Algebra II

Pacing and Curriculum Guide

2016­2017

1

Greene County Public Schools

2

Greene County Public Schools

Algebra II Pacing and Curriculum Guide

Course Outline

Quarter 1 Quarter 2 Quarter 3 Quarter 4

AII.4a ­ Absolute Value Equations and AII.9 – Curve of Best Fit AII.6/AII.7 – Polynomial Functions AII.7a­h – Graphing Functions Review Inequalities AII.1bc – Radical Expressions and AII.8 – Solution/zero/x­intercept/factors AII.5 – Systems of Non­Linear Equations

AII.6/A11.7 – Absolute Value Functions Rational Exponents AII.10 – Variations AII.11 – Normal Distribution and Z­scores AII.1d ­ Factoring AII.4d – Radical Equations AII.6/AII.7 – Rational Functions AII.1­AII.12 – SOL Review AII.3 – Complex Numbers AII.7h – Composite Functions AII.1a – Rational Expressions

A11.4b – Solve Quadratic Equations AII.7g – Inverse Functions AII.6/AII.7 – Exponential and A11. 6/AII.7 – Quadratic Functions Logarithmic Functions

AII.2 – Sequences and Series AII.12 – Permutations and Combinations

Big Ideas

1. Equations and Inequalities 2. Factoring 3. Radicals & Complex Numbers 4. Quadratics & Systems 5. Function Families & Transformations

6. Rational Expressions 7. Sequences & Series 8. Normal Distribution & Z­scores

9. Variation 10. Curve of Best Fit & Counting Principles

Algebra II SOL Test Blueprint (50 questions total)

Expressions and Operations 13 Questions 26% of the Test

3

Equations and Inequalities 13 Questions 26% of the Test Functions and Statistics 24 Questions 48% of the Test

Resources

Text: Algebra 2 , 2004, McDougal Littell Virginia Department of Education Mathematics SOL Resources http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml DOE Enhanced Scope and Sequence Lesson Plans http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_2009/index.php VDOE Vertical Alignment Charts http://www.doe.virginia.gov/instruction/mathematics/professional_development/institutes/2011

/opening_session/2009sol_vertical_articulation_by_topic_eoc_alg_9­15­11.pdf HCPS Algebra 2 Online Module Homepage http://teachers.henrico.k12.va.us/math/HCPSAlgebra2/modules.html GCPS Math Instructional Strategies Guide GCPS SPBQ Review Document w/Strategies

Common Assessments:

Pre/Post Test IA Benchmark Tests Unit Tests Quizzes

Common Unit Plans:

The Algebra 2 Professional Learning Community meets once a week to make common lesson plans

4

Greene County Public Schools

Algebra II Curriculum & Pacing Guide 2015­2016 Quarter 1 August 18, 2015 – October 16, 2015

Time/Date

s

SOL/Strand Objective/Content/Essential

Questions/Cognitive Level

Vertical

Alignment

Vocabulary Cross­curricular

Connections

8/18­8/26

Textbook

1­7

AII.4a Absolute Value

The student will solve, algebraically and

graphically,

a) absolute value equations and

inequalities

Graphing calculators will be used for

solving and for confirming the

algebraic solutions.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections, and

representations to

SOL 7.14 a) solve one‐ and two ‐step linear equations; b) solve practical problems in one variable SOL 8.15 a) solve multistep linear equations in one variable (variable

Absolute value Absolute value

equation Absolute value

inequality Compound

inequality Compound

sentence Extraneous

solution Intersection

Biology

range of normal body temperatures (Textbook page 54

#69)

Sports

weight range of balls

(Textbook page 55 #72)

5

Solve absolute value equations and inequalities algebraically and graphically

Blooms = Apply

on one and two sides of equations); c) ID properties of operations used to solve SOL A.4 solve multistep linear/ quad equation (2 vars)

Union

6

8/27­9/4

Textbook

2­8

AII.6 Absolute Value

Functions

AII.7a­d Graphing

The student will recognize the

general shape of function (absolute

value, square root, cube root,

rational, polynomial, exponential,

and logarithmic) families and will

convert between graphic and

symbolic forms of functions. A

transformational approach to

graphing will be employed. Graphing

calculators will be used as a tool to

investigate the shapes and behaviors

of these functions.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Recognize graphs of parent

functions.

