· web viewf-if.7c graph polynomial functions, identifying zeros when suitable factorizations are...

Bensalem Township School DistrictAlgebra 2

Unit 1: Tools of Algebra Suggested Sequence: 6 Days

PA Common Core Standards PAStandards

Skills Expectation is that all students will be able to

answer questions at this level on the Common Assessment

Lesson 1.1

2.1.8.E.1Distinguish between rational and irrational numbers using their properties.

2.1.8.E.4Estimate irrational numbers by comparing them to rational numbers.

2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problems.

A1.1.1.1.1Compare and/or order any real numbers. Note: Rational and irrational may be mixed.

Use a Venn Diagram to represent the subset of real numbers.

Identify properties of real numbers.

Define and find additive inverse, multiplicative inverse, and absolute value.

Page 8 #1-55

CP: #56-83

Honors: #85-89

Lesson 1.2

A-REI.1Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution.

Define and identify key vocabulary: variable, algebraic expression, variable expression, evaluate, term, and coefficient.

Find the perimeter of shapes involving combining like terms.

5 #1-37

CP: #38-64

Lesson 1.3Solve equations with variables on both sides, equations that involve the distributive property, equations with fractions and literal equations.

Solve problems that require writing and solving equations.

Page 21 #1-35

CP: #36-50, 53-64

Lesson 1.4Solve and graph linear Page 29 #1-28


A-REI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

inequalities.

Solve inequalities with no solution or all real number solutions.

Solve and graph compound inequalities.

Solve real-world problems that require you to write and solve inequalities.

CP: #29-38, 41-50

Honors: #51-55

Lesson 1.5Solve absolute value equations.

Solve absolute value inequalities

Page 36 #1-33

CP: #34-53

Honors: #61-66

Unit 2: Functions, Equations and Graphs Suggested Sequence: 8 Days

Common Core Standards PA Standards Skills Required Activities

Lesson 2.1F-IF.1Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.

F-IF.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

A2.2.1.1.3Determine the domain, range, or inverse of a relation.

Determine the domain and range of a relation.

Classify whether a relation is a function or not.

Determine if a relation is a function using the vertical line test.

Evaluate functions.

Page 59: 1-7, 12-31, 43-47, 50-54

CP: 55-57

Lesson 2.2

F-IF.7Graph functions expressed symbolically and show key features of the graph, by hand in

Graph a linear function in any of the three forms.

Use algebraic manipulation to change a linear function from one form to another.

Page 67: #1-41

CP: Page 68 #42-65, 69, 71-78

Honors: Page 69 #79-


simple cases and using technology for more complicated cases.

F-LE.1Distinguish between situations that can be modeled with linear functions and with exponential functions.

A-REI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Change from slope-intercept to standard to point-slope form.

Calculate the slope of a line given two points on the line.

Determine the slope of a line given its graph.

Write an equation of a line given a point on the line and it’s slope.

Write an equation of a line given two points on the line.

Recognize and graph a horizontal or vertical line from its equation.

Determine if two lines are parallel or perpendicular based on the equations.

Write an equation of a line parallel or perpendicular to another given a point on the line.

84

Lesson Piecewise FunctionsF-IF.7bGraph square root, cube root, and piecewise – defined functions, including step functions and absolute value functions.

Understand that a piecewise function has different rules for different parts of the domain.

Graph piecewise functions.

Graph step functions

CP: Page 71 #1-6

Lesson 2.3Classify if a function as a direct variation from a table.

Classify if a function is a direct variation from an equation.

Determine the constant of variation

Page 74: #1-27

CP: Page 75 #33-51

Honors: Page 76: #52, 55-59


given a table or equation.

Use direct variation to write and solve a proportion.

Lesson 2.4S-ID.7Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

F-IF.4For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F-BF.1Write a function that describes a relationship between two quantities.

A2.2.3.1.1Draw, identify, find, interpret, and/or write an equation for a regression model (lines and curves of best fit) for a scatterplot.

A2.2.3.1.2Make predictions using the equations or graphs of regression models (lines and curves of best fit) of scatter plots.

Write linear equations to model real-world problems.

Draw a scatter plot given two sets of data.

Draw and find the equation of a trend line for a scatter plot.

Use a scatter plot to make predictions.

Use a graphing calculator to determine the line of best fit for a scatter plot and make predictions.

