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PLEASANT VALLEY SCHOOL DISTRICT PLANNED COURSE CURRICULUM GUIDE Algebra II Grade 10 - 11 I. COURSE DESCRIPTION AND INTENT: Algebra II is primarily an extension of Algebra I. However, a more rigorous approach is taken in the study of the real number system. The first part of the course involves real number concepts and skills, the solution of linear equations and inequalities, solving verbal problems, properties of polynomials, and rational expressions. The second part of the course deals with relations and functions, irrational numbers and quadratic relations. Students must have successfully completed Algebra I. *Note: All students enrolled in this course are required to take the Keystone Exam. Note: The course can be taken to meet the school and state requirement as one of three mathematics credits necessary for graduation. Enrollment in this course is not limited to sophomores. To the reader: The topics of this course are grouped according to Algebraic Structure, they do not necessarily appear in sequential order. II. INSTRUCTIONAL TIME: Class Periods: Six (6) per six (6) day cycle Length of Class Periods (minutes): 56 Length of Course: 180 days Unit of Credit: 1.0 May 2012 COURSE: Algebra II STRAND: 2.2B Algebraic Concepts GRADE(S): 10-11 TIME FRAME: full year (180 days) PA CORE STANDARDS CC2.2.HS.D.4 - Understanding the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. CC.2.2.HS.D.7 – Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 – Apply inverse operations to solve equations or formulas for a given variable. ASSESSMENT ANCHORS A2.1.3 A2.2.2 RESOURCES McDougal Little Algebra II Houghton Mifflin Algebra II Glencoe Algebra II Prentice Hall Algebra II Resource packets Teacher designed materials Algebra With Pizzazz OBJECTIVES The learner will identify families of functions; solve equations of all types, and graph linear and absolute value functions. ESSENTIAL CONTENT Simplify/evaluate expressions containing zero and negative exponents, roots and/or absolute value. Write, solve, and/or apply a linear equation. Distinguish between a relation and a function. Identify the domain, range, or inverse of a relation. Evaluate a function f(x). Find the slope of a linear equation. Identify a linear equation in different forms. Write and/or graph a linear equation or inequality in different forms using two variables. Determine perpendicularity/parallelism given two lines. Solve problems using direct or inverse proportions. Match the graph of a function to its table or equation. Identify, write and/or graph an absolute value equation. INSTRUCTIONAL STRATEGIES Diagnostic Test of Algebra I skills. I have….who has? Game to reinforce skills of translating English expressions into mathematical phrases. Students make up word problems to fit given algebraic expressions. Use guided practice activity to help develop logical reasons to complete proofs. SAT problems Inner/Outer circle Jigsaw Keystone Type Problems ASSESSMENTS Teacher designed tests and quizzes Activities which demonstrate knowledge of the concepts taught Worksheets designed to demonstrate knowledge of the concepts taught Portfolio assessment Group assessment CORRECTIVES/EXTENSIONS Correctives: Utilize text generated reteaching worksheets Group work to reteach concepts Extensions: Utilize text generated enrichment worksheets Student generated worksheets COURSE: Algebra II STRAND: 2.2C Algebraic concepts GRADE(S): 10-11 TIME FRAME: full year (180 days) PA CORE STANDARDS CC2.2.HS.D.4 - Understanding the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. CC.2.2.HS.D.7 - Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 - Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.C.2 – Graph and analyze functions and use their properties to make connections between the different representations. ASSESSMENT ANCHORS A2.1.3 A2.2.2 A2.1.2 RESOURCES McDougal Little Algebra II Houghton Mifflin Algebra II Glencoe Algebra II Prentice Hall Algebra II Resource packets Teacher designed materials