Algebra II Pacing Guide

Algebra II Pacing Guide

 

South Carolina College-and Career-Ready

Algebra 2

Mathematical Process Standards

 

Standards

Explanations   and Examples

1. Make sense of problems and persevere in   solving them.

 

 

a. Relate a problem to prior knowledge.

b. Recognize there may be multiple entry points to a problem and   more than one path to a solution.

c. Analyze what is given, what is not given, what is being   asked, and what strategies are needed, and make an initial attempt to solve a   problem.

d. Evaluate the success of an approach to solve a problem and   refine it if necessary.

 

2. Reason both contextually and abstractly.

 

 

a. Make sense of quantities and their relationships in   mathematical and real-world situations.

b. Describe a given situation using multiple mathematical   representations.

c. Translate among multiple mathematical representations and   compare the meanings each representation conveys about the situation.

d. Connect the meaning of mathematical operations to the context   of a given situation.

 

3. Use critical thinking skills to justify   mathematical reasoning and critique the reasoning of others.

 

 

a. Construct and justify a solution to a problem.

b. Compare and discuss the validity of various reasoning   strategies.

c. Make conjectures and explore their validity.

d. Reflect on and provide thoughtful responses to the reasoning   of others.

 

 

 

 

 

 

 

 

 

 

Standards

Explanations   and Examples

4. Connect mathematical ideas and real-world   situations through modeling.

 

 

a. Identify relevant quantities and develop a model to describe   their relationships.

b. Interpret mathematical models in the context of the   situation.

c. Make assumptions and estimates to simplify complicated   situations.

d. Evaluate the reasonableness of a model and refine if   necessary.

 

5. Use a variety of mathematical tools   effectively and strategically.

 

 

a. Select and use appropriate tools when solving a mathematical   problem.

b. Use technological tools and other external mathematical   resources to explore and deepen understanding of concepts.

 

6. Communicate mathematically and approach   mathematical situations with precision.

 

 

a. Express numerical answers with the degree of precision   appropriate for the context of a situation.

b. Represent numbers in an appropriate form according to the   context of the situation.

c. Use appropriate and precise mathematical language.

d. Use appropriate units, scales, and labels.

 

7. Identify and utilize structure and   patterns.

 

 

a. Recognize complex mathematical objects as being composed of   more than one simple object.

b. Recognize mathematical repetition in order to make   generalizations.

c. Look for structures to interpret meaning and develop solution   strategies.

 

 

 

 

WCSD   Pacing Guide

Algebra   2-CP

SCCCRS

1st   Quarter

SCCCRS Algebra 2

Unit 1 – Functions:   Arithmetic/Geometric Sequences and Absolute Value, Step, and Piece-Wise   Functions

                                         
   

A2.FBF.1*    

   
   

Write a     function that describes a relationship between two quantities.

   

(Note:     IA.FBF.1a is not a Graduation Standard.)

   

a.     Write a function that models a relationship between two quantities using     both explicit expressions and a recursive process and

   

by     combining standard forms using addition, subtraction, multiplication and     division to build new functions.

   
   

A2.FBF.2*    

   
   

Write     arithmetic and geometric sequences both recursively and with an explicit     formula, use them to model situations, and

   

translate     between the two forms.

   
   

A2.FBF.3*    

   
   

Describe     the effect of the transformations ??(?), ?(?)+?, ?(?+?), and     combinations of such transformations on the graph of

   

?=?(?)     for any real number ?. Find     the value of ? given the graphs and write the equation of a     transformed parent function

   

given     its graph.

   

 

                                                                     
   

A2.FIF.3*    

   
   

Define     functions recursively and recognize that sequences are functions, sometimes     defined recursively, whose domain

   

is a     subset of the integers.

   
   

A2.FIF.7*    

   
   

Graph     functions from their symbolic representations. Indicate key features     including intercepts; intervals where the

   

function     is increasing, decreasing, positive, or negative; relative maximums and     minimums; symmetries; end behavior

   

and     periodicity. Graph simple cases by hand and use technology for complicated     cases.

   
   

A2.FIF.9*    

   
   

Compare     properties of two functions given in different representations such as     algebraic, graphical, tabular, or verbal.

   
   

A2.FLQE.2*    

   
   

Create     symbolic representations of linear and exponential functions, including     arithmetic and geometric sequences,

   

given     graphs, verbal descriptions, and tables.

   
   

A2.FLQE.5*    

   
   

Interpret     the parameters in a linear or exponential function in terms of the context.    