Page 81: #1-11

Lesson 2.5

F-IF.7bGraph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Determine the vertex of an absolute value function.

Graph an absolute value function with a graphing calculator.

Graph an absolute value function using a table of values.

Page 90: #1-32

CP: Page 91: #33-52

Honors: Page 91: #53-59

Lesson 2.6F-BF.3Identify the effect of the graph of replacing f(x) by f(x) + K for

A2.2.2.2.1Identify or describe the effect of

Graph transformations of parent functions.

Write equations for vertical

Page 97: #1-14, 17-28

CP: Page 98: #29-38, 40, 42-47

Honors: Page 99: #48-51

Bensalem Township School DistrictAlgebra 2specific values of k (both positive and negative); find the value of k given the graphs.

changing parameters within a family of functions.

translations of absolute value functions.

Write equations for horizontal translations of absolute value functions.

Write equations that require both a vertical and horizontal translation of an absolute value function.

Given a function, describe the translations as vertical, horizontal or combined.


Unit 3: Linear Systems Suggested Sequence: 6 Days

Common Core Standards PAStandards

Skills Activities

Lesson 3.1

2.2.8.B.3Analyze and solve linear equations and pairs of simultaneous linear equations.

2.2.HS.D.10Represent, solve and interpret equations / inequalities and systems of equations / inequalities algebraically and graphically.

A1.1.2.2Write, solve, and / or graph systems of linear equations using various methods.

Classify systems as independent, dependent or inconsistent

Graph and solve linear systems by graphing.

Solve systems of linear equations by using a graphing calculator.

Page 120: 1-9 odd, 13-23 odd, 37, 444

CP: need to do problems from 25-36, 45

Honors: 46-48

Lesson 3.2

2.2.HS.D.10Represent, solve and interpret equations / inequalities and systems of equations / inequalities algebraically and graphically.

A1.1.2.2Write, solve, and / or graph systems of linear equations using various methods.

Solve systems of linear equations by substitution.

Solve systems of linear equations by elimination.

Solve systems without a unique solution.

Solve real world problems that involve systems of linear equations.

Interpret and determine the reasonableness of the algebraic or graphical solution of a system of two linear equations that describes a practical situation.

Page 128; 1-42, 54-59

CP: page 129: 44-53, 61-62

Lesson 2.7

2.2.HS.D.10Represent, solve

A1.1.3.2.1Write and / or solve

Graph linear inequalities in two variables.

Page 104: 1-22

CP: Page 105: 23-42

Bensalem Township School DistrictAlgebra 2and interpret equations / inequalities and systems of equations / inequalities algebraically and graphically.

a system of linear inequalities using graphing.

A1.1.3.2.2Interpret solutions to problems in the context of the problem situation.

Graph linear inequaltities in one-variable on a coordinate plane.

Use test points to show that all solutions to a linear inequality fall on one side of the inequality.

Solve application problems that require students to write and solve one-variable inequalities.

Solve compound inequalities.Lesson 3.32.2.HS.D.7Create and graph equations or inequalities to describe numbers or relationships.

2.2.HS.D.10Represent, solve and interpret equations / inequalities and systems of equations / inequalities algebraically and graphincally.

A1.1.3.2.1Write and/ or solve a system of linear inequalities using graphing.

A1.1.3.2.2Interpret solutions to problems in the context of the problem situation.

Model situations by writing a system of linear inequalities or a system that combines equations and inequalities.

Solve systems of linear inequalities or a system that combines equations and inequalities by graphing.

Page 136: #1-40

CP: Page 136 #43-48

Lesson 3.42.2.8.B.3Analyze and solve linear equations and pairs of simultaneous linear equations.

2.2.HS.D.10Represent, solve and interpret equations / inequalities and systems of equations / inequalities algebraically and graphically

A1.1.2.2.2Interpret solutions to problems in the context of the problem situatin.

Discuss the feasible region is the area of the graph that contains all the points that satisfy all the constraints.

If there is a maximum or a minimum value of the linear objective function, it occurs at one or more vertices of the feasible region.

Page 142: 1-10

Big State UniversityCookiesRock and Rap

Unit 4: Suggested Sequence: 13 Days


Chapter 5: Quadratics



answer questions at this level on the Common

Assessment

Lesson 5.1

Classify functions as linear or quadratic.