Given a transformation of a parent function, identify the graph of the transformed function.

Given the equation and using a transformational approach, graph a function.

SOL 7.12

represent relationships with tables, graphs, rules, and words

SOL 7.15

a) solve one‐step inequalities; b) graph solutions on

number line

SOL 8.14

make connections between any two representations (tables, graphs, words, rules)

SOL 8.15

b) solve two ‐step linear inequalities and graph results on number line; c) ID properties of operations used to solve SOL 8.16

Graph linear equations in two variables SOL 8.17

Absolute value function

Dilation Family of

functions Intercepts (x and

y) Parent function Reflection Transformation

of graphs Translation

(vertical and horizontal)

Vertex Domain Range Zeroes of

functions x and

y­intercepts End behavior Increasing

intervals Decreasing

intervals Axis of

symmetry

Music

Finding sound level of musical

pieces (Textbook 127

#44­45)

7

Given the graph of a function, identify the parent function.

Given the graph of a function, identify the transformations that map the preimage to the image in order to determine the equation of the image.

Using a transformational approach, write the equation of a function given its graph.

The student will investigate and analyze

functions algebraically and graphically.

Key concepts include

a) domain and range,

including limited and

discontinuous domains and

ranges; b) zeros; c) x ­ and y ­intercepts; d) intervals in which a

function is increasing or

decreasing;

ID domain, range, indep/dep variable

SOL A.2

perform operations on polynomials c) factor first‐/second ‐degree binomials/ trinomials (1

or 2 vars) SOL A.6

graph linear equations/linear inequal (2 vars)

SOL A.7 investigate/analyze function (linear/quad) families and characteristics (alg/graph) ‐ a) determine relation is function; b) domain/range; c) zeros; d) x‐ and y­intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/

8

Graphing calculators will be used as a

tool to assist in investigation of

functions.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.

Given the graph of a function, identify intervals on which the function is increasing and decreasing.

Blooms = Analyze

numeric/graphic/algebraic) SOL AFDA.1 investigate/analyze function (linear/quad/exp/log) families/characteristics ‐ a) continuity; b) local/abs max/min; c) domain/range; d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes

SOL AFDA.2

use transformations to write equations, given graph of function (linear/quad/exp/log)

SOL AFDA.4

transfer between/analyze mult representations of functions

9

9/8­9/14

Textbook

5­2 6­4

AII.1d Factor

The student, given rational, radical, or

polynomial expressions, will

d) factor polynomials

completely.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Factor polynomials by applying

general patterns including difference of squares, sum and difference of cubes, and perfect square trinomials.

Factor polynomials completely over the integers.

Verify polynomial identities including the difference of squares, sum and difference of cubes, and perfect square trinomials

Blooms = Evaluate

Factoring Polynomial Difference of

squares Difference of

cubes Sum of cubes Perfect square

trinomial

10

9/15­9/22

Textbook

5­3 5­4

AII.3 Complex Numbers

The student will perform operations

on complex numbers, express the

results in simplest form using

patterns of the powers of i , and

identify field properties that are

valid for the complex numbers.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Recognize that the square root of –1 is represented as i .

Determine which field properties apply to the complex number system.

Simplify radical expressions containing negative rational numbers and express in a+bi form.

Simplify powers of i .

Add, subtract, and multiply complex numbers.

Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole, and natural.

Write a real number in a+bi form.

SOL 7.16

apply properties w/ real numbers: a) commutative and associative properties for add/mult; b) distrib property; c) add/mult identity properties; d) add/mult inverse properties; e) mult property of zero

SOL 8.15

c) ID properties of operations used to solve equations

SOL A.2

perform operations on polynomials ‐ a) apply laws of exponents to perform ops on expressions; b) add/sub/ mult/div poly;

Complex numbers

Real numbers Imaginary

numbers Pure imaginary

numbers Rational

numbers Irrational

numbers Integers Whole numbers Natural numbers Conjugate

Physics

Finding the impedance of a series circuits (Textbook page 279 #95­96)

11

Write a pure imaginary number in a+bi form.

