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Algebra 2 Curriculum & Pacing Guide Pacing Guide 1st Marking Period 2nd Marking Period I. Pretest I. Matrices (2 Weeks) II. Fundamentals of Algebra (2 Weeks) II. Quadratics (5 Weeks) III. Linear Functions (3 Weeks) III. 2nd Quarterly Exam IV. Systems (3 Weeks) V. 1st Quarterly Exam 3rd Marking Period 4th Marking Period I. Exponential & Logarithmic Functions (5 Weeks) I. Complete Rational Functions & Polynomials (Last 3 of 6 Weeks) II. Begin Rational Functions & Polynomials (First 3 of 6 Weeks) II. Radical Functions (4 Weeks) III. 3rd Quarterly Exam III. Probability & Data Analysis – Optional (2 Weeks) IV. 4th Quarterly (Final) Exam Fundamentals of Algebra (2 weeks) Why are functions and relations represented in multiple ways? How are functions and relations useful? How are patterns of change represented in functions? Students should be able to… Evaluate expressions using the Order of Operations Algebra 2 Adv: 1-1–1-4 Algebra 2 Coll: 1.1, 1.2 Solving equations & inequalities Algebra 2 Adv: 1-5, 1-6 Algebra 2 Coll: 1.3, 1.6 Identify domain & range, dependent & independent variables Algebra 2 Adv: 2-1–2-4 Algebra 2 Coll: 2.1 Apply the vertical line test Algebra 2 Adv: 2-5 Algebra 2 Coll: 2.1 Apply this discussion to real world problems Middletown Public Schools Grade-Level Expectations Instructional Strategies and Activities SAT Correlation or Real World Applications 2.2.a.1 Recognize vectors and matrices as systems that have some, but not all, of the properties of real numbers. 1.3.a.1 Model and solve problems with linear, quadratic and absolute value equations and linear inequalities. 1.1.a.3 Identify the characteristics of functions and relations, including domain and range. Scientific Method 1.1.a.3 Identify the characteristics of functions and relations, including domain and range. 1.1.a.2 Make and justify predictions based on patterns. 3.1.a.2 Test the validity of logical arguments. August 2010 2 Linear Functions (3 weeks) What makes a relationship linear? Why are linear functions useful? What are the different ways that rate-of-change (slope) can be used to represent various concepts? How do I generate a line of best fit from a given set of data? What different information is obtained from equivalent forms of algebraic equations? Students should be able to… Graph Equations & Inequalities Algebra 2 Adv: 1-7, 2-1, 22, 3-1, 3-2 Algebra 2 Coll: 2.2, 2.3, 2.6 Write the equation of a line given information Algebra 2 Adv: 3-3–3-5 Algebra 2 Coll: 2.4 Grade-Level Expectations 1.2.a.1 Represent functions and relations on the coordinate plane. 1.2.a.2 Recognize the effect of changes in parameters on the graphs of functions or relations. 1.1.a.2 Make and justify predictions based on patterns. Fit a trend line to a data set Algebra 2 Adv: Supplement Algebra 2 Coll: 2.5 1.1.a.2 Make and justify predictions based on patterns. Apply linear functions to real world problems 1.1.a.2 Make and justify predictions based on patterns. 3.1.a.2 Test the validity of logical arguments. Middletown Public Schools Instructional Strategies and Activities Linear Functions Mini-Poster http://www.teachforever.com/2008/1 2/project-idea-linear-functionsmini.html August 2010 SAT Correlation or Real World Applications Interpolation, Extrapolation, Predictions, Simple Interest, Fixed/Variable Cost, Stock Market 3 *Advanced Algebra 2 will teach the Systems Unit and Matrices Unit simultaneously.* Systems (3 weeks) How are systems of equations and inequalities useful? How does the solution to a system of inequalities relate to the solution to a system of equations? Which problem-solving strategy is most appropriate in each situation? Students should be able to… Grade-Level Expectations Instructional Strategies and Activities SAT Correlation or Real World Applications Solve a system of equations 1.3.a.3 Use logarithms, vectors and matrices Algebra 2 Adv: 4-1, 4-2, 4-6 to solve problems. Algebra 2 Coll:3.1, 3.2 Graph a systems of inequalities Algebra 2 Adv: 4-10 Algebra 2 Coll: 3.3 Apply solving systems of equations and graphing inequalities for Linear Programming Algebra 2 Adv: 4-11 Algebra 2 Coll: 3.4 Apply systems of equations and inequalities to real world problems Algebra 2 Adv: 3-5 Algebra 2 Coll: Middletown Public Schools 1.3.a.1 Determine equivalent representations of an algebraic equation or inequality to simplify and solve problems. Optimization, Profit Maximization, Resource Allocation, Statisticians, Accounting 1.1.a.6 Understand and use optimization strategies, including linear programming. 