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