hardin county schools 2019-2020 algebra ii pacing guide

Hardin County Schools

Algebra II of 9 2019-2020

2019-2020 Algebra II Pacing Guide

Big Idea(s) and Topic(s) Student-Friendly Learning Targets ***The pacing included in this document is flexible, and should be adjusted as needed to meet the individual needs of your students,

as well as to allow for sufficient time for assessment and re-teaching as needed.

Introductory Unit Trimester: 3 weeks

•Create equations and inequalities in one variable and use them tosolve problems. (A.CED.1, F.BF.1)

•Create, model and solve systems of equations and inequalities.(A.CED.2, A.REI.11) •Create equations and inequalities in two variables and use themto represent relationships between quantities including scatterplots. (A.CED.2)

•Represent constraints for and interpret solutions for systems ofequations and inequalities using linear programming. (A.CED.3)

•Rearrange formulas to solve for specific variables. (A.CED.4)

Introductory Unit A.CED.1I can identify the variables and quantities represented in a real-world problem.I can determine the best model for the real-world problem (linear equation, linear inequality).I can write the equation or inequality that best models the problem.I can solve the equation or inequality.I can interpret the solution in the context of the problem.A.CED.2I can identify the variables and quantities in a real world problem.I can determine the best model for a linear real-world problem.I can write the equation that best models the problem.I can set up coordinate axes using an appropriate scale and label the axes.I can graph equations on coordinate axes with appropriate label and scales.A.CED.3I can recognize when to use constraints to model a problem.I can interpret solutions in the context of the situation modeled and decide if they arereasonable.I can determine when a problem should be represented by an equation, inequality or systemof either.I can represent constraints by equations, inequalities or systems of either.A.CED.4I can define the variable to be isolated.I can identify operations necessary to isolate the variable.I can solve formulas for a specified variable.A.REI.11I can explain that a point of intersection on the graph of a system of equations, y = f(x) and y= g(x), represents a solution to both equations.I can determine that since y = f(x) and y = g(x), then f(x) = g(x) by the substitution property.I can determine that the x-coordinate of the points of intersection for y = f(x) and y = g(x)are also solutions for f(x) and g(x).I can use a graphing calculator to determine the approximate solutions to a system ofequations f(x) and g(x).



•Graph linear equations and show key features of graphs. (F.IF.4,F.IF.7)

•Calculate and interpret the average rate of change for a linearfunction. (F.IF.6)

Interpreting Functions

Trimester: 1.5 weeks;

•Graph piece-wised defined functions, step functions and absolutevalue functions and show key features of the graphs. (F.IF.4,F.IF.7, 7b)

•Relate the domain of a function to its graph and the quantitativerelationship it describes. (F.IF.5)

•Identify the effect of algebraic transformations on graphs ofabsolute value functions. (F.BF.3)

F.IF.4I can identify x and y intercepts.I can interpret the meaning of an ordered pair related to any given function, table or graph.

F.IF.6I can recognize slope as an average rate of change.I can calculate the average rate of change of a function (presented symbolically or as a table)over a specified interval.I can estimate the rate of change from a graph.I can interpret the average rate of change of a function (presented symbolically or as a table)

over a specified interval.F.IF.7I can graph linear functions by hand and show key features of the graphs such as interceptsand slopes.F.BF.1I can write a linear function which describes a relationship between two quantities.

Interpreting Functions F.IF.4I can identify x and y intercepts.I can interpret the meaning of an ordered pair related to any given function, table or graph.F.IF.5I can identify and describe the domain of the function given the graph or a verbal written

description of a function.I can explain why a domain is appropriate for a given situation.I can explain how the domain of a function is represented in its graph.F.IF.7bI can graph piecewise defined functions, including step functions and absolute value functions,by hand in simple cases or using technology for more complicated cases, and show/label keyfeatures of the graph.I can compare and contrast the domain and range of absolute value, step and piecewisedefined functions.I can identify type of function to be graphed.F.BF.3I can identify effects of single transformations on graphs of functions, using technology.

I can graph a given function by replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) forspecific values of k (both positive and negative).I can identify the effect on the graph given a single transformation on a function (symbolic orgraphic).I can describe the differences and similarities between a parent function and the transformedfunction.I can find the value of k, given the graphs of a parent function, f(x), and the transformedfunction: f(x) + k, k f(x), f(kx), or f (x + k).I can experiment with cases and illustrate an explanation of the effects on the graph usingtechnology.

Rectangular Numbers, Triangle Patterns



Quadratic Functions Trimester – 5 weeks:

•Recognize and perform operations using complex numbers andwrite in a + bi form.(N.CN.1, N.CN.2)

•Interpret parts of an expression such as terms, factors andcoefficients. (A.SSE.1) •Solve for the zeroes of quadratic equations using square rootsand factoring. (A.SSE.2, F.IF.8a) •Graph quadratic functions and show key features. (F.IF.4, F.IF.7)Identify the effect of algebraic transformations on graphs ofquadratic functions. (F.BF.3)

•Create and model quadratic equations. (A.CED.1, A.CED.2)

•Solve for the zeroes of quadratic equations by completing thesquare and using the quadratic formula (include complexsolutions) (F.IF.8a. N.CN.7)

Quadratic Functions

N.CN.1I can identify and apply the definition of a complex number.I can write imaginary numbers in standard form (a+bi).N.CN.2I can recognize how the rules for real numbers relate to complex numbers.I can simplify algebraic expressions using the formula i2 = -1.N.CN.7I can solve quadratic equations that have complex solutions.

A.SSE.1I can interpret the individual parts of the expressions based on the context of the problem.

A.SSE.1aI can define and recognize parts of an expression such as terms, factors, and coefficients.

A.SSE.2I can identify ways to write expressions, such as difference of squares, factoring out acommon monomial, regrouping, etc.I can verify that two expressions are equivalent.I can apply models for factoring and multiplying polynomials to rewrite expressions.A.CED.1I can identify the variables and quantities represented in a real-world problem.I can determine the best model for the real-world problem (linear equation, linear inequality,quadratic equation).I can write the equation or inequality that best models the problem.I can solve the equation or inequality.I can interpret the solution in the context of the problem.A.CED.2I can identify the variables and quantities in a real world problem.I can determine the best model for the real-world problem (e.g. linear, quadratic).I can write the equation that best models the problem.I can set up coordinate axes using an appropriate scale and label the axes.I can graph equations on coordinate axes with appropriate label and scales.F.IF.8a

I can identify the key features of a quadratic function.I can find zeros, extreme values, and line of symmetry of the graph of a quadratic function.



Polynomial Functions Trimester – 2.5 weeks

•Interpret parts of an expression. (A.SSE.1a)•Solve polynomial functions for zeroes by factoring. (A.SSE.2, A.APR.4)

•Add, subtract and multiply polynomials. (A.APR.1)

•Apply the Remainder Theorem using long and synthetic division.(A.APR.2, A.APR.6)

•Identify zeroes of polynomials from given factorizations.(A.APR.3)

•Graph polynomial functions identifying key features such asintercepts, degree, multiplicity, end behavior and increasingdecreasing intervals. (F.IF.4, F.IF.7c)

End of 1st Trimester End of 1st Semester

Polynomial Functions A.SSE.1aI can define and recognize parts of an expression such as terms, factors, and coefficients.A.SSE.2I can identify ways to write expressions, such as difference of squares, factoring out acommon monomial, regrouping, etc.I can verify that two expressions are equivalent.I can apply models for factoring and multiplying polynomials to rewrite expressions.I can identify ways to rewrite rational expressions (i.e. conjugates).

A.APR.1I can define “closure”.I can add, subtract, and multiply two polynomials to always obtain a polynomial.A.APR.2I can define the remainder theorem for polynomial division and divide polynomials.I can divide p(x) by (x – a) to find p(a), given a polynomial p(x) and a number a.I can apply the remainder theorem and conclude that p(x) is divisible by (x – a) if and only ifp(a) = 0.A.APR.3I can identify the zeros of factored polynomials.I can identify the multiplicity of the zeros of a factored polynomial.I can explain now the multiplicity of zeros determines how the graph will behave when itapproaches and leaves the x-intercept.

I can sketch a rough graph using the zeros of a polynomial and other easily identifiable pointssuch as the y-intercept.A.APR.6I can simplify rational expressions using long division.F.IF.4I can identify the type of function, given its table or graph.I can create a graph that matches the description and indicates all the key features of thefunction.I can define the increasing and decreasing intervals of a table or a graph.I can identify the relative max or min on a table or a graph.I can identify x and y intercepts.I can interpret the meaning of an ordered pair related to any given function, table or graph.

I can determine and interpret end behavior of a graph.F.IF.7cI can graph polynomials by hand labeling maxima/minima, zeros, and showing end behavior.I can use technology to graph complicated polynomial functions when appropriate.I can relate the relationship between the zeros of a quadratic and its factors to polynomials ofhigher degree.



Rational Exponents and Radical Equations

Trimester – 2 weeks

•Use and apply properties of integer and rational exponentsincluding nth roots. (N.RN.2)

•Solve radical equations in one variable and identify extraneoussolutions. (A.REI.2)

•Graph square root and cube root functions. (F.IF.7b)

•Find inverse functions. (F.BF.4)

Exponential and Logarithmic Functions Trimester – 3 weeks

•Create and solve simple exponential equations. (A-CED 1)

•Use technology to solve systems of equations which includeexponential and logarithmic functions. (A.REI.11)

Rational Exponents and Radical Equations

N.RN.2I can apply the properties of exponents to simplify algebraic expressions with integerexponents.I can apply the properties of exponents to simplify algebraic with rational exponents.I can write radical expressions with rational exponents.