1.1.a.2 Make and justify predictions based on patterns. 3.1.a.2 Test the validity of logical arguments. Mixture Problems August 2010 4 Matrices (2 weeks) How can matrices help organize information and how do I manipulate them? Why are matrices useful in displaying data and solving problems? Students should be able to… Grade-Level Expectations Instructional Strategies and Activities 2.2.a.1 Select and use appropriate methods for computing to solve problems in a variety of contexts. 2.2.a.2 Solve problems involving scientific notation and absolute value. Use the determinant to solve 2.2.a.1 Select and use appropriate methods a system of equations for computing to solve problems in a (Cramer’s Rule) variety of contexts. Algebra 2 Adv: 4-3, 4-9 2.2.a.2 Solve problems involving scientific Algebra 2 Coll: 4.3 notation and absolute value. Solve systems with 32.2.a.1 Select and use appropriate methods Variables using Inverse for computing to solve problems in a Matrices variety of contexts. Algebra 2 Adv: 4-8 2.2.a.2 Solve problems involving scientific Algebra 2 Coll: 4.4 notation and absolute value. Apply systems of equations and matrices to real world 1.1.a.2 Make and justify predictions based on problems patterns. Algebra 2 Adv: 4-11 3.1.a.2 Test the validity of logical arguments. Algebra 2 Coll: 4.5 SAT Correlation or Real World Applications Perform matrix operations Algebra 2 Adv: 4-7 Algebra 2 Coll: 4.1, 4.2 Middletown Public Schools Data Entry, Computer Programming, Using Spreadsheets, Engineers, Astronomers, Marketing, Announcers, Statisticians August 2010 5 Quadratics & Complex Numbers (5 weeks) Which problem-solving strategy is most appropriate in each situation? How do quadratic relations model real-world problems and their solutions? Why are complex numbers important? How are real, imaginary, and complex numbers related? How can graphical and analytic methods be used to support each other in the solution of a problem? Students should be able to… Identify a quadratic function Algebra 2 Adv: 5-1, 5-2 Algebra 2 Coll: 5.1 Graph a quadratic function Algebra 2 Adv: 5-2 Algebra 2 Coll: 5.1 Solve a quadratic equation using the quadratic formula, by factoring, by graphing, and by completing the square Algebra 2 Adv: 5-3 Algebra 2 Coll: 5.2, 5.3, 5.5 Solve quadratic equations with imaginary solutions Algebra 2 Adv: 5-4, 10-2, 10-3 Algebra 2 Coll: 5.4, 5.6 Middletown Public Schools Grade-Level Expectations 1.1.a.1 Identify, describe, create and generalize numeric, geometric and statistical patterns with tables, graphs, words and symbolic rules. 1.1.a.1 Identify, describe, create and generalize numeric, geometric and statistical patterns with tables, graphs, words and symbolic rules. 1.2.a.1 Represent functions and relations on the coordinate plane. 1.2.a.2 Recognize the effect of changes in parameters on the graphs of functions or relations. 2.1.a.2 Select and use an appropriate form of number (integer, fraction, decimal, ratio, percent, exponential, scientific notation, irrational) to solve practical problems involving order, magnitude, measures, labels, locations and scales. 2.1. a.1 Compare, locate, label and order real numbers on number lines, scales, coordinate grids and measurement tools. 2.2.a.2 Perform operations with complex Instructional Strategies and Activities Basics of Quadratics Poster http://www.teachforever.com/2009/04/b asics-of-quadratic-functionsproject.html August 2010 SAT Correlation or Real World Applications Projectile Trajectories, Stopping Distance, Economics, Finance, Architecture 6 numbers, matrices, determinants and logarithms. Evaluate a quadratic expression Algebra 2 Adv: 5-5, 5-6 Algebra 2 Coll: 5.1 Apply quadratic equations and functions to real world problems Algebra 2 Adv: 5-7 Algebra 2 Coll: 5.8 Middletown Public Schools 1.3.a.1 Determine equivalent representations of an algebraic equation or inequality to simplify and solve problems. 