Identify the vertex and the axis of symmetry of a parabola.

Page 241: #1-15, 21-22, 32-37

Lesson 5.2

F-IF.7aGraph linear and quadratic functions and show intercepts, maxima, and minima


A2.2.1.1.4Identify and/or determine the characteristics of a quadratic function (intervals of increase/decrease, intercepts, zeros)

A2.2.2.1.1Create, interpret, and/or use the equation, graph, or table of a polynomial function (including quadratics)

A2.2.2.1.3Determine, use, and/or interpret minimum and maximum values

Graph a function of the form y=ax2+c

Determine the maximum or minimum value of a quadratic equation.

Determine the domain and range of a quadratic equation.

Find the axis of symmetry of a quadratic equation using x=-b/(2a)

Find the vertex of a quadratic equation of the form y=ax2+bx+c.Graph functions of the form y=ax2+bx+c.

Page 247 #1-39


over a specified interval of a graph.

Lesson 5.3F-IF.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

A2.2.2.2.1Identify or describe the effect of changing parameters within a family of functions.

Write a quadratic equation in vertex form.

Write and graph translations of quadratics.

Translate a polynomial from one representation of a function to another (graph, table, and equation)

Page 255 #1-56

Lesson 5.4A-SSE.3aFactor a quadratic expression to reveal the zeros of the function it defines.

A2.1.2.2.1Factor algebraic expressions, including difference of squares and trinomials.

Factor quadratics by factoring out the Greatest Common Factor

Factor algebraic expressions, including difference of squares, difference of trinomials and sum/difference of cubes.

Page 263 #1-48, 50-67

Lesson Radicals ReviewSimplify Radicals Page 266

Lesson 5.5A-SSE.3aFactor a quadratic expression to reveal the zeros of the function it defines.

A-REI.4Solve quadratic equations in one-variable

A-REI.4bSolve quadratic equations by inspection (e.g. x2=49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

A2.1.3.1.1Write and/or solve quadratic equations (including factoring and using the Quadratic Formula)

Solve quadratic equations by factoring and using the Zero-Product Property.

Solve quadratic equations by finding Square Roots.

Solve application problems that require you to understand the zeroes of a function are the x-intercepts of

Page 270 #1-19, 35-53


the graph.

Lesson 5.6N-CN.1Know there is a complex number I such that i2 = -1, and every complex number has a form a+bi with and and b real.

N-CN.2Use the relation i2=-1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

A2.1.1.1.1Simplify / write square roots in terms of I

A2.1.1.1.2Simplify / evaluate expressions involving powers of i.

A2.1.1.2.1Add and subtract complex numbers.

A2.1.1.2.2Multiply and divide complex numbers.

Identify complex numbers.

Add, subtract and multiply complex numbers.

Page 278 #1-53, 57-66

Lesson 5.7A.SSE.3bComplete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

N-CN.7Solve quadratic equations with real coefficients that have complex solutions.

F-IF.8aUse the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

A-REI.4Solve quadratic equations in one variable.

A-REI.4bSolve quadratic equations by inspection (e.g. x2=49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.


Solve a quadratic equation by completing the square, including equations where a≠1.

Rewrite a quadratic equation in vertex form to find the maximum or minimum values.

Page 285 #1-48

Lesson 5.8

Bensalem Township School DistrictAlgebra 2N-CN.7

A-REI.4bSolve quadratic equations by inspection (e.g. x2=49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a+_bi for real numbers a and b.


Solve quadratic equations by using the Quadratic Formula.

Determine the types of solutions by using the discriminant.

Solve quadratic equations using the Quadratic Formula that has complex solutions.

Describe how the solutions of a quadratic equation relate to the graph of the function.

Page 293 #1-40

Chapter 6 Polynomial Functions Suggested Sequence:




Assessment

Lesson 6.1

A-APR.1Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract and multiply polynomials.

Classify polynomials by their degree and number of terms

Write polynomial functions in standard form.

Page 309 #1-12, 25-58

Lesson 6.2 Polynomials and Linear FactorsVocabulary: relative maximum, relative minimum, multiple zero, multiplicity, Factor Theorem


F-IF.7cGraph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F-IF.4For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities , and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts, intervals where the function is increasing , decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity.

A2.1.2.2.1Factor algebraic expressions, including difference of squares and trinomials.