Blooms = Analyze 9/23­10/6

Textbook

5­2 5­3 5­5 5­6

AII.4b Quadratic Equations

The student will solve, algebraically and

graphically,

b) quadratic equations over

the set of complex

numbers; Graphing calculators will be used for

solving and for confirming the

algebraic solutions.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Solve a quadratic equation over the

set of complex numbers using an appropriate strategy.

Calculate the discriminant of a quadratic equation to determine the number of real and complex solutions.

Apply an appropriate equation to solve a real­world problem.

SOL 7.14

a) solve one‐ and two ‐step linear equations; b) solve practical problems in one variable

SOL 8.15

a) solve multistep linear equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve

SOL A.4

solve multistep linear/ quad equation (2 vars) ‐ c) solve quad equations (alg/graph); d) solve multistep linear equations (alg/graph)

Roots Solutions Discriminant Factor Quadratic

equation Standard form

of a quadratic equation

General form of a quadratic equation

Completing the square

Quadratic Formula

Building Trades

Area of a parking lot

(Textbook page 261 #91)

Fashion Design

Quilting (Textbook page

261 #90)

Urban Planning

Landscaping (Textbook page

260 #22)

Environmental

Science

Planning an ecology garden (Textbook page

262 #98)

Astronomy

Height of a falling object

12

Recognize that the quadratic formula can be derived by applying the completion of squares to any quadratic equation in standard form.

Blooms = Analyze

(Textbook page 268 #71)

Firefighting

Horizontal and vertical water

stream (Textbook page

298 #91)

10/7­10/16

Textbook

5­1

AII.6 Quadratic Functions

AII.7a­d,f Graphing

The student will recognize the general

shape of function (absolute value, square

root, cube root, rational, polynomial,

exponential, and logarithmic) families

and will convert between graphic and

symbolic forms of functions. A

transformational approach to graphing

will be employed. Graphing calculators

will be used as a tool to investigate the

shapes and behaviors of these functions.

The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations

to

Recognize graphs of parent functions.

SOL 7.12

represent relationships with tables, graphs, rules, and words

SOL 7.15

a) solve one‐step inequalities;

b) graph solutions on number line

SOL 8.14

make connections between any two representations (tables, graphs, words, rules)

SOL 8.15

b) solve two‐step linear inequalities and graph

Quadratic function

Dilation Family of

functions Intercepts (x and

y) Parent function Reflection Transformation

of graphs Translation

(vertical and horizontal)

Vertex Domain Range Zeroes of

functions

Physics

Maximizing torque

(Textbook page 254 #51)

Sports

Surface of football field

(Textbook page 254 #52)

Physiology

Energy consumed while walking (Textbook page

254 #53)

13

Given a transformation of a parent function, identify the graph of the transformed function.

Given the equation and using a transformational approach, graph a function.

Given the graph of a function, identify the parent function.

Given the graph of a function, identify the transformations that map the preimage to the image in order to determine the equation of the image.

Using a transformational approach, write the equation of a function given its graph.

The student will investigate and analyze

functions algebraically and graphically. Key

concepts include

a) domain and range, including

limited and discontinuous

domains and ranges;

b) zeros;

c) x ­ and y ­intercepts;

d) intervals in which a function

is increasing or decreasing;

f) end behavior;

Graphing calculators will be used as a tool

to assist in investigation of functions.

results on number line; c) ID properties of operations used to solve SOL 8.16

Graph linear equations in two variables SOL 8.17

ID domain, range, indep/dep variable

SOL A.6

graph linear equations/linear inequal (2 vars)

SOL A.7 investigate/analyze function (linear/quad) families and characteristics (alg/graph) ‐ a) determine relation is function; b) domain/range; c) zeros; d) x‐ and y­intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/

x and y­intercepts

End behavior Increasing

intervals Decreasing

intervals Axis of

symmetry Parabola

14

The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations

to

Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.

Given the graph of a function, identify intervals on which the function is increasing and decreasing.

Describe the end behavior of a function.