1.1.a.2 Make and justify predictions based on patterns. 3.1.a.2 Test the validity of logical arguments. August 2010 7 Exponential Functions & Logarithmic Functions (5 weeks) How do exponential functions model real-world problems and their solutions? How are the properties of exponential and logarithmic functions used to evaluate functions and solve problems? Students should be able to … Simplify and apply the exponential properties Algebra 2 Adv: 6-1, 6-4, 6-10 Algebra 2 Coll: 6.1 Grade-Level Expectations Instructional Strategies and Activities 1.1.a.1 Describe and compare properties and classes of functions, including exponential, polynomial, rational, logarithmic and trigonometric. 2.1.a.2 Select and use an appropriate form of number (integer, fraction, decimal, ratio, percent, exponential, scientific notation, irrational, complex) to solve practical problems involving order, magnitude, measures, labels, locations and scales. Compound Interest, Population Growth, Exponential Decay, Richter Scale, Measuring pH, Measuring Sound (dB) 1.2.a.1 Relate the graphical representation of Graph exponential functions a function to its function family and Algebra 2 Adv: Supplement find equations, intercepts, maximum Algebra 2 Coll: 8.1, 8.2, 8.3 or minimum values, asymptotes and line of symmetry for that function. Evaluate an exponential 2.1.a.4 Judge the effects of computations expression with powers and roots on the Algebra 2 Adv: 6-5 magnitude of results Algebra 2 Coll: 8.1, 8.2, 8.3 Simplify and apply the 1.1.a.1 Describe and compare properties and logarithmic properties classes of functions, including Algebra 2 Adv: 6-8, 6-9 exponential, polynomial, rational, Algebra 2 Coll: 8.4, 8.5 logarithmic and trigonometric. Middletown Public Schools SAT Correlation or Real World Applications August 2010 8 Graph logarithmic functions Algebra 2 Adv: Supplement Algebra 2 Coll: 8.4 Solve exponential equations using logarithms Algebra 2 Adv: 6-9, 6-10 Algebra 2 Coll: 8.6 Simplify logarithmic expressions Algebra 2 Adv: 6-11 Algebra 2 Coll: 8.5 1.2.a.1 Relate the graphical representation of a function to its function family and find equations, intercepts, maximum or minimum values, asymptotes and line of symmetry for that function. 1.1.a.4 Solve problems involving financial applications including compound interest, amortization of loans, and investments. 1.3.a.3 Use logarithms, vectors and matrices to solve problems. 2.2.a.2 Perform operations with complex numbers, matrices, determinants and logarithms. 2.2.a.2 Perform operations with complex numbers, matrices, determinants and logarithms. 1.1.a..2 Analyze essential relations in a Apply exponential and problem to determine possible logarithmic equations to functions that could model the solve real world applications situation Algebra 2 Adv: 6-14 3.1.a.2 Test the validity of logical arguments. Algebra 2 Coll: 8.7 Middletown Public Schools Census Project August 2010 9 Rational Functions & Polynomials (6 weeks) How do polynomial functions model real-world problems and their solutions? How can the properties of fractions be extended to algebraic rational expressions? When do we solve for a variable and when do we leave it factored form? How are the zeros of the polynomial function, the factors of the polynomial, and the solution to the polynomial related? Students should be able to… Grade-Level Expectations Graph functions including asymptotes, discontinuities, and complex solutions Algebra 2 Adv: 7-1, 7-2, 10-3, 10-4 Algebra 2 Coll: 6.2, 9.2 1.1.a.7 Apply the concepts of limits to sequences and asymptotic behavior of functions. 