Algebra With Pizzazz OBJECTIVES The learner will solve and/or graph a linear system or quadratic-type equation. The learner will simplify, solve, and graph exponential and logarithmic expressions and equations. ESSENTIAL CONTENT Solve systems of equations containing three variables. Identify a quadratic function and the parts thereof. Graph a quadratic equation in both standard and vertex forms Find the vertex of a parabola. Find the greatest common factor for sets of monomials. Use the methods of arithmetic and Algebra I (GCF, special products, and grouping terms) to factor polynomials. Solve quadratic equations by factoring, completing the square, or using the quadratic formula. Apply the operations of arithmetic (addition, subtraction, multiplication, and division) to rational expressions. Identify and graph complex numbers. Add, subtract, and multiply complex numbers. Solve related word problems. Tell the nature of the roots of a quadratic equation from the value of the discriminant. Restate the laws of exponents to include all real numbers. Define a logarithmic function including natural logarithms. Express a logarithmic function in terms of its corresponding exponential function. Graph exponential and logarithmic functions. Use the three basic laws of logarithms to solve logarithmic equations, and simplify logarithmic expressions. Evaluate products, quotients and powers using logarithms. INSTRUCTIONAL STRATEGIES Have students create a pattern, which can be translated into an algebraic sentence. Use an equal arm balance to illustrate the need to keep both sides of an equation balanced. Use Algebra with Pizzazz puzzles. Use Accent on Algebra from Creative Publications for reinforcement of fundamentals. Use graph Gallery for pictorial renderings of graphing equations with two variables. Use geometric models to illustrate completing the square. Use the TI81 and TI82 Calculator either as a demonstration tool or as a hands-on student activity. Use computer center lab with appropriate software. Use "Inner/Outer" Circle. Use Jigsaw Activity. SAT Problems. ASSESSMENTS Teacher designed tests and quizzes Activities which demonstrate knowledge of the concepts taught Worksheets designed to demonstrate knowledge of the concepts taught Portfolio assessment Group assessment CORRECTIVES/EXTENSIONS Correctives: Utilize text generated reteaching worksheets. Additional worksheets on solving open sentences. Group work to reteach concepts. Extensions: Student generated worksheet. Utilize text generated enrichment worksheets. Student generated word problems. COURSE: Algebra II STRAND: 2.2A Algebraic Concepts GRADE(S): 10-11 TIME FRAME: full year (180 days) PA CORE STANDARDS CC2.2.HS.C.1 – Use the concept and notation of functions to interpret and apply them in terms of their context. CC2.2.HS.D.3 – Extend the knowledge of arithmetic operations and apply to polynomials. CC2.2.HS.D.5 – Use polynomial identities to solve problems. ASSESSMENT ANCHORS A2.2.2 RESOURCES McDougal Little Algebra II Houghton Mifflin Algebra II Glencoe Algebra II Prentice Hall Algebra II Resource packets Teacher designed materials Algebra With Pizzazz OBJECTIVES The learner will define and identify polynomial functions, find linear factors of polynomials, divide polynomials, and learn to solve polynomial equations. ESSENTIAL CONTENT Classify polynomials by degree and by the number of terms. Add, subtract, and multiply polynomials. Factor higher order polynomials using the GCF and various factoring techniques such as the difference of squares pattern. Find the rational roots of equations in the form ax^3+bx^2+cx+d=0. Use long or synthetic division to divide a polynomial by another polynomial. Use the remainder, factor, irrational root, and imaginary root theorems to factor and solve polynomial equations. Use Descartes Rule of Signs to determine the number and nature of the roots of a polynomial. Write polynomial functions with integral coefficients given their zeros. Use the graphs of polynomial functions to approximate the zeros