Pacing - Rochester City School District



Pacing |Unit/Essential Questions |Essential Knowledge- Content/Performance Indicators

(What students must learn) |Essential Skills

(What students will be able to do) |Vocabulary |Resources

Pearson NYS Algebra 2 | |Sept

2nd -22nd

|Unit 1: Equations and Inequalities

How do you solve absolute value equation/inequality and plot on the number line?

|A2.A.1 Solve absolute value equations and inequalities involving linear expressions in one variable |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 and Trig. 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

|Term

✓ Constant term

✓ Like terms

✓ Coefficient

✓ Expression

✓ Equation

✓ Literal Equation

✓ Inequality

✓ Absolute Value

✓ Extraneous solution |1-3: Algebraic Expressions

(1 day)

1-4: Solving equations.

(4 day)

Supplement with additional worksheets on equations with fractional coefficients

1-5: Solving Inequalities

(1 day)

1-6 Absolute Value Equations

(3 - 4 days)

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|Sept 23rd |Unit 2: Linear Equations and|A2.A.5 Use direct and inverse variation to solve for |Review of Algebra Topics |Relation |2.1 Relations and functions |

|– Oct 19th |Functions |unknown values |Student will be able to |Function |Emphasis on domain and Range |

| | | | |Vertical line test |(2 days) |

| |How do you distinguish |A2.A.37 Define a relation and function |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? |A2.A.38 Determine when a relation is a function |Find the Slope of a linear function given an equation, |Domain |(2 days) |

| | | |graph or 2 points |Range | |

| |How do you distinguish |A2.A.39 Determine the domain and range of a function |Find the equation for a linear function given two points|Direct Variation |2.3 Linear Functions and |

| |between a relation and a |from its equation |or a point and a graph. |Constant of Variation |slope-intercept Form |

| |function? | | |Linear function |(3 days) |

| | |A2.A.40 Write functions in functional notation |Algebra 2 and Trig. Topics |Linear equation | |

| |How do you find the domain | |Student will be able to |x-intercept |2.4 More about Linear Equations |

| |and range of a function? |A2.A.41 Use functional notation to evaluate functions| |y-intercept |(1 day) |

| | |for given values in the domain |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 |2.5 Using Linear Model |

| |with functions? |A2.A.46 Perform transformations with functions and |ordered pair, mapping diagram, graph or table of values |function |(1 day) |

| | |relations: |Distinguish between direct and indirect variation |Slope intercept form of | |

| | |f(x + a) , f(x) + a, f(−x), − f(x), af(x) |Determine of a given function is direct given a function|linear function |2.6 Families of functions |

| | | |rule, graph or table of values |Point slope form of linear |(2 – 3 days) |

| | | |Solve word problems related to direct and indirect |function | |

| | | |variation (ref. to regents questions from ) |Line of best fit |2.7 Absolute value Functions and |

| | | |Distinguish between parallel and perpendicular lines. |Scatter plot |Graphs |

| | | |Do linear regression using a graphing calculator |Correlation |(1 - 2 days) |

| | | |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 20th – |Unit 3: Linear Systems |A.G.7 Graph and solve systems of linear equations |Review of Algebra Topics |System of equations |3 -1 Solving System Using Tables and |

|Nov 5th | |and inequalities with rational coefficients in two |Student will be able to |Linear system solution of a |Graphs |

| |How can you use a graph to |variables | |system |(1 - 2 days) |

| |find the solution of a | |Find the point where the two lines intersect |inconsistent system | |

| |system? |A.A.10 Solve systems of two linear equations in two |Identify the solution to a system of two lines |consistent system |3 - 2 Solving Systems Algebraically |

| | |variables algebraically. |Identify a consistent system |independent system |(2 - 3 days) |

| |How do you solve a system of| |Identify an inconsistent system |dependent system | |

| |equations by substitution or|A2.PS.5 Choose an effective approach to solve |Identify an independent and dependent system |equivalent systems |3 - 3 Systems of |

| |elimination? |systems a problem from a variety of strategies |Solve a system of equations by substitution |at least |Inequalities |

| | |(numeric, graphic, algebraic) |Solve a system of equations by elimination |at most |(2 - 3 days) |

| |How can you solve a system | |Use substitution or elimination to solve word problems | | |

| |of inequalities graphically?| | | |3 - 5 Systems with Three Variables |

| | | |Algebra 2 and Trig. Topics | |OPTIONAL |

| |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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|Nov 8th – |Unit 4: Quadratic Equations |A2.A.46 Perform transformations with functions and |Review of Algebra Topics |Parabola |4-1 Quadratic functions and |