   

 

Unit 2 –Linear Equations/Inequalities and   Systems of Equations/Inequalities

                                                       
   

A2.ACE.1*    

   
   

Create     and solve equations and inequalities in one variable that model real-world     problems involving linear, quadratic, simple

   

rational,     and exponential relationships. Interpret the solutions and determine     whether they are reasonable.

   
   

A2.ACE.2*    

   
   

Create     equations in two or more variables to represent relationships between     quantities. Graph the equations on coordinate axes

   

using     appropriate labels, units, and scales.

   
   

A2.ACE.3    

   
   

Use     systems of equations and inequalities to represent constraints arising in     real-world situations. Solve such systems using

   

graphical     and analytical methods, including linear programing. Interpret the solution     within the context of the situation.

   

(Limit     to linear programming.)

   
   

A2.ACE.4*    

   
   

Solve     literal equations and formulas for a specified variable including equations     and formulas that arise in a variety of disciplines.

   

 

Unit 3 – Polynomials

                           
   

A2.AAPR.1*    

   
   

Add,     subtract, and multiply polynomials and understand that polynomials are     closed under these operations.

   
   

A2.AAPR.3    

   
   

Graph     polynomials identifying zeros when suitable factorizations are available     and indicating end behavior. Write a polynomial

   

function     of least degree corresponding to a given graph. (Limit to polynomials with     degrees 3 or less.)

   

 

                           
   

A2.ASE.1*    

   
   

Interpret     the meanings of coefficients, factors, terms, and expressions based on     their real-world contexts. Interpret complicated

   

expressions     as being composed of simpler expressions.

   
   

A2.ASE.2*    

   
   

Analyze     the structure of binomials, trinomials, and other polynomials in order to     rewrite equivalent expressions.

   

 

Unit 4-Quadratic Functions, Equations, and Inequalities

                                                       
   

A2.ACE.1*    

   
   

Create     and solve equations and inequalities in one variable that model real-world     problems involving linear, quadratic, simple

   

rational,     and exponential relationships. Interpret the solutions and determine     whether they are reasonable.

   
   

A2.ACE.2*    

   
   

Create     equations in two or more variables to represent relationships between     quantities. Graph the equations on coordinate axes

   

using     appropriate labels, units, and scales.

   
   

A2.ACE.3    

   
   

Use     systems of equations and inequalities to represent constraints arising in real-world     situations. Solve such systems using

   

graphical     and analytical methods, including linear programing. Interpret the solution     within the context of the situation.

   

(Limit     to linear programming.)

   
   

A2.ACE.4*    

   
   

Solve     literal equations and formulas for a specified variable including equations     and formulas that arise in a variety of disciplines.

   

 

                                         
   

A2.AREI.4*    

   
   

Solve     mathematical and real-world problems involving quadratic equations in one     variable.

   

b.     Solve quadratic equations by inspection, 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     ?+?? for real numbers ? and ?. (Note:     A2.AREI.4b is not a Graduation Standard.)

   
   

A2.AREI.7    

   
   

Solve a     simple system consisting of a linear equation and a quadratic equation in     two variables algebraically and graphically.

   

Understand     that such systems may have zero, one, two, or infinitely many solutions.     (Limit to linear equations and quadratic

   

functions.)    

   
   

A2.AREI.11*    

   
   

Solve     an equation of the form ?(?)=?(?) graphically     by identifying the ?-coordinate(s) of the point(s) of intersection of the

   

graphs     of ?=?(?) and ?=?(?).

   

 

             
   

A2.ASE.3*    

   
   

Choose     and produce an equivalent form of an expression to reveal and explain     properties of the quantity represented by the

   

expression.    

   

(Note:     A2.ASE.3b and 3c are not Graduation Standards.)

   

b.     Determine the maximum or minimum value of a quadratic function by     completing the square.

   

 

   

 

                                         
   

A2.FBF.1*    

   
   

Write a     function that describes a relationship between two quantities.

   

(Note:     IA.FBF.1a is not a Graduation Standard.)

   

a.     Write a function that models a relationship between two quantities using     both explicit expressions and a recursive process and

   

by     combining standard forms using addition, subtraction, multiplication and     division to build new functions.

   

b.     Combine functions using the operations addition, subtraction,     multiplication, and division to build new functions that describe

   

 the relationship between two quantities in     mathematical and real-world situations.

   

 

   
   

A2.FBF.2*    

   
   

Write     arithmetic and geometric sequences both recursively and with an explicit     formula, use them to model situations, and

   

translate     between the two forms.

