muskogee public schools curriculum map, 2010-2011 algebra ii, … · 2015-05-22 · page 1 muskogee...
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Muskogee Public Schools Curriculum Map, 2010-2011
Algebra II, Grades 8-12
The ACE Algebra II End of Instruction Test Blueprint reflects the degree to which each PASS Standard and Objective is represented on the test.
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
1st Nine Weeks
Standard 1: Number Systems and Algebraic Operations - The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers.
1.1b Add, subtract, multiply, divide, and simplify radical expressions and expressions containing exponents.
1.2. Polynomial and Rational Expressions 1.2a Divide polynomial expressions by lower degree polynomials.
FOIL, distributive property, absolute value, base term, like terms, exponent, complex numbers, square roots, power, common denominator, descending and ascending order, radical symbol, radicand, principal root, rationalize the denominator, like radical terms, function notation, dependent/independent variables
Degree of a polynomial, division, dividend, quotient, polynomial expression, greatest common factor
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
1st Nine Weeks
Standard 1: Number Systems and Algebraic Operations - The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers.
1.2b Add, subtract, multiply, divide, and simplify rational expressions, including complex fractions.
1.3. Complex Numbers 1.3a. Recognize that to solve certain problems and equations, number systems need to be extended from real numbers to complex numbers. *Assessed locally 1.3b Add, subtract, multiply, divide, and simplify expressions involving complex numbers.
Simplify, complex fractions, common denominator, scientific notation, trinomial factoring, difference of two perfect squares, monomial, polynomial, degree of monomial, degree of polynomial, leading coefficient, binomial , trinomial, polynomial function
Complex numbers, imaginary unit, imaginary number, real part, imaginary part , complex conjugate
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
1st Nine Weeks
Standard 1: Number Systems and Algebraic Operations - The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers. Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.1. Functions and Function Notation 2.1a. Recognize the parent graphs of polynomial, exponential, radical, quadratic, and logarithmic functions and predict the effects of transformations on the parent graphs, using various methods and tools which may include graphing calculators.
Parent function, parent graph, polynomial, exponential, radical, quadratic functions, transformations, reflection, stretch, compression, coordinate plane, x- and y-intercept, slope intercept form, standard form, vertical line test
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
1st Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.1d. Use algebraic, interval, and set notations to specify the domain and range of functions of various types.
Relation, domain, Domain and range of a relation/ function, ordered pair, algebraic, interval, and set notation, constraints, restrictions, zero of a function, factors of a polynomial expression, solution of an equation
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
1st Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.2 System of Equations 2.2a. Model a situation that can be described by a system of equations or inequalities and use the model to answer questions about the situation.
System of equations/ inequalities, linear system, consistent, inconsistent, dependent, independent, parallel, infinite systems/ solutions, models, real life experiences
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
1st Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.2b Solve systems of linear equations and inequalities using various methods and tools which may include substitution, elimination, matrices, graphing, and graphing calculators.
System of equations, linear systems, consistent systems, inconsistent systems, independent systems ,dependent systems, system of linear inequalities, Quadrants order, coordinate plane, substitution, elimination, graphing, parallel, infinite systems/ solutions, Three-dimensional coordinate system, ordered triple, z-axis, elimination, substitution, matrix addition/multiplication, dimensions, entry , address, scalar identity matrix, matrix product, multiplicative identity matrix, square matrix, translation/reflection/rotation matrix
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
1st Nine Weeks
Standard 3: Data Analysis and Statistics - The student will use data analysis and statistics to formulate and justify predictions from a set of data.
3.1 Analysis of Collected Data Involving Two Variables 3.1a Interpret data on a scatter plot using a linear, exponential, or quadratic model/equation.
Scatter Plot, Positive, Negative, and Relatively No Correlation, variables, data, linear, exponential, or quadratic model/equation, regression, correlation, line of best fit, correlation coefficient Recommended Math resources: Math Tools, Grades 3-12, 64 Ways to differentiate Instruction and Increase Student Engagement, by Harvey F. Silver, 2008 (Excellent tool) http://mathforum.org/dr.math www.coolmath.com/algebra/Algebra2 http://nlvm.usu.edu www.internet4classrooms.com/eoc_algebra2.htm http://www.purplemath.com/ http://mypages.iit.edu/~smile
Benchmark 1: http://www.sde.state.ok.us/AcctAssess/pdf/Core/Released/AlgebraII09-10.pdf 25 question EOI practice test Also available to create test is the Test and Item Specification document for Algebra II: http://www.sde.state.ok.us/AcctAssess/pdf/Core/Comb/AlgebraII.pdf
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
2nd Nine Weeks
Standard 1: Number Systems and Algebraic Operations - The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers.