1.2.a.1 Relate the graphical representation of a function to its function family and find equations, intercepts, maximum or minimum values, asymptotes and line of symmetry for that function. Factor polynomials Algebra 2 Adv: 7-3, 7-4 Algebra 2 Coll: 6.4, 6.5 2.2.a.2 Perform operations with complex numbers, matrices, determinants and logarithms. Divide polynomials using synthetic division Algebra 2 Adv: 7-5 Algebra 2 Coll: 6.5 Factor higher degree polynomials (factor theorem) Algebra 2 Adv: 7-6 Algebra 2 Coll: 6.4, 6.5 Find products and quotients of polynomials Algebra 2 Adv: 7-7 Algebra 2 Coll: 6.3 Middletown Public Schools Instructional Strategies and Activities SAT Correlation or Real World Applications http://www.parkridge.k12.nj.us/dcaine/T he%20Birthday%20Polynomial%20Proj ect.pdf Lifetime Cost of Appliances, Unit Conversions, Potential Energy, Cryptography, Robotics, Forestry 2.2.a.2 Perform operations with complex numbers, matrices, determinants and logarithms. 2.2.a.2 Perform operations with complex numbers, matrices, determinants and logarithms. 1.3.a.2 Combine, compose and invert functions 2.2.a.2 Perform operations with complex numbers, matrices, determinants and logarithms. August 2010 10 Find the sums and Differences of polynomials Algebra 2 Adv: 7-8 Algebra 2 Coll: 6.3 1.3.a.2 Combine, compose and invert functions 2.2.a.2 Perform operations with complex numbers, matrices, determinants and logarithms. Solve fractional equations (identify domain and extraneous solutions) Algebra 2 Adv: 7-9, 7-10 Algebra 2 Coll: 9.6 1.1.a.5 Solve problems involving direct and inverse variation Apply polynomial and fractional equations to solve real world applications Algebra 2 Adv: 7-11 Algebra 2 Coll: 6.9 Middletown Public Schools 1.1.a.2 Analyze essential relations in a problem to determine possible functions that could model the situation. 3.1.a.2 Analyze essential relations in a problem to determine possible functions that could model the situation. August 2010 11 Radical Functions (4 weeks) How do radical functions model real-world problems and their solutions? Students should be able to… Graph radical functions Algebra 2 Adv: 8-1, 8-2 Algebra 2 Coll: 7.5 Grade-Level Expectations Instructional Strategies and Activities 1.2.a.2 Relate the graphical representation of a function to its function family and find equations, intercepts, maximum or minimum values, asymptotes and line of symmetry for that function. Simplify radical expressions 2.1.a.4 Judge the effects of computations Algebra 2 Adv: 8-3 with powers and roots on the Algebra 2 Coll: 7.1, 7.2, 7.3 magnitude of results Solve radical equations Algebra 2 Adv: 8-4 Algebra 2 Coll: 7.4, 7.6 Apply radical equations to solve real world applications Algebra 2 Adv: 8-5 Algebra 2 Coll: Middletown Public Schools SAT Correlation or Real World Applications Astronomy, Engineering, Meteorology, Genetics, Radiology 2.1.a.4 Judge the effects of computations with powers and roots on the magnitude of results 1.1.a.2 Analyze essential relations in a problem to determine possible functions that could model the situation. 3.1.a.2 Test the validity of logical arguments. August 2010 12 Probability & Data Analysis (2 Weeks) – Optional, if time allows. How can probability be used to make wise decisions in life? Students should be able to… Define probability Algebra 2 Adv: 12-1, 12-2 Algebra 2 Coll: 12.1, 12.3 Apply combinations and permutations Algebra 2 Adv: 12-4, 12-5 Algebra 2 Coll: 12.1, 12.2 Apply the fundamental counting principles Algebra 2 Adv: 12-3 Algebra 2 Coll: 12.1 Apply Conditional probability Algebra 2 Adv: 12-5 Algebra 2 Coll: 12.5 Be able to find the probability of unions and intersections Algebra 2 Adv: 12-6 Algebra 2 Coll: 12.4 Apply Probability to solve real-world problems. Algebra 2 Adv: 12-7, 12-9 Algebra 2 Coll: Middletown Public Schools Grade-Level Expectations Instructional Strategies and Activities SAT Correlation or Real World Applications 4.2.a.1 Determine statistical measures to describe univariate data. 4.2.a.1 Determine statistical measures to describe univariate data. 4.3.a.1 Understand and use permutations, combinations, recursion and mathematical induction to solve problems. Predictions, Expected Value, Decision Making, Gambling 4.2.a.1 Determine statistical measures to describe univariate data. 4.2.a.1 Determine statistical measures to describe univariate data. 4.2.a.1 Determine statistical measures to describe univariate data. 4.2.a.1 Determine statistical measures to describe univariate data. August 2010 13 Middletown Public Schools August 2010 14