Blooms = Analyze

numeric/graphic/algebraic) SOL AFDA.1 investigate/analyze function (linear/quad/exp/log) families/characteristics ‐ a) continuity; b) local/abs max/min; c) domain/range; d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes

SOL AFDA.2

use transformations to write equations, given graph of function (linear/quad/exp/log) SOL AFDA.4

transfer between/analyze mult representations of functions

Greene County Public Schools

Algebra II Curriculum & Pacing Guide 2015­2016 Quarter 2 October 19, 2015 – December 22, 2015

15

Time/Date

s

SOL/Strand Objective/Content/Essential

Questions/Cognitive Level

Vertical

Alignment

Vocabulary Cross­curricular

Connections

10/19­10/23

Textbook

2­5

AII.9 Curve of Best

Fit

The student will collect and analyze data,

determine the equation of the curve of best

fit, make predictions, and solve real­world

problems, using mathematical models.

Mathematical models will include

polynomial, exponential, and logarithmic

functions.

The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations

to

Collect and analyze data.

Investigate scatterplots to determine if patterns exist and then identify the patterns.

Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, and logarithmic functions.

Make predictions, using data, scatterplots, or the equation of the curve of best fit.

Given a set of data, determine the model that would best describe the data.

SOL 7.11

a) construct/analyze histograms; b) compare/contrast histograms SOL 8.13

a) make comparisons/predictions/ inferences, using information displayed in graphs; b) construct/ analyze scatterplots SOL A.10

compare/contrast mult univ data sets with box‐and‐whisker plots SOL A.11

collect/analyze data/determine equation of curve best fit to make predictions/solve real‐world problems, using models (linear/quad) SOL AFDA.3

collect data/generate equ for curve (linear/quad/ exp/log) of best fit/use best fit equ to interpolate function values/make decisions/justify conclusions (alg/graph models)

Scatter plot Curve of best fit Regression

equation Linear

regression Quadratic

regression Positive

correlation Negative

correlation No correlation Correlation

coefficient

Earth Science

Find the correlation

coefficient for interval time

between eruptions (Textbook page

104 #23)

Business

Use data to predict future business investments

(Textbook page 103 #6­7)

16

Blooms = Evaluate

10/26­11/10

Textbook

6­1 7­1 7­2

AII.1b,c Radical

Expressions

The student, given rational, radical, or

polynomial expressions, will

b) add, subtract, multiply,

divide, and simplify radical

expressions containing

rational numbers and

variables, and expressions

containing rational

exponents; c) write radical expressions as

expressions containing

rational exponents and vice

versa

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Convert from radical notation to

exponential notation, and vice versa.

Add and subtract radical expressions.

SOL 7.13

b) evaluate algebraic expressions

SOL 8.1

a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, properties; SOL 8.4

evaluate algebraic expressions using order of operations

SOL A.1

represent verbal quantitative situations algebraically/evaluate expressions for given replacement values of variables

Square root Cube root nth root indices radical radicand rational

exponent

Biology

Comparing surface areas of

lynx (Textbook page 411 example #9)

Business

Inflation rates (Textbook page

405 #64)

17

Multiply and divide radical expressions not requiring rationalizing the denominators.

Simplify radical expressions containing positive rational numbers and variables.

Blooms = Apply

11/11­11/18

Textbook

7­6

AII.4d Radical Equations

The student will solve, algebraically and

graphically,

d) equations containing

radical expressions. Graphing calculators will be used for

solving and for confirming the

algebraic solutions.

The student will use problem solving,

mathematical communication,

mathematical reasoning,

connections, and representations

to

Solve an equation containing a radical expression algebraically and graphically.

SOL 7.14

a) solve one‐ and two ‐step linear equations; b) solve practical problems in one variable

SOL 8.15

a) solve multistep linear equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve

SOL A.4

solve multistep linear/quad equation (2 vars) ‐ a) solve literal equation; b)

Extraneous roots Radical Solution Root

Sports

Minimum requirements for America’s Cup (Textbook page

443 #68)

Business

Manufacturing plumb bobs

(Textbook page 442 #66)

Medicine

Population of women doctors (Textbook page

442 #65)

18

Verify possible solutions to an equation containing rational or radical expressions.

Blooms = Evaluate

justify steps used in simplifying expressions and solving equations; c) solve quad equations (alg/graph); d) solve multistep linear equations (alg/graph); f) solve real‐world problems involving equations and systems of equations

19

11/19­11/24

Textbook

7­3

AII.7h Composite Functions

The student will investigate and analyze

functions algebraically and graphically.

Key concepts include

h) composition of multiple

functions.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Find the composition of two

functions.

Use composition of functions to verify two functions are inverses.

Blooms = Analyze

SOL A.7

e) find values of functions for elements in domain

Composition of functions

Personal Finance

Sale price of clothing

(Textbook page 419 #54­55)

Paleontology

Relationship between height and footprint length of a dinosaur

(Textbook page 419 #56)

20

11/30­12/11

Textbook

7­4 7­5

AII.7g Inverse Functions

The student will investigate and analyze

functions algebraically and graphically.

Key concepts include

g) inverse of a function

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Find the inverse of a function.

Graph the inverse of a function as a reflection across the line y = x .

Blooms = Apply

SOL 7.12

represent relationships with tables, graphs, rules, and words SOL 8.14

make connections between any two representations (tables, graphs, words, rules) SOL 8.17

ID domain, range, indep/dep variable SOL A.7 investigate/analyze function (linear/quad) families and characteristics (alg/graph) ‐ a) determine relation is function; b) domain/range; d) x‐ and yintercepts; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic) SOL AFDA.1 investigate/analyze function (linear/quad/exp/log) families/characteristics ‐ a) continuity; c) domain/

Inverse of a function

Cube root function

Square root function

Physics

Using Hooke’s Law and inverse functions

(Textbook page 423 example #3)

Astronomy

Inverse model to find age of nebula as a function of its

volume (Textbook page 425

example #6)

Business

Using inverse of the function to find the value of a US dollar

in terms of Canadian dollars

(Textbook page 427 #57)

Science

Using inverse to convert from

Celsius to degree Fahrenheit

(Textbook page 427 #58)

21

range; e) intercepts; h) asymptotes SOL AFDA.4

transfer between/analyze mult representations of functions (alg formulas/ graphs/tables/words)

Biology

Using inverse to determine length of

a hake fish (Textbook page 428

#61)

Greene County Public Schools Algebra II Curriculum & Pacing Guide 2015­2016 Quarter 3

January 5, 2015 – March 13, 2015

Time/Date

s

SOL/Strand Objective/Content/Essential

Questions/Cognitive Level

Vertical

Alignment

Vocabulary Cross­curricular

Connections

1/5­1/11

Textbook

6­2

AII.6 Polynomial Functions

AII.7

Polynomial Functions

AII.8

Solution/Zero/

X­intercept/ Factors

The student will recognize the general

shape of function (absolute value, square

root, cube root, rational, polynomial,

exponential, and logarithmic) families

and will convert between graphic and

symbolic forms of functions. A

transformational approach to graphing

will be employed. Graphing calculators

will be used as a tool to investigate the

shapes and behaviors of these functions.

The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations

to

SOL 7.12

represent relationships with tables, graphs, rules, and words

SOL 7.15

a) solve one‐step inequalities; b) graph solutions on

number line

SOL 8.14

make connections between

22

Recognize graphs of parent functions.

Given a transformation of a parent function, identify the graph of the transformed function.

Given the equation and using a transformational approach, graph a function.

Given the graph of a function, identify the parent function.

Given the graph of a function, identify the transformations that map the preimage to the image in order to determine the equation of the image.

Using a transformational approach, write the equation of a function given its graph.

The student will investigate and analyze

functions algebraically and graphically. Key

concepts include

a) domain and range, including

limited and discontinuous

domains and ranges;

b) zeros;

c) x ­ and y ­intercepts;

d) intervals in which a function

is increasing or decreasing;

f) end behavior;

any two representations (tables, graphs, words, rules)

SOL 8.15

b) solve two ‐step linear inequalities and graph results on number line; c) ID properties of operations used to solve SOL 8.16

Graph linear equations in two variables SOL 8.17

ID domain, range, indep/dep variable

SOL A.6

graph linear equations/linear inequal (2 vars)

SOL A.7 investigate/analyze

23

Graphing calculators will be used as a tool

to assist in investigation of functions.

The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations

to

Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.