|Dec 17th |and Functions |relations: |Students will be able to |Quadratic function |transformations |

| | |f (x + a) , f(x)+ a, f (−x), − f (x), af (x) |use definitions of domain and range to sketch a |Vertex form |(2 – 3 days) |

| | | |quadratic |Axis of symmetry | |

| |How do you perform |A2.A.40 Write functions in functional notation |factor the difference of two squares |Vertex of the parabola |4-2 Standard form of a quadratic |

| |transformations of | |factor completely |Maximum |function |

| |functions? |A2.A.39 Determine the domain and range of a |solve quadratic equations by factoring |Minimum |(2 days) |

| | |function from its |use a quadratic equation to model a real situation |Standard form | |

| |How do you factor completely|equation |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 |(1 - 2 days) |

| |expressions? |A2.A.7 Factor polynomial expressions completely, | |Factoring | |

| | |using any combination of the following techniques: |Algebra 2 and Trig Topics |Greatest Common Factor |4-4 Factoring quadratic expressions |

| |How do you use the |common factor extraction, difference of two perfect |Students will be able to |Perfect square trinomial |(4 days) |

| |calculator to find |squares, quadratic trinomials | |Difference of two squares | |

| |appropriate regression | |perform horizontal and vertical translations of the |Zero of a function (root) |4-5 Quadratic equations (1-2 days) |

| |formulas? |A2.S.7 Determine the function for the |graph of y = x2 |Discriminant | |

| | |regression model, using appropriate |graph a quadratic in vertex form: f(x) =a(x - h)2 + k |Imaginary numbers |4-6 Completing the square (2 -3 days)|

| |How do you use imaginary |technology, and use the regression |identify and label the vertex as ( h , k ) |Complex numbers | |

| |numbers to find square roots|function to interpolate and extrapolate |identify and label the axis of symmetry of a parabola |Conjugates |4-7 Quadratic Formula (2 days) |

| |of negative numbers? |from the data |graph parabolas in the form of y = a x2 with various | | |

| | | |values of a | |4-8 Complex Numbers |

| |How do you solve quadratic |A2.A.20 Determine the sum and |graph a quadratic in vertex form: | |(4 - 5 days) |

| |equations using a variety of|product of the roots of a quadratic |f(x) = ax2+bx+c | |Additional resource at |

| |techniques? |equation by examining its coefficients |find the axis of symmetry algebraically using the | | |

| | | |standard form of the equation | | |

| |How do you determine the |A2.A.21 Determine the quadratic |identify the y-intercept as ( 0, c ) | |Quadratic Inequalities Page 256-257 |

| |kinds of roots a quadratic |equation, given the sum and product of |find the vertex of a parabola algebraically using the | |(1 day) |

| |will have from its equation?|its roots |standard form of the equation | | |

| | | |identify the range of parabolas | |4-9 Quadratic Systems |

| |How do you find the solution|A2.A.13 Simplify radical expressions |sketch a graph of a parabola after finding the axis of | |(2 days) |

| |set for quadratic | |symmetry, the vertex, and the y-intercept | | |

| |inequalities? |A2.A.24 Know and apply the |use the calculator to find a quadratic regression | | |

| | |technique of completing the square |equation | | |

| |How do you solve systems of | |factor using “FOIL” | | |

| |linear and quadratic |A2.A.25 Solve quadratic equations, |finding a GCF | | |

| |equations graphically and |using the quadratic formula |perfect square trinomials | | |

| |algebraically? | |difference of two squares | | |

| | |A2.A.2 Use the discriminant to |zero product property | | |

| | |determine the nature of the roots of a |finding the sum and product of roots | | |

| | |quadratic equation |writing equations knowing the roots or knowing the sum | | |

| | | |and product of the roots | | |

| | |A2.A.4 Solve quadratic inequalities in one and two |solve by taking square roots | | |

| | |variables, algebraically and graphically |solve by completing the square | | |

| | | |solve by using the quadratic formula | | |

| | |A2.A.3 Solve systems of equations |use the discriminant to find the nature of the roots | | |

| | |involving one linear equation and one |simplify expressions containing complex numbers (include| | |

| | |quadratic equation algebraically |rationalizing the denominator) | | |

| | |Note: This includes rational |solve quadratic inequalities | | |

| | |equations that result in linear |solve systems of quadratics algebraically | | |

| | |equations with extraneous roots. | | | |

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| | |A2.N6 Write square roots of negative numbers in | | | |