A2.2.1.1.4Identify and / or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increase/ decrease, intercepts, zeros, and asymptotes.

A2.2.2.1.1Create, interpret, and/or use the equation, graph, or table of a polynomial function (including quadratics)

A2.2.2.1.3Determine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential, or logarithmic function.

Rewrite a polynomial in factored form in standard form.

Rewrite a polynomial in standard form in factored form.

Find the zeros of a polynomial equation.

Find the relative maximum and minimum of a polynomial function.

Determine the end behavior of a polynomial function.

Determine the domain and range.

Find the multiplicity of a zero.

Page 317 #1-56

Lesson 6.3 Dividing PolynomialsVocabulary: synthetic division, Remainder TheoremA-APR.6Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x) using inspection or long division.

Use Polynomial Long Division

Use Synthetic Division

Use the Remainder Theorem to evaluate polynomials.

Page 324 #1-55

Lesson 6.4 Solving Polynomial EquationsVocabulary: sum of cubes, difference of cubesA-SSE.3a Factor a quadratic

Factor a sum and / or difference of cubes.

Page 330 #12-32, 42-59

Bensalem Township School DistrictAlgebra 2expression to reveal the zeros of the function it defines.

Solve polynomial equations using sum and/or difference of cubes.

Factor polynomials using a quadratic pattern.

Lesson 6.5 Theorems about Roots of Polynomial EquationsVocabulary: Rational Root Theorem, conjugates, Irrational Root Theorem, complex conjugates, Imaginary RootTheorem, rootsA-APR.2Know and apply the Remainder Theorem.

Use the Rational Root Theorem (p/q test) to find possible rational roots.

Find all rational roots of a polynomial equation.

Use the Irrational Root Theorem to find Irrational Roots

Find the imaginary roots of a polynomial equation.

Write a polynomial equation from the given roots.

Page 339 #1-31


Chapter 7: Radical Functions and Rational Exponents Suggested Sequence:




Assessment

Lesson Properties of Exponents

A2.1.2.1.2Simplify / evaluate expressions involving positive and negative exponents and / or roots.

A2.1.2.1.3Simplify / evaluate expressions involving multiplying with exponents, powers of powers, and powers of products.

Review the Properties of Exponents from Algebra 1

Page 368

Lesson 7-1 Roots and Radical ExpressionsVocabulary: nth root, radicand, index, principal root

A2.1.2.1.2Simplify / evaluate expressions involving positive and negative exponents and / or roots.

A2.1.2.1.3Simplify / evaluate expressions involving multiplying with exponents, powers of powers, and powers of products.

Find real-number roots.

Simplify Radical Expressions, more than just square roots.

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Lesson 7-2 Multiplying and Dividing Radical ExpressionsVocabulary: rationalize the denominator

Multiply radical expressions.

Simplify radical expressions.

Divide radical expressions.

Page 377 #1-54


Rationalize the denominator – square and cube root denominators only

Lesson 7-3 Binomial Radical ExpressionsVocabulary: like radicals

Add and subtract like radicals.

Simplify radicals before adding and subtracting.

Multiply Binomial Radical Expressions.

Multiply Conjugates.

Rationalize Binomial Radical Denominators.

Page 382 #1-44

Lesson 7-4 Rational ExponentsVocabulary: rational exponent

A2.1.2.1.1Use exponential expressions to represent rational numbers.

Simplify Expressions with Rational Exponents.

Convert to and from Radical Form.

Simplify numbers with rational exponents.

Write expressions in simplest form.

Page 388 #1-25, 20-76

Lesson 7-5 Solving Square Root and other Radical EquationsVocabulary: radical equation, square root equation, extraneous solution

A2.1.3.1.2Solve equations involving rational and / or radical expressions.

Solve square root equations.

Solve radical equations.

Solve radical equation with rational exponents.

Page 394 #1-30, 34-42

Lesson 7-6 Function OperationsVocabulary: composite functionF-BF.1Write a function that describes a relationship between two quantities.


Add and subtract functions.

Multiply and divide functions.

Evaluate composite functions.

Find the domain of a function.

Pages 400-402, #1-68

Lesson 7-7 Inverse Relations and FunctionsVocabulary: inverse relations, inverse functions



Find the inverse of a relation.

Graph a relation and its inverse.

Find the domain and range of a relation and its inverse.