Given the graph of a function, identify intervals on which the function is increasing and decreasing.

Describe the end behavior of a function.

The student will investigate and describe the

relationships among solutions of an equation,

zeros of a function, x ­intercepts of a graph,

and factors of a polynomial expression.

The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations

to

Describe the relationships among

solutions of an equation, zeros of a

function (linear/quad) families and characteristics (alg/graph) ‐ a) determine relation is function; b) domain/range; c) zeros; d) x‐ and y­intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic)

SOL AFDA.1 investigate/analyze function (linear/quad/exp/log) families/characteristics ‐ a) continuity; b) local/abs max/min; c) domain/range; d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes

SOL AFDA.2

24

function, x ­intercepts of a graph, and factors of a polynomial expression.

Define a polynomial function, given its zeros.

Determine a factored form of a polynomial expression from the x­intercepts of the graph of its corresponding function.

For a function, identify zeros of multiplicity greater than 1 and describe the effect of those zeros on the graph of the function.

Given a polynomial equation, determine the number of real solutions and nonreal solutions.

Blooms = Analyze

use transformations to write equations, given graph of function (linear/quad/exp/log)

SOL AFDA.4

transfer between/analyze mult representations of functions (alg formulas/graphs/tables/ words)

25

1/12­1/15

Textbook

9­1

AII.10 Variations

The student will identify, create, and

solve real­world problems involving

inverse variation, joint variation, and a

combination of direct and inverse

variations.

The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations

to

Translate “y varies jointly as x and z ” as y = kxz .

Translate “y is directly proportional to x ” as y = kx .

Translate “y is inversely proportional to x ” as y = .

Given a situation, determine the value of the constant of proportionality.

Set up and solve problems, including real­world problems, involving inverse variation, joint variation, and a combination of direct and inverse variations.

Blooms = Analyze

SOL A.8

given real ‐world context, analyze relation to determine direct/inverse variation/represent direct variation (alg/graph)/inverse variation (alg)

Direct Variation Inverse

Variation Joint Variation Proportional Constant of

Variation Constant of

Proportionality

Physics

Law of Universal Gravitation.

(Textbook 536, Example #6.)

Astronomy

Stars diameter vs luminosity.

(Textbook 538, #s 51­53)

26

1/19­1/26

Textbook

9­2 9­3

AII.6 Rational Functions

AII.7

Rational Functions

The student will recognize the general

shape of function (absolute value,

square root, cube root, rational,

polynomial, exponential, and

logarithmic) families and will convert

between graphic and symbolic forms

of functions. A transformational

approach to graphing will be

employed. Graphing calculators will

be used as a tool to investigate the

shapes and behaviors of these

functions.

The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations

to

Recognize graphs of parent functions.

Given a transformation of a parent function, identify the graph of the transformed function.

Given the equation and using a transformational approach, graph a function.

Given the graph of a function, identify the parent function.

Given the graph of a function, identify the transformations that map the

SOL 7.12

represent relationships with tables, graphs, rules, and words

SOL 7.15

a) solve one‐step inequalities;

b) graph solutions on number line

SOL 8.14

make connections between any two representations (tables, graphs, words, rules)

SOL 8.15

b) solve two‐step linear inequalities and graph results on number line; c) ID properties of operations used to solve SOL 8.16

Graph linear equations in two variables SOL 8.17

ID domain, range, indep/dep variable

Rational function Intercepts (x and y Domain Range Zeroes of functions End behavior Increasing intervals Decreasing

intervals Multipicities Degree of Function

Economics

Laffer’s Theory (Textbook page 544, #s 45 & 46)

Physics

Doppler Effect (Textbook Page 545, #s 47 & 48)

Earth Science

Mean Temperature between given latitudes.

(Textbook page 551, #40.)

Physics

Acceleration due to gravity of a falling object. (Textbook page 552, #s 43­45.)

27

preimage to the image in order to determine the equation of the image.

Using a transformational approach, write the equation of a function given its graph.

The student will investigate and analyze

functions algebraically and graphically.

Key concepts include

a) domain and range, including

limited and discontinuous

domains and ranges;

b) zeros;

c) x ­ and y ­intercepts;

d) intervals in which a function

is increasing or decreasing;

f) end behavior;

Graphing calculators will be used as a tool

to assist in investigation of functions.