of the function. INSTRUCTIONAL STRATEGIES Use string, pencil, tacks, and paper to stretch ellipses. Measure the Focal Radii to verify the definition of an ellipse. Using an inclined plane, carbon paper, paper and a small metal ball create a parabola. Use various paper folding techniques to create any or all of the conic sections -- Max Sobel's book, Teaching Mathematics. SAT problems. Inner/Outer Circle. Jigsaw. ASSESSMENTS Teacher designed tests and quizzes Activities which demonstrate knowledge of the concepts taught Worksheets designed to demonstrate knowledge of the concepts taught Portfolio assessment Group assessment CORRECTIVES/EXTENSIONS Correctives: Utilize text generated reteaching worksheets. Additional worksheets on conic sections. Extensions: Utilize the graphing calculator to graph polynomial functions. Utilize text generated enrichment worksheets. COURSE: Algebra II STRAND: 2.2D Algebraic Expressions GRADE(S): 10-11 TIME FRAME: full year (180 days) PA CORE STANDARDS CC2.2.HS.D.8 - Apply inverse operations to solve equations or formulas for a given variable. CC.2.1.HS.F.1 – Apply and extend the properties of exponents to solve problems with rational exponents. ASSESSMENT ANCHORS A2.1.1 A2.1.2 RESOURCES McDougal Little Algebra II Houghton Mifflin Algebra II Glencoe Algebra II Prentice Hall Algebra II Resource packets Teacher designed materials Algebra With Pizzazz OBJECTIVES The learner will simplify radical expressions, solve radical equations, graph and perform operations of functions including inverses and compositions. ESSENTIAL CONTENT Find the nth root. Find the composition of two given functions. Identify a function as being one-to-one or not. Find the inverse of a given function. Graph different types of functions. Simplify, add, subtract, multiply, and divide radical expressions. Simplify expressions with rational exponents. Solve square root and other radical equations. INSTRUCTIONAL STRATEGIES Various pieces of graphing software can be utilized to clarify and/or discover the properties of these functions. SAT Problems. Inner/Outer Circle. Jigsaw. ASSESSMENTS Teacher designed tests and quizzes Activities which demonstrate knowledge of the concepts taught Worksheets designed to demonstrate knowledge of the concepts taught Portfolio assessment Group assessment CORRECTIVES/EXTENSIONS Correctives: Group work to reteach concepts. Utilize text generated reteaching worksheets. Extensions: Utilize text generated enrichment worksheets. Student generated worksheets/quiz. COURSE: Algebra II STRAND: 2.1D Numbers and Operations GRADE(S): 10-11 TIME FRAME: full year (180 days) PA CORE STANDARDS CC.2.1.HS.F.2 – Apply properties of rational and irrational numbers to solve real world or mathematical problems. CC2.2.HS.D.6 – Extend the knowledge of rational functions to rewrite in equivalent forms. ASSESSMENT ANCHORS A2.1.2 A2.1.3 RESOURCES McDougal Little Algebra II Houghton Mifflin Algebra II Glencoe Algebra II Prentice Hall Algebra II Resource packets Teacher designed materials Algebra With Pizzazz OBJECTIVES The learner will perform all operations on rational expressions and solve rational equations. ESSENTIAL CONTENT Apply the operations of arithmetic (addition, subtraction, multiplication, and division) to rational expressions. Solve rational equations. Identify the domain of rational functions. INSTRUCTIONAL STRATEGIES Various pieces of graphing software can be utilized to clarify and/or discover the properties of these functions. SAT Problems. Inner/Outer Circle. Jigsaw. ASSESSMENTS Teacher designed tests and quizzes Activities which demonstrate knowledge of the concepts taught Worksheets designed to demonstrate knowledge of the concepts taught Portfolio assessment Group assessment CORRECTIVES/EXTENSIONS Correctives: Group work to reteach concepts. Utilize text generated reteaching worksheets. Extensions: Utilize text generated enrichment worksheets. Student generated worksheets/quiz. COURSE: Algebra II STRAND: 2.1F Numbers and Operations GRADE(S): 10-11 TIME FRAME: full