   
   

A2.FBF.3*    

   
   

Describe     the effect of the transformations ??(?), ?(?)+?, ?(?+?), and     combinations of such transformations on the graph of

   

?=?(?)     for any real number ?. Find     the value of ? given the graphs and write the equation of a     transformed parent function

   

given     its graph.

   

 

                                                       
   

A2.FIF.3*    

   
   

Define     functions recursively and recognize that sequences are functions, sometimes     defined recursively, whose domain is a subset

   

 of the integers.

   
   

A2.FIF.4*    

   
   

Interpret     key features of a function that models the relationship between two     quantities when given in graphical or tabular form.

   

Sketch     the graph of a function from a verbal description showing key features. Key     features include intercepts; intervals where

   

the     function is increasing, decreasing, constant, positive, or negative;     relative maximums and minimums; symmetries; end

   

behavior     and periodicity.

   
   

A2.FIF.5*    

   
   

Relate     the domain and range of a function to its graph and, where applicable, to     the quantitative relationship it describes.

   
   

A2.FIF.6*    

   
   

Given a     function in graphical, symbolic, or tabular form, determine the average     rate of change of the function over a specified

   

interval.     Interpret the meaning of the average rate of change in a given context.

   

 

                           
   

A2.FIF.8*    

   
   

Translate     between different but equivalent forms of a function equation to reveal and     explain different properties of the function.

   

(Note:     A2.FIF.8b is not a Graduation Standard.)

   

b.     Interpret expressions for exponential functions by using the properties of     exponents.

   

 

   
   

A2.FIF.9*    

   
   

Compare     properties of two functions given in different representations such as     algebraic, graphical, tabular, or verbal.

   

 

                           
   

A2.NCNS.1*    

   
   

Know     there is a complex number ? such that ?2=−1, and     every complex number has the form ?+??     with ? and ? real.

   
   

A2.NCNS.7*    

   
   

Solve     quadratic equations in one variable that have complex solutions.

   

 

 

 

WCSD   Pacing Guide

Algebra   2-CP

SCCCRS

2nd   Quarter

Unit   5: Radical and Simple Rational Functions and Equations

                           
   

A2.ACE.1*    

   
   

Create     and solve equations and inequalities in one variable that model real-world     problems involving linear, quadratic, simple rational, and exponential     relationships. Interpret the solutions and determine whether they are     reasonable.

   
   

A2.ACE.4*    

   
   

Solve     literal equations and formulas for a specified variable including equations     and formulas that arise in a variety of disciplines.

   

 

                           
   

A2.AREI.2*    

   
   

Solve     simple rational and radical equations in one variable and understand how     extraneous solutions may arise.

   
   

A2.AREI.11*    

   
   

Solve     an equation of the form ?(?)=?(?) graphically     by identifying the ?-coordinate(s) of the point(s) of intersection of the     graphs of ?=?(?) and ?=?(?).

   

 

             
   

A2.FBF.1*

   

 

   

 

   

 

   

 

   

 

   

A2.FBF.3* 

   
   

Write     a function that describes a relationship between two quantities.

   

(Note:     IA.FBF.1a is not a Graduation Standard.)

   

a.     Write a function that models a relationship between two quantities using     both explicit expressions and a recursive process and by combining standard     forms using addition, subtraction, multiplication and division to build new     functions.

   

b.     Combine functions using the operations addition, subtraction,     multiplication, and division to build new functions that describe the     relationship between two quantities in mathematical and real-world     situations.

                             
     

 

     
     

Describe       the effect of the transformations ??(?), ?(?)+?, ?(?+?),       and combinations of such transformations on the graph of ?=?(?)       for any real number ?.       Find the value of ? given the graphs and write the equation of a       transformed parent function given its graph.

     
   

 

   

 

                                                                     
   

A2.FIF.4*    

   
   

Interpret     key features of a function that models the relationship between two     quantities when given in graphical or tabular form. Sketch the graph of a function     from a verbal description showing key features. Key features include     intercepts; intervals where the function is increasing, decreasing,     constant, positive, or negative; relative maximums and minimums;     symmetries; end behavior and periodicity.

   
   

A2.FIF.5*    

   
   

Relate     the domain and range of a function to its graph and, where applicable, to     the quantitative relationship it describes.

   
   

A2.FIF.6*    

   
   

Given     a function in graphical, symbolic, or tabular form, determine the average     rate of change of the function over a specified interval. Interpret the     meaning of the average rate of change in a given context.

   
   

A2.FIF.7*    

   
   

Graph     functions from their symbolic representations. Indicate key features     including intercepts; intervals where the function is increasing, decreasing,     positive, or negative; relative maximums and minimums; symmetries; end     behavior and periodicity. Graph simple cases by hand and use technology for     complicated cases.