I can write expressions with rational exponents as radical expressions.A.REI.2I can determine the domain of a radical function.I can solve radical equations in one variable.I can define extraneous solutions.I can determine which numbers cannot be solutions of a radical equation and explain whythey cannot be solutions.F.IF.7bI can graph square root and cube root functions, including step, by hand in simple cases orusing technology for more complicated cases, and show/label key features of the graph.I can identify the type of function to be graphed.F.BF.4aI can define inverse functions.

I can determine if a function has an inverse.I can write the inverse of a function

Exponential and Logarithmic Functions

A.CED.1I can identify the variables and quantities represented in a real-world problem.I can determine the best model for the real-world problem (linear equation, linear inequality,quadratic equation, rational equation, exponential equation).I can write the equation or inequality that best models the problem.I can solve the equation or inequality.I can interpret the solution in the context of the problem.

A.REI.11I can recognize and use function notation to represent linear, polynomial, rational, absolutevalue, exponential, and radical equations.I can explain that a point of intersection on the graph of a system of equations, y = f(x) and y= g(x), represents a solution to both equations.I can determine that since y = f(x) and y = g(x), f(x) = g(x) by the substitution property.I can determine that the x-coordinate of the points of intersection for y = f(x) and y = g(x)are also solutions for f(x) and g(x).I can use a graphing calculator to determine the approximate solutions to a system ofequations f(x) and g(x).



•Graph exponential functions using technology identifying endbehavior and intercepts (include exponential growth and decayapplications). ( F.IF.4, F-IF 7e, F.BF.1)

•Evaluate logarithmic expressions using a calculator for bases of10 or e and change of base formula for base of 2. (F.LE.4)

Rational Functions Trimester – 1.5 weeks

•Rewrite simple rational expressions in different forms usingaddition, subtraction, multiplication and division. (A.APR.6)

•Create and solve simple rational equations in one variableidentifying extraneous solutions. (A.CED.1, A.REI.2) •Use technology to graph systems of rational functions, maketables of values and calculate points of intersection. (A.REI.11)

F.IF.4I can identify the type of function, given its table or graph.I can create a graph that matches the description and indicates all the key features of thefunction.I can define the increasing and decreasing intervals of a table or a graph.I can identify the relative max or min on a table or a graph.I can identify x and y intercepts.I can interpret the meaning of an ordered pair related to any given function, table or graph.I can determine and interpret end behavior of a graph.

F.IF.7eI can graph exponential, logarithmic and trigonometric functions by hand in simple cases.I can graph exponential logarithmic and trigonometric functions using technology forcomplicated cases.I can identify intercepts and end behavior of exponential and logarithmic functions.I can identify period, midline, and amplitude of trigonometric functions.I can distinguish between simple and complicated exponential, logarithmic and trigonometricfunctions to know when to use technology to graph.I can identify domain and range of exponential, logarithmic and trigonometric functions.F.BF.1bI can create functions that represent relationships in real-world situations and relate thefunction to the context of the problem.F.LE.4

I can recognize the laws and properties of logarithms, including change of base.I can recognize and describe the key features logarithmic functions.I can recognize and know the definition of a logarithm base b.I can evaluate a logarithm using technology.I can express as a logarithm the solution to a · bct = d, where a, b and d are numbers and thebase is 2, 10, or e for exponential models.

Rational Functions

A.APR.6I can determine the best method of simplifying the given rational expression (inspection, long

division, computer algebra system).I can simplify rational expressions by inspection.I can simplify rational expressions using long division.A.CED.1I can identify the variables and quantities represented in a real-world problem.I can determine the best model for the real-world problem (linear equation, linear inequality,quadratic equation, rational equation, exponential equation).I can write the equation or inequality that best models the problem.I can solve the equation or inequality.I can interpret the solution in the context of the problem.



•Find inverse functions. (F.BF.4)

Geometric Sequences and Series Trimester – 0.5 week

•Derive the formula for the sum of a finite geometric series anduse the formula to solve problems involving real world situations.(A.SSE.4)

Statistics Trimester – 2 weeks

•Use the mean and standard deviation to fit data to a normaldistribution. (S.ID.4) •Recognize situations for which the normal curve is not anappropriate representation. (S.ID.4)

•Understand statistics as a process for making inferences aboutpopulation parameters based on random samples. (S.IC.1)

A.REI.2I can determine the domain of a rational function.I can solve rational equations in one variable.I can define extraneous solutions.I can determine which numbers cannot be solutions of a rational equation and explain whythey cannot be solutions.I can generate examples of rational equations with extraneous solutions.A.REI.11I can recognize and use function notation to represent linear, polynomial, rational, absolutevalue, exponential, and radical equations.I can explain that a point of intersection on the graph of a system of equations, y = f(x) and y

= g(x), represents a solution to both equations.I can determine that since y = f(x) and y = g(x), f(x) = g(x) by the substitution property.I can determine that the x-coordinate of the points of intersection for y = f(x) and y = g(x)are also solutions for f(x) and g(x).I can use a graphing calculator to determine the approximate solutions to a system ofequations f(x) and g(x).F.BF.4I can define inverse function.I can determine if a function has an inverse.I can write the inverse of a function

Geometric Sequences and Series

A.SSE.4I can define a finite geometric series and common ratio.I can derive the formula for the sum of a finite geometric series; Sn = a1 (1 – rn/1 – r).I can express and calculate the sum of a finite geometric series. I can recognize real-world situations that are modeled by geometric sequences and apply the formula for the sum of a finite geometric series.

Statistics

S.ID.4

I can describe the characteristics of a normal distribution.I can use a calculator, spreadsheet, and table to estimate the areas under the normal curve.I can use the mean and standard deviation of a data set to fit it to a normal distribution.I can use a normal distribution to estimate population percentages.I can recognize that there are data sets for which such a procedure is not appropriate.S.IC.1I can define/describe the uses of statistics.I can explain the importance of a random sample to draw conclusions about a population.



•Decide if a specified model is consistent with data generatedresults. (S.IC.2)

•Recognize the purposes of and differences among samplesurveys, experiments and observational studies. (S.IC.3)

•Use data from a sample survey to estimate a population mean.(S.IC.4)

•Use data from a randomized experiment to compare twotreatments and use simulations to decide if differences betweenparameters are significant. (S.IC.5)

•Evaluate reports based on data. (S.IC.6)

Trigonometry Trimester – 2 weeks

•Understand radian measure of an angle as the length of the arcon the unit circle. (F.TF.1)

•Explain how the unit circle can be used to evaluate trig functionsof all real number angle measures. (F.TF.2)

•Choose trigonometric functions to model periodic phenomenawith specified amplitude, frequency and midline. (F.TF.5)

S.IC.2I can recognize data that various models produce.I can identify data or discrepancies that provide the basis for rejecting a statistical model.I can choose probability model for a probability simulation.I can decide if the data collected is consistent with the selected model or if another model isrequired.S.IC.3I can define and describe the purpose of a sample survey, an experiment, and anobservational study.I can explain the role of randomization in sample surveys, experiments, and observationalstudies.

I can describe the differences among sample surveys, experiments, and observational studies.I can apply random sampling techniques to draw a sample from a population.S.IC.4I can explain the relation of margin of error to variation within a set of data.I can use a simulation model to generate data for random sampling.I can use data from a sample survey to estimate a population mean or proportion.I can interpret the data generated by a simulation model in terms of the context.I can develop a margin of error.S.IC.5I can use the confidence interval to determine if the parameters are significantly differentbased on the original difference of means.I can use data from a randomized experiment to compare two treatments.I can choose the appropriate method to simulate a randomized experiment.

I can establish a reasonable level of significance.S.IC.6I can define population, population parameter, random sample, and inference. I can drawconclusions based on graphical and numerical summaries.I can explain why randomization is used to draw a sample that represents a population well.I can recognize that statistics involves drawing conclusions about a population based on theresults obtained from a random sample of the population.

Trigonometry F.TF.1I can define the terminal and initial side of an angle on the unit circle.I can define the radian measure as the length of the arc of the unit circle.

F.TF.2I can identify the relationship between the central angle and the arc length of a unit circle ona number line.I can apply the properties of the unit circle to the trigonometric functions.F.TF.5I can define amplitude, frequency, and midline of a trigonometric function.I can explain the connection between frequency and period.I can recognize real-world situations that can be modeled with a periodic function byidentifying the amplitude, frequency (or period) and midline.I can write a function notation for the trigonometric function that models a problem situation,



•Prove the Pythagorean identity

sin 2 + cos

2 = 1 and use it to find other trig function values.

(F.TF.8)

given the amplitude, frequency (or period), and midline of a periodic situation. F.TF.8I can define trigonometric rations as related to the unit circle.I can prove the Pythagorean identify sin2 (θ ) + cos2 (θ) = 1.I can use the Pythagorean identity, sin2 (θ) + cos2 (θ) = 1, to find sin (θ), cos (θ), or tan (θ ),given sin (θ ), cos (θ), or tan (θ), and the quadrant of the angle.

hardin county schools 2019-2020 algebra ii pacing guide

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