Evaluate the composition of Inverse Functions.

Page 410 #1-43

Lesson 7-8 Graphing Square Root and Other Radical FunctionsVocabulary: radical function, square root function


Graph a square root function.

Graph cube root functions.

Page 417 #1-24

Probability and Data Analysis Suggested Sequence: 9 Days

Common Core Standards

PAStandards

Skills Required Activities

Lesson 1.6 Simple Probability

2.4.HS.B4 – recognize and evaluate random processes underlying statistical experiments

2.4.HS.B7 – apply rules of probability to compute probabilities of compound events in a uniform probability model

A2.2.3.2.3Use probability for independent, dependent, or compound events to predict outcomes.

A2.2.3.2.3Use probability for independent, dependent, or compound events to predict outcomes.

Compare and contrast experimental/theoretical probability

Use mathematical concepts to find theoretical probability

Use geometric concepts to find theoretical probability

Pg 39. Hands On ActivityPg 42-43 1-20, 24-33

Lesson 6.7 Permutations and Combinations

2.4.HS.B4 – A2.2.3.2.1Use combinations,

Define and find permutation/combinations Pg 348 1,5,7,14-


recognize and evaluate random processes underlying statistical experiments

2.4.HS.B7 – apply rules of probability to compute probabilities of compound events in a uniform probability model

permutations, and the fundamental counting principal to solve problems involving probability.

Show how to determine whether a situation involves a permutation or a combination.

Show how to mathematically solve permutations and combinations using given formulas

20,25-32,46-49

Lesson 12.1 Probability Distribution

2.4.HS.B.1 – summarize, represent, and interpret data on a single count or measurement variable

2.4.HS.B.3 – Analyze linear models to make interpretations based on the data

2.4.HS.B.5 – make inferences and justify conclusions based on sample surveys, experiments, and observational studies

A1.2.3.2.1 – Estimate or calculate to make predictions based on a circle, line, bar graph, measure of central tendency, or other representations.

-show students how to read problems and make frequency tables

-explain what is meant by probability distribution and how we use

-use probability distribution to answer questions based on problems presented

Pg 651-6521-5, 7-10, 16

Lesson 12.3 Analyzing Data(2 days)2.4.HS.B.1 – summarize, represent, and interpret data on a single count or measurement variable

2.4.HS.B.3 – Analyze linear


-show what are the measures of central tendencies and what each means

-explain how to use and how to mathematically find measures of central tendencies

-explain what is meant by

Pg 664-6661,4,6,8,10-12,16-17,19,21

Bensalem Township School DistrictAlgebra 2models to make interpretations based on the data


A1.2.3.2.3 – make predictions using the equations of graphs of best-fit lines of scatter plots

A1.2.3.2.2 – analyze data, make predictions, and/or answer questions based on displayed data (box-and-whiskers plots, stem-and-leaf plots, scatter plots, measure of central tendency, etc.)

quartiles and how to find each by splitting up the dat

-show how to create a Box and Whiskers graph

-discuss what is meant by Percentiles, how to find them, and how to use them

Lesson 12.4 Standard Deviation(2 days)2.4.HS.B.1 – summarize, represent, and interpret data on a single count or measurement variable

2.4.HS.B.3 – Analyze linear models to make interpretations based on the data


A1.2.3.1.1 – calculate and/or interpret the range, quartiles, and interquartile range of data


-explain what is meant by range of data

-show how to find range

-explain what is meant by interquartile range and how to find it

-define standard deviation and show where and when we use it

-show mathematically how to find S.D. and how we need to us it to make distribution charts

Pg 668 ActivityPg 672-673 1-5, 8-9,17-19

Lesson 12.7 Normal Distribution

2.4.HS.B.1 – summarize, represent, and interpret data on a single count or measurement variable

2.4.HS.B.3 – Analyze linear

A1.2.3.1.1 – calculate and/or interpret the range, quartiles, and interquartile range of data

A1.2.3.2.1 – Estimate or calculate to make

-explain what normal distribution is and why we use it

-show how to make a bell curve using S.D.

Pg 695 1,3,5-8, 15

Bensalem Township School DistrictAlgebra 2models to make interpretations based on the data


predictions based on a circle, line, bar graph, measure of central tendency, or other representations.

· web viewf-if.7c graph polynomial functions, identifying zeros when suitable factorizations are...

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