| | |terms of i | | | |

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| | |A2.N9 Perform arithmetic operations on complex | | | |

| | |numbers and write the answer in the form a+bi | | | |

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|Jan 3rd – |Unit 5: Polynomials |A2.N.3 Perform arithmetic operations with polynomial |Review of Algebra Topics |Polynomial |5-1 Polynomial Functions |

|Jan 14th | |expressions containing rational coefficients |Student will be able to |Monomial |(1 day) |

| |How do you perform | | |Binomial | |

| |arithmetic operations with |A2.A.7 Factor polynomial expressions completely, |combine like terms |Trinomial |5-2 Polynomials, Linear Factors and |

| |polynomial expressions? |using any combination of the following techniques: |subtract polynomial expressions |Degree |Zeros |

| | |common factor extraction, difference of two perfect |multiply monomials, binomials and trinomials |Root |(1 day) |

| |How do you factor |squares, quadratic trinomials | |Solution | |

| |polynomials? | |Algebra 2 and Trig Topics |Zero Property |5-3 Solving Polynomial Equations |

| | |A2.A.26 Find the solution to polynomial equations of |Students will be able to | |(2 days) |

| |How do you solve polynomial |higher degree that can be solved using factoring | | | |

| |equation? |and/or the quadratic formula |recognize and classify polynomials | |5-4 Dividing Polynomials |

| | | |factor polynomials using common factor extraction, | |(2 days) |

| |How do you expand a |A2.A.50 Approximate the solution to polynomial |difference of two perfect squares and or trinomial | | |

| |polynomial to the nth |equations of higher degree by inspecting the graph |factoring. | |5-7 The Binomial Theorem |

| |Order? | |Write a polynomial function given its roots. | |(2 days) |

| | |A2.A.36 Apply the binomial theorem to expand a |Solve polynomial equations /find the roots graphically. | | |

| |How do you find the nth term|binomial and determine a specific term of a binomial |Divide polynomials by factoring, long division or | | |

| |of a binomial expansion? |expansion |synthetic division | | |

| | | |Apply the Binomial Theorem to expand a binomial | | |

| | | |expression | | |

| | | |Find a specific term of a binomial expansion. | | |

|Jan 18th – |MIDTERM REVIEW |

|Jan 28th | |

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|Jan 31st – |Unit 6: Rational Expressions| |Review of Algebra Topics |Simplest form |8-4 Rational Expressions (3-4 days) |

|Feb 18th |and Functions |A2.A.16 Perform arithmetic operations with rational |All topics in this unit except complex fractions are |Rational Expression | |

| | |expressions and rename to lowest terms |taught in Integrated Algebra. In Algebra most problems |Common factors |8-5 Adding and Subtracting Rational |

| |How do we perform arithmetic| |involve monomials and simple polynomials. In Algebra 2 |Reciprocal |Expressions- includes simplifying |

| |operations on rational |A2.A.17 Simplify complex fractional expressions |factoring becomes more complex and may require more than|Least Common Multiple |complex fractions (4-5 days) |

| |expressions? | |one step to factor completely. |Lowest Common Denominator | |

| | |A2.A.23 Solve rational equations and inequalities | |Common factors |8-6 Solving Rational Equations (2 -3 |

| |How do we simplify a complex| |Algebra 2 Topics |Complex Fraction |days) |

| |fraction? | |Students will be able to |Rational equation | |

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| |How do we solve a rational | |Simplify a rational expression to lowest terms by | | |

| |equation? | |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) | | |

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|Feb 28th – |Unit 7:Exponential and |A2.A.6 Solve an application with results in an |Students will be able to: |asymptote |7 -1 Exploring Exponential Models |

|Mar 25th |Logarithmic Functions |exponential function. |model exponential growth and decay |change of base formula |(1 day) |

| | | |explore the properties of functions of the form [pic] |common logarithm | |

| |How do you model a quantity |A2.A.12 Evaluate exponential expressions, including |graph exponential functions that have base e |exponential equation |7 - 2 Properties of Exponential |

| |that changes regularly over |those with base e. |write and evaluate logarithmic expressions |exponential function |functions |

| |time by the same percentage?| |graph logarithmic functions |exponential decay |(2 days) |

| | |A2.A.53 Graph exponential functions of the form. |derive and use the properties of logarithms to simplify |exponential growth | |

| |How are exponents and |[pic] for positive values of b, including b = e. |and expand logarithms. |logarithm |7 – 3 Logarithmic Functions as |

| |logarithms related? | |solve exponential and logarithmic equations |logarithmic equation |Inverses |

| | |A2.A.18 Evaluate logarithmic expressions in any base|evaluate and simplify natural logarithmic expressions |logarithmic function |(2 days) |

| |How are exponential | |solve equations using natural logarithms |natural logarithmic function| |

| |functions and logarithmic |A2.A.54 Graph logarithmic functions, using the | | |- Fitting Curves to Data |

| |functions related? |inverse of the related exponential function. | | |Page 459 (1 day) |