   
   

A2.FIF.8*    

   
   

Translate     between different but equivalent forms of a function equation to reveal and     explain different properties of the function.

   

(Note:     A2.FIF.8b is not a Graduation Standard.)

   

b.     Interpret expressions for exponential functions by using the properties of     exponents.

   

 

   

 

Unit 6:Exponential Functions and   Equations

                                                       
   

A2.ACE.1*    

   
   

Create     and solve equations and inequalities in one variable that model real-world     problems involving linear, quadratic, simple rational, and exponential     relationships. Interpret the solutions and determine whether they are     reasonable.

   
   

A2.ACE.2*    

   
   

Create     equations in two or more variables to represent relationships between     quantities. Graph the equations on coordinate axes using appropriate     labels, units, and scales.

   
   

 

   
   

 

   
   

A2.ACE.4*    

   
   

Solve     literal equations and formulas for a specified variable including equations     and formulas that arise in a variety of disciplines.

   

 

             
   

A2.ASE.3*    

   
   

Choose     and produce an equivalent form of an expression to reveal and explain     properties of the quantity represented by the expression.

   

(Note:     A2.ASE.3b and 3c are not Graduation Standards.)

   

c. Use     the properties of exponents to transform expressions for exponential     functions.

   

 

   

 

             
   

A2.AREI.11*    

   
   

Solve     an equation of the form ?(?)=?(?) graphically     by identifying the ?-coordinate(s) of the point(s) of intersection of the     graphs of ?=?(?) and ?=?(?).

   

 

                                         
   

A2.FBF.1*    

   
   

Write     a function that describes a relationship between two quantities.

   

(Note:     IA.FBF.1a is not a Graduation Standard.)

   

a.     Write a function that models a relationship between two quantities using     both explicit expressions and a recursive process and by combining standard     forms using addition, subtraction, multiplication and division to build new     functions.

   

b.     Combine functions using the operations addition, subtraction,     multiplication, and division to build new functions that describe the     relationship between two quantities in mathematical and real-world     situations.

   

 

   
   

A2.FBF.2*    

   
   

Write     arithmetic and geometric sequences both recursively and with an explicit     formula, use them to model situations, and translate between the two forms.    

   
   

A2.FBF.3*    

   
   

Describe     the effect of the transformations ??(?), ?(?)+?, ?(?+?), and     combinations of such transformations on the graph of ?=?(?)     for any real number ?. Find     the value of ? given the graphs and write the equation of a     transformed parent function given its graph.

   

 

                                                                     
   

A2.FIF.3*    

   
   

Define     functions recursively and recognize that sequences are functions, sometimes     defined recursively, whose domain is a subset of the integers.

   
   

A2.FIF.4*    

   
   

Interpret     key features of a function that models the relationship between two     quantities when given in graphical or tabular form. Sketch the graph of a     function from a verbal description showing key features. Key features     include intercepts; intervals where the function is increasing, decreasing,     constant, positive, or negative; relative maximums and minimums;     symmetries; end behavior and periodicity.

   
   

A2.FIF.5*    

   
   

Relate     the domain and range of a function to its graph and, where applicable, to     the quantitative relationship it describes.

   
   

A2.FIF.6*    

   
   

Given     a function in graphical, symbolic, or tabular form, determine the average     rate of change of the function over a specified interval. Interpret the     meaning of the average rate of change in a given context.

   
   

A2.FIF.8*    

   
   

Translate     between different but equivalent forms of a function equation to reveal and     explain different properties of the function.

   

(Note:     A2.FIF.8b is not a Graduation Standard.)

   

b.     Interpret expressions for exponential functions by using the properties of     exponents.

   

 

   

 

                                         
   

A2.FLQE.1*

   
   

Distinguish between     situations that can be modeled with linear functions or exponential     functions by recognizing situations in which one quantity changes at a     constant rate per unit interval as opposed to those in which a quantity     changes by a constant percent rate per unit interval.

   

(Note: A2.FLQE.1b is     not a Graduation Standard.)

   

b. Recognize situations     in which a quantity grows or decays by a constant percent rate per unit     interval relative to another.

   

 

   
   

A2.FLQE.2*

   
   

Create symbolic     representations of linear and exponential functions, including arithmetic     and geometric sequences, given graphs, verbal descriptions, and tables.

   
   

A2.FLQE.5*

   
   

Interpret the     parameters in a linear or exponential function in terms of the context.

   

 

Vocabulary:

 

 

 

 

 

Resources:

 

 

 

 

 

 

Strategies   for Infusing Technology: