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Algebra 2 Curriculum Map 2015-16 Pacing Sept 2– Sept. 18th Unit/Essential Questions Unit 1: Equations and Inequalities How do you solve absolute value equation/inequality and plot on the number line? Essential KnowledgeContent/Performance Indicators (What students must learn) Essential Skills (What students will be able to do) Review of Algebra Topics Student will be able to - - simplify expressions write and evaluate algebraic expressions represent mathematical phrases and real world quantities using algebraic expressions solve multi step equations and check distinguish between solution, no solution and identity solve literal equations solve multi step inequalities and graph them write inequality from a sentence using key word at least, at most, fewer, less, more … Algebra 2 Topics Students will be able to - solve absolute value equations and check solve absolute value inequalities and check for extraneous solution distinguish between an “and” problem and an “or” problem and accordingly write the solution Vocabulary Term Constant term Like terms Coefficient Expression Equation Literal Equation Inequality Absolute Value Extraneous solution Resources Pearson NYS Algebra 2 1-3: Algebraic Expressions 1-4: Solving equations. Supplement with additional worksheets on equations with fractional coefficients 1-5: Solving Inequalities 1-6 Absolute Value Equations Algebra 2 Curriculum Map 2015-16 Sept 21 – Oct 8 Unit 2: Linear Equations and Functions How do you distinguish between Direct and Inverse variation? How do you distinguish between a relation and a function? How do you find the domain and range of a function? How do you transformation with functions? Review of Algebra Topics Student will be able to - - Determine if a function is linear Graph a linear function with/without a calculator. Find the Slope of a linear function given an equation, graph or 2 points Find the equation for a linear function given two points or a point and a graph. Algebra 2 topics Student will be able to - - - - - Distinguish between a relation and a function. Determine if a relation is a function given a set of ordered pair, mapping diagram, graph or table of values Distinguish between direct and indirect variation Determine of a given function is direct given a function rule, graph or table of values Solve word problems related to direct and indirect variation (ref. to regents questions from jmap.org) Distinguish between parallel and perpendicular lines. Do linear regression using a graphing calculator Determine the correlation between the data sets by viewing or plotting a scatter-plot. Perform vertical and horizontal translations Graph absolute value equations and perform related translations Relation Function Vertical line test Function Rule Function notation Domain Range Direct Variation Constant of Variation Linear function Linear equation x-intercept y-intercept Slope Standard form of linear function Slope intercept form of linear function Point slope form of linear function Line of best fit Scatter plot Correlation Correlation coefficient Regression Absolute value 2.1 Relations and functions Emphasis on domain and Range 2.2 Direct Variation 2.3 Linear Functions and slope-intercept Form 2.4 More about Linear Equations 2.5 Using Linear Model 2.6 Families of functions 2.7 Absolute value Functions and Graphs Algebra 2 Curriculum Map 2015-16 Oct 13 – 23 Unit 3: Linear Systems Review of Algebra Topics Student will be able to How can you use a graph to find the solution of a system? - How do you solve a system of equations by substitution or elimination? - - How can you solve a system of inequalities graphically? - How can you solve systems involving three equations? Find the point where the two lines intersect Identify the solution to a system of two lines Identify a consistent system Identify an inconsistent system Identify an independent and dependent system Solve a system of equations by substitution Solve a system of equations by elimination Use substitution or elimination to solve word problems Algebra 2 Topics Student will be able to - Solve a system of inequalities graphically. Use a system of inequalities to model a real situation Solve a linear and absolute-value system solve a system of three equations using elimination System of equations Linear system solution of a system inconsistent system consistent system independent system dependent system equivalent systems at least at most 3 -1 Solving System Using Tables and Graphs 3 - 2 Solving Systems Algebraically 3 - 3 Systems of Inequalities 3 - 5 Systems with Three Variables OPTIONAL Algebra 2 Curriculum Map 2015-16 Oct. 26 – Jan 8 Unit 4: Quadratic Equations and Functions How do you perform transformations of functions? How do you factor completely all types of quadratic expressions? How do you use the calculator to find appropriate regression formulas? Review of Algebra Topics Students will be able to - use definitions of domain and range to sketch a quadratic - factor the difference of two squares - factor completely - solve quadratic equations by factoring - use a quadratic equation to model a real situation - determine a quadratic equation, given integer roots - graph linear and quadratic functions Algebra 2 Topics Students will be able to - How do you use imaginary numbers to find square roots of negative numbers? How do you solve quadratic equations using a variety of techniques? How do you determine the kinds of roots a quadratic will have from its equation? How do you find the solution set for quadratic inequalities? How do you solve systems of linear and quadratic equations graphically and algebraically? - - - - perform horizontal and vertical translations of the graph of y = x2 graph a quadratic in vertex form: f(x) =a(x - h)2 + k identify and label the vertex as ( h , k) identify and label the axis of symmetry of a parabola graph parabolas in the form of y = a x2 with various values of a graph a quadratic in vertex form: f(x) = ax2+bx+c find the axis of symmetry algebraically using the standard form of the equation identify the y-intercept as ( 0, c ) find the vertex of a parabola algebraically using the standard form of the equation identify the range of parabolas sketch a graph of a parabola after finding the axis of symmetry, the