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| |Which type of function |A2.A.51 Determine the domain and range of a function| | |7 - 4 Properties of Logarithms |

| |models the data best? |from its graph. | | |(2 – 3 days) |

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| | |A2.A.19 Apply the properties of logarithms to | | |7 - 5 Exponential and Logarithmic |

| | |rewrite logarithmic expressions in equivalent forms. | | |Equations |

| | | | | |(3 days) |

| | |A2.A. 27 Solve exponential equations with and | | | |

| | |without common bases. | | |7 - 6 Natural Logarithms pg 478 |

| | | | | |(2 days) |

| | |A2.A. 28 Solve a logarithmic equations by rewriting | | | |

| | |as an exponential equation. | | | |

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| | |A2.S. 6 Determine from a scatter plot whether a | | | |

| | |linear, logarithmic, exponential, or power regression| | | |

| | |model is most appropriate. | | | |

|Mar 28th – |Unit 8: Probability |A2.S.9 Differentiate between situations requiring |Algebra 2 Topics |Permutation |11-1 Permutations and Combinations |

|April 15th | |permutations and those requiring combinations |Students will be able to |Combination |(2-3 days) |

| |How do you calculate the | | |Factorial | |

| |probability of an event? |A2.S.10 Calculate the number of possible permutations|Use permutations, combinations, and the Fundamental |Counting Principle |11-2 Probability(1-2 days) |

| | |(nPr) of n items taken r at a time |Principle of Counting to determine the number of |Event | |

| | | |elements in a sample space and a specific subset (event)|Outcome |11-3 Probability of Multiple |

| | |A2.S.12 Use permutations, combinations, and the |Determine theoretical and experimental probabilities for|Sample Space |Events(1-2 days) |

| | |Fundamental Principle of Counting to determine the |events, including geometric applications |Theoretical probability | |

| | |number of elements in a sample space and a specific |Find the probability of the event A and B |Experimental Probability |11-8 Binomial Distributions (2-3 |

| | |subset (event) |Find the probability of event A or B |Dependent events |days) |

| | | |Know and apply the binomial probability formula to |Independent events | |

| | |A2.S.13 Calculate theoretical probabilities, |events involving the terms exactly, at least, and at |Mutually exclusive | |

| | |including geometric applications |most | | |

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| | |A2.S.14 Calculate empirical probabilities | | | |

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| | |A2.S.15 Know and apply the binomial probability | | | |

| | |formula to events involving the terms exactly, at | | | |

| | |least, and at most | | | |

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|April 25th |Unit 9: Statistics |A2.S.1 Understand the differences among various kinds|Algebra 2 Topics |Survey |11-5 Analyzing Data (1-2 days) |

|– May 13th | |of studies (e.g., survey, observation, controlled |Students will be able to |Experiment | |

| |What methods are there for |experiment) | |Bias |11-6 Standard Deviation (1-2 days) |

| |analyzing data? | |Calculate measures of central tendency given a frequency|Sample | |

| | |A2.S.2 Determine factors which may affect the outcome|table |Population |11-7 Samples and Surveys (1-2 days) |

| | |of a survey |Calculate measures of dispersion |Standard deviation | |

| | | |(range, quartiles, interquartile range, standard |Variance |11-9 Normal Distributions (2-3 days) |

| | |A2.S.3 Calculate measures of central tendency with |deviation, variance) for both samples and populations |Central tendency | |

| | |group frequency distributions |(standard deviation & variance using graphing |Outlier | |

| | | |calculator) |Frequency distribution | |

| | |A2.S.4 Calculate measures of dispersion (range, |Calculate probabilities using the normal distribution |Dispersion | |

| | |quartiles, interquartile range, standard deviation, |(use the normal curve given on the Algebra 2 reference |Quartiles | |

| | |variance) for both samples and populations |sheet) |Interquartile range | |

| | | | |Binomial probability | |

| | |A2.S.5 Know and apply the characteristics of the | |Normal Distribution | |

| | |normal distribution | | | |

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|May 16th – |REVIEW and FINALS |

|June 14th | |

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