2 to May 18, 2012 Unit Description This unit focuses on the analysis and synthesis of graphs and equations of conic sections and their real-world applications. Student Understandings The study of conics helps students relate the cross- curriculum concepts of art and architecture to math. They define parabolas, circles, ellipses, and hyperbolas in terms of the distance of points from the foci and describe the relationship of the plane and the double- napped cone that forms each conic. Students identify various conic sections in real- life examples and in symbolic equations. Students solve systems of conic and linear equations with and without technology. 10 th 16 Represent and solve problems involving distance on a number line or in the plane (G-3-H) Midpoint and distance Can students use the distance formula to define and generate the equation of each conic? Sect. 8.1 Midpoint and Distance Formulas 15 Identify conic sections, including the degenerate conics, and describe the relationship of the plane and double-napped cone that forms each conic (G-1-H) Also 5, 6, 9, 16, 24, 27, 28 Write equations and identify equations Can students transform the standard form of the equations of parabolas, circles, ellipses, and hyperbolas to graphing form? Can students identify the major parts of each of the conics from their graphing equations and can they graph the conics? Can students formulate the equations of each of these conics from their graphs? Can students find real-life examples of these conics, determine their equations, and use the equations to solve real-life problems? Can students identify these conics given their stand and graphing equations? Can the students predict how the graphs will be transformed when certain parameters are changed? Quiz Sect. 8.2 Parabolas Review/optional Sect. 8.3 Circles Sect. 8.4 Ellipses Sect. 8.5 Hyperbolas Sect. 8.6 Conic Sections Review Test Unit 8:Activitits 2, 3, 4 BLM Unit 8 Act 10 6 days Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high of test items on state assessment; mastery in current year 1