vertex, and the y-intercept use the calculator to find a quadratic regression equation factor using “FOIL” finding a GCF perfect square trinomials Parabola Quadratic function Vertex form Axis of symmetry Vertex of the parabola Maximum Minimum Standard form Domain and Range Regressions Factoring Greatest Common Factor Perfect square trinomial Difference of two squares Zero of a function (root) Discriminan t Imaginary numbers Complex numbers Conjugates 4-1 Quadratic functions and transformations 4-2 Standard form of a quadratic function 4-3 Modeling with quadratic functions 4-4 Factoring quadratic expressions 4-5 Quadratic equations 4-6 Completing the square 4-7 Quadratic Formula 4-8 Complex Numbers Additional resource at www.emathinstruction.com Quadratic Inequalities Page 256-257 4-9 Quadratic Systems Algebra 2 Curriculum Map 2015-16 - - - difference of two squares zero product property finding the sum and product of roots writing equations knowing the roots or knowing the sum and product of the roots solve by taking square roots solve by completing the square solve by using the quadratic formula use the discriminant to find the nature of the roots simplify expressions containing complex numbers (include rationalizing the denominator) solve quadratic inequalities solve systems of quadratics algebraically Algebra 2 Curriculum Map 2015-16 Jan 11 – Feb 26 Unit 5: Polynomials How do you perform arithmetic operations with polynomial expressions? How do you factor polynomials? How do you solve polynomial equation? Review of Algebra Topics Student will be able to - Algebra 2 Topics Students will be able to - How do you expand a polynomial to the nth Order? How do you find the nth term of a binomial expansion? - - Feb 29 – Mar 18 Unit 6: Radical Functions, Rational Exponents, Function Operations How do you write algebraic expressions in simplest radical form? How do you simplify by rationalizing the denominator? How do you express sums and differences of radical expressions in simplest form? combine like terms subtract polynomial expressions multiply monomials, binomials and trinomials - - 5-2 Polynomials, Linear Factors and Zeros 5-3 Solving Polynomial Equations 5-4 Dividing Polynomials 5-6 Fundamental Theorem of Algebra 5-7 The Binomial Theorem (2 days) Apply the Binomial Theorem to expand a binomial expression Find a specific term of a binomial expansion. Use rules of positive and negative exponents in algebraic computations Use squares and cubes of numbers Know square roots of perfect squares from 1-15 Algebra 2 Topics Students will be able to - 5-1 Polynomial Functions 5-5 Theorems About Roots of Polynomial Equations recognize and classify polynomials factor polynomials using common factor extraction, difference of two perfect squares and or trinomial factoring. Write a polynomial function given its roots. Solve polynomial equations /find the roots graphically. Review of Algebra Topics Student will be able to - Polynomial Monomial Binomial Trinomial Degree Root Solution Zero Property Simplify radical expressions Multiply and divide radical expressions Add and subtract radical expressions Use rational exponents Solve radical equations and check Exponents Conjugates Radicals Rationalize the denominator Extraneous roots f- 1(x) inverse of a function one to one onto Page 360 Properties of exponents 6-1 Simplify radical expressions 6-2 Multiply and divide radical expressions 6-3 Binomial Radical Expressions 6-4 Rational Exponents 6-5 Solve radical equations Algebra 2 Curriculum Map 2015-16 How do you write radicals with fractional exponents? How do you change an expression with a fractional exponent into a radical expression? How do you solve radical equations? How do you add, subtract, multiply, and divide functions? - for extraneous roots Add, subtract, multiply, and divide functions Algebra 2 Curriculum Map 2015-16 March 21-Apr 29 Unit 7:Exponential and Logarithmic Functions How do you model a quantity that changes regularly over time by the same percentage? How are exponents and logarithms related? How are exponential functions and logarithmic functions related? Students will be able to: - model exponential growth and decay - explore the properties of functions of the form y ab graph exponential functions that have base e write and evaluate logarithmic expressions graph logarithmic functions derive and use the properties of logarithms to simplify and expand logarithms. solve exponential and logarithmic equations evaluate and simplify natural logarithmic expressions solve equations using natural logarithms x - - asymptote change of base formula common logarithm exponentia l equation exponentia l function exponentia l decay exponentia l growth logarithm logarithmic equation logarithmic function natural logarithmic function 7 -1 Exploring Exponential Models (1 day) 7 – 3 Logarithmic Functions as Inverses (2 days) 7 - 4 Properties of Logarithms (2 – 3 days) 7 - 5 Exponential and Logarithmic Equations (3 days) 7 - 6 Natural Logarithms pg 478 (2 days) Algebra 2 Curriculum Map 2015-16 May 2Jun 3 How do we perform arithmetic operations on rational expressions? Review of Algebra Topics All topics in this unit except complex fractions are taught in Integrated Algebra. In Algebra most problems involve monomials and simple polynomials. In Algebra 2 factoring becomes more complex and may require more than one step to factor completely. How do we simplify a complex fraction? Algebra 2 Topics Students will be able to Unit 8: Rational Expressions and Functions How do we solve a rational equation? - - Simplify a rational expression to lowest terms by factoring and reducing State any restrictions on the variable Multiply and divide rational expressions Add and subtract rational expressions Simplify a complex fraction Solve rational equations (inequalities will be saved for the Alg 2 course) Simplest form Rational Expression Common factors Reciprocal Least Common Multiple Lowest Common Denominato r Common factors Complex Fraction Rational equation 8-1 Inverse Variation 8-2 The reciprocal Function Family 8-3 Rational functions and Their Graphs 8-4 Rational Expressions 8-5 Adding and Subtracting Rational Expressionsincludes simplifying complex fractions 8-6 Solving Rational Equations Algebra 2 Curriculum Map 2015-16 Algebra 2 Curriculum Map 2015-16