year (180 days) PA CORE STANDARDS CC.2.2.HS.C.3 – Write functions or sequences that model relationships between two quantities. ASSESSMENT ANCHORS A2.2.1 RESOURCES McDougal Little Algebra II Houghton Mifflin Algebra II Glencoe Algebra II Prentice Hall Algebra II Resource packets Teacher designed materials Algebra With Pizzazz OBJECTIVES The learner will generate sequences and series. ESSENTIAL CONTENT Analyze a set of data for a particular pattern. Generate an arithmetic or geometric sequence. Find an explicit and recursive formula for a particular sequence. Write and evaluate an arithmetic or geometric series. Use summation notation to simplify a series. INSTRUCTIONAL STRATEGIES Various pieces of graphing software can be utilized to clarify and/or discover the properties of these functions. SAT Problems. Inner/Outer Circle. Jigsaw. ASSESSMENTS Teacher designed tests and quizzes Activities which demonstrate knowledge of the concepts taught Worksheets designed to demonstrate knowledge of the concepts taught Portfolio assessment Group assessment CORRECTIVES/EXTENSIONS Correctives: Group work to reteach concepts. Utilize text generated reteaching worksheets. Extensions: Utilize text generated enrichment worksheets. Student generated worksheets/quiz. COURSE: Algebra II STRAND: 2.4B Measurements, Data, and Probability GRADE(S): 10-11 TIME FRAME: full year (180 days) PA CORE STANDARDS CC.2.4.HS.B.6 – Use the concepts of independence and conditional probability to interpret data. CC.2.4.HS.B.7 – Apply the rules of probability to compute probabilities of compound events in a uniform probability model. ASSESSMENT ANCHORS A2.2.3 RESOURCES McDougal Little Algebra II Houghton Mifflin Algebra II Glencoe Algebra II Prentice Hall Algebra II Resource packets Teacher designed materials Algebra With Pizzazz OBJECTIVES The learner will count permutations and combinations, calculate the probability of events and analyze data. ESSENTIAL CONTENT Counting permutations and combinations. Make and use a probability distribution. Find conditional probability. Use formulas and tree diagrams. Calculate measures of central tendencies. Draw and interpret box and whisker plots. INSTRUCTIONAL STRATEGIES Various pieces of graphing software can be utilized to create a box and whisker plot and a bar graph. SAT Problems. Inner/Outer Circle. Jigsaw. ASSESSMENTS Teacher designed tests and quizzes Activities which demonstrate knowledge of the concepts taught Worksheets designed to demonstrate knowledge of the concepts taught Portfolio assessment Group assessment CORRECTIVES/EXTENSIONS Correctives: Group work to reteach concepts. Utilize text generated reteaching worksheets. Extensions: Utilize text generated enrichment worksheets. Student generated worksheets/quiz. COURSE: Algebra II STRAND: 2.3A Geometry GRADE(S): 10-11 TIME FRAME: full year (180 days) PA CORE STANDARDS CC.2.3.HS.A.10 – Translate between the geometric description and the equation for a conic section. ASSESSMENT ANCHORS A2.2.1 RESOURCES McDougal Little Algebra II Houghton Mifflin Algebra II Glencoe Algebra II Prentice Hall Algebra II Resource packets Teacher designed materials Algebra With Pizzazz OBJECTIVES The learner will identify, write, and graph conic sections. ESSENTIAL CONTENT Identify and graph conic sections. Write the equation of conic sections. Identify the domain and range of conic sections. Write the equation of a translated conic section. Identify a translated conic section from an equation. INSTRUCTIONAL STRATEGIES Various pieces of graphing software can be utilized to graph conic sections. SAT Problems. Inner/Outer Circle. Jigsaw. ASSESSMENTS Teacher designed tests and quizzes Activities which demonstrate knowledge of the concepts taught Worksheets designed to demonstrate knowledge of the concepts taught Portfolio assessment Group assessment CORRECTIVES/EXTENSIONS Correctives: Group work to reteach concepts. Utilize text generated reteaching worksheets. Extensions: Utilize text generated enrichment worksheets. Student generated worksheets/quiz.