1.1 Rational Exponents 1.1a Convert expressions from radical notation to rational exponents and vice versa.
1.2. Polynomial and Rational Expressions 1.2a Divide polynomial expressions by lower degree polynomials.
1.3b Add, subtract, multiply, divide, and simplify expressions involving complex numbers.
Complex numbers, imaginary numbers, imaginary unit, real part, imaginary part, complex conjugate, Radical notation, rational exponents, polynomial expressions, convert, index, indices, square root function, complex numbers
Polynomial / rational expressions, Degree of a polynomial, division, dividend, quotient, synthetic division Complex numbers, imaginary numbers, imaginary unit, real part, imaginary part, complex conjugate, Radical notation, rational exponents, polynomial expressions, convert, index, indices, square root function, complex numbers
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
2nd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.1e. Find and graph the inverse of a function, if it exists.
2.3 Quadratic equations and functions 2.3a Solve quadratic equations by graphing, factoring, completing the square and quadratic formula.
Inverse function, inverse relation, reciprocal, symmetrical, horizontal line test, one to one function,
Root of an equation, quadratic formula, quadratic equation, completing the square, zero of a function, binomial, trinomial, discriminant, axis of symmetry formula, factoring
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
2nd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.3b. Graph a quadratic function and identify the x- and y- intercepts and maximum or minimum value, using various methods and tools which may include a graphing calculator.
Parabola, vertex of a parabola, vertex form, standard form, minimum/ maximum value, x-/y-intercepts, axis of symmetry, direction of opening, compression, stretching
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
2nd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.3c. Model a situation that can be described by a quadratic function and use the model to answer questions about the situation.
Quadratic model, quadratic regression, maximize, minimize
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
2nd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions. Standard 3: Data Analysis and Statistics - The student will use data analysis and statistics to formulate and justify predictions from a set of data.
3.1b Identify whether the model (equation) is a curve of best fit for the data, using various methods and tools which may include a graphing calculator.
Curve of best fit, logarithmic, exponential, linear, quadratic, Benchmark 2: http://www.sde.state.ok.us/AcctAssess/pdf/Core/Released/AlgebraII09-10.pdf 25 question EOI practice test Also available to create test is the Test and Item Specification document for Algebra II: http://www.sde.state.ok.us/AcctAssess/pdf/Core/Comb/AlgebraII.pdf
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
3rd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.1 Functions and Function Notation 2.1b Add, subtract, multiply, and divide functions using function notation.
2.1c Combine functions by composition.
Function notation, composition, zero of a function, x-intercept of a graph, relations, solution of an equation.
Composition of a function, define a composition of a function
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
3rd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.1e. Find and graph the inverse of a function, if it exists.
2.2c. Use either one quadratic equation and one linear equation or two quadratic equations to solve problems
Inverse function, inverse relation, reciprocal, symmetrical, horizontal line test, one to one function,
Quadratic equation, Parabola, linear equation, slope intercept form, standard form, non linear systems, vertex form
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
3rd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.4. Identify, graph, and write the equations of the conic sections (circle, ellipse, parabola and hyperbola.)
Conic section, hyperbola, ellipse, parabola, asymptote, conjugate axis, transverse axis, circle, tangent, focus of an ellipse/hyperbola, major axis, vertices of an ellipse/ hyperbola, minor axis, co-vertices, branch of a hyperbola
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
3rd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions
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2.5. Exponential and logarithmic functions 2.5a Graph exponential and logarithmic functions.
Exponential function, base, horizontal/vertical asymptote, exponential growth / decay, logarithm, common logarithm, logarithmic function, natural logarithmic function
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
3rd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions
2.5b. Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another.
Exponential/ logarithmic equations, vertical/ horizontal translations, vertical/ horizontal compression/ stretch
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
3rd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions
2.5c. Model a situation that can be described by an exponential or logarithmic function and use the model to answer questions about the situation.
Interest formula, exponential growth formula, base, asymptote, exponential decay, logarithmic function, logarithm, common logarithm, natural logarithm/function, inverse function/relationship, logarithmic equation
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
3rd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.6 Polynomial equations and functions 2.6a. Solve polynomial equations using various methods and tools, which may include factoring and synthetic division
2.6b. sketch the graph of a polynomial function.
Synthetic division, factoring, polynomial, monomial, degree of a monomial/polynomial, leading coefficient, binomial, trinomial, Pascal’s Triangle,
Polynomial function, multiplicity, Rational/Irrational Roots Theorem, turning point, end behavior, local maximum/minimum
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
3rd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.6c. Given the graph of a polynomial function, identify the x- and y-intercepts, relative maximums and relative minimums, using various methods and tools, which may include a graphing calculator.
Relative maximum/minimums, end behavior, turning point
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
3rd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
3rd Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions. Standard 3: Data Analysis and Statistics - The student will use data analysis and statistics to formulate and justify predictions from a set of data.
2.6d. Model a situation that can be described by a polynomial function and use the model to answer questions about the situation.
3.1b Identify whether the model (equation) is a curve of best fit for the data, using various methods and tools which may include a graphing calculator.
Polynomial function, real world problems
Exponential regression, logarithmic regression, real world model
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
3rd Nine Weeks
Standard 3: Data Analysis and Statistics - The student will use data analysis and statistics to formulate and justify predictions from a set of data.
Benchmark 3: http://www.sde.state.ok.us/AcctAssess/pdf/Core/Released/AlgebraII09-10.pdf 25 question EOI practice test Also available to create test is the Test and Item Specification document for Algebra II: http://www.sde.state.ok.us/AcctAssess/pdf/Core/Comb/AlgebraII.pdf
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
4th Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.7 Rational equations and functions 2.7a. Solve rational equations
2.7 b. Sketch the graph of a rational function.
Rational equations/ functions, extraneous solution, rational inequality, rational equation/functions
Rational function, discontinuous function, continuous function, hole in a graph
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
4th Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.7c. Given the graph of a rational function, identify the x- and y-intercepts, vertical asymptotes, using various methods and tools which may include a graphing calculator.
Rational function, x-/y-intercepts, vertical/horizontal asymptotes
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
4th Nine Weeks
Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.
2.7d. Model a situation that can be described by a rational function and use the model to answer questions about the situation.
Rational function, discontinuous function, continuous function, hole in a graph
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
4th Nine Weeks
Standard 3: Data Analysis and Statistics - The student will use data analysis and statistics to formulate and justify predictions from a set of data.
3.2 Measures of Central Tendency and Variability 3.2a. Analyze and synthesize measures of central tendency (mean, median, mode, weighted average). 3.2b. Analyze and synthesize data from a sample using appropriate measures of variability (range, variance, standard deviation). 3.2c. Use the characteristics of the Gaussian normal distribution (bell-shaped curve) to solve problems. 3.2d. Identify how given outliers affect representations of data. *Assessed locally (review from Algebra 1) 3.3 Identify and use arithmetic and geometric sequences and series to solve problems.
Central tendency, mean, median, mode, range, weighted average, box-whisker plot, probability of distribution, expected value, variance, standard deviation, outlier, first/ third quartile Sequence, term of a sequence, infinite sequence, finite sequence, recursive formula explicit formula , iteration, summation notation, geometric sequence/ series, geometric mean, arithmetic sequence/series, nth term
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Nine-Weeks
Content Area and PASS Muskogee Academic Standards
Academic Skills Expected Strategies, Vocabulary & Assessment
4th Nine Weeks
Standard 3: Data Analysis and Statistics - The student will use data analysis and statistics to formulate and justify predictions from a set of data.
Trigonometric Functions: Connecting algebra to geometry Find and graph the inverse of a function, if it exists.
http://www.sde.state.ok.us/AcctAssess/pdf/Core/Released/AlgebraII09-10.pdf 25 question EOI practice test Also available to create review tests is the Test and Item Specification document for Algebra II: http://www.sde.state.ok.us/AcctAssess/pdf/Core/Comb/AlgebraII.pdf Also available are EOC released tests from other state including but not limited to: Virginia: http://www.doe.virginia.gov/testing/sol/released_tests/2008/released_tests2008.shtml North Carolina: http://www.ncpublicschools.org/accountability/testing/releasedforms California: http://www.cde.ca.gov/ta/tg/sr/css05rtq.asp Law of Sines/Cosines/ Tangent, Pythagorean formula, polar coordinates,
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NOTES