The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations

to

Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.

Given the graph of a function, identify intervals on which the function is increasing and decreasing.

SOL A.6

graph linear equations/linear inequal (2 vars)

SOL A.7 investigate/analyze function (linear/quad) families and characteristics (alg/graph) ‐ a) determine relation is function; b) domain/range; c) zeros; d) x‐ and y­intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic) SOL AFDA.1 investigate/analyze function (linear/quad/exp/log) families/characteristics ‐ a) continuity; b) local/abs max/min; c) domain/range; d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes

SOL AFDA.2

28

Describe the end behavior of a function.

Blooms = Analyze

use transformations to write equations, given graph of function (linear/quad/exp/log) SOL AFDA.4

transfer between/analyze mult representations of functions

29

1/27­2/1

Textbook

9­4 9­5

AII.1a Rational

Expressions

The student, given rational, radical, or

polynomial expressions, will

a) add, subtract, multiply,

divide, and simplify

rational algebraic

expressions;

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Add, subtract, multiply, and divide

rational algebraic expressions.

Simplify a rational algebraic expression with common monomial or binomial factors.

Recognize a complex algebraic fraction, and simplify it as a quotient or product of simple algebraic fractions.

Blooms = Apply

SOL 8.1

a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, properties. SOL A.1

represent verbal quantitative situations algebraically/evaluate expressions for given replacement values of variables

Rational Expressions

Complex Fractions

Business Finance

Monthly payment of a loan.

(Textbook page 565, # 11.)

Physics

Resistance of parallel circuits. (Textbook page 567, #s 52 & 53.)

30

2/2­2/3

Textbook

9­6

AII.4c Rational Equations

The student will solve, algebraically and

graphically,

c) equations containing

rational algebraic

expressions; and

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Solve equations containing rational

algebraic expressions with monomial or binomial denominators algebraically and graphically.

Verify possible solutions to an equation containing rational or radical expressions.

Blooms = Evaluate

SOL 7.14

a) solve one‐ and two ‐step linear equations; b) solve practical problems in one variable SOL 8.15

a) solve multistep linear equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve SOL A.4

solve multistep linear/ quad equation (2 vars) ‐ a) solve literal equation; b) justify steps used in simplifying expresessions and solving equations; c) solve quad equations (alg/graph); d) solve multistep linear equations (alg/graph); f) solve real‐world problems involving equations.

Rational Equation Restricted variable Extraneous Roots

Nursing

Drug Absorption Amount

(Textbook page 566, #s 48­51.)

31

2/4­2/11

Textbook

8­1 8­2 8­4

AII.6 Exponential Logarithmic Functions

AII.7

Exponential Logarithmic Functions

The student will recognize the

general shape of function (absolute

value, square root, cube root,

rational, polynomial, exponential,

and logarithmic) families and will

convert between graphic and

symbolic forms of functions. A

transformational approach to

graphing will be employed.

Graphing calculators will be used

as a tool to investigate the shapes

and behaviors of these functions.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Recognize graphs of parent

functions.

Given a transformation of a parent function, identify the graph of the transformed function.

Given the equation and using a transformational approach, graph a function.

SOL 7.12

represent relationships with tables, graphs, rules, and words

SOL 7.15

a) solve one‐step inequalities; b) graph solutions on

number line

SOL 8.14

make connections between any two representations (tables, graphs, words, rules)

SOL 8.15

b) solve two ‐step linear inequalities and graph results on number line; c) ID properties of operations used to solve SOL 8.16

Graph linear equations in two variables SOL 8.17

Exponential

function Logarithmic

function Intercepts (x and

y) Domain Range Zeroes of

functions End behavior Increasing

intervals Decreasing

intervals Asymptotes Inverse of

function Translation

(vertical/horizontal)

Biology

Exponential Decay model for amount of air left

in lungs. (Textbook page 479, # 56)

Government

Exponential Growth model for Federal Debt (Textbook page 470, #s 52­54)

Physics

Radioactive Decay

(Textbook page 478, # 46)

Chemistry

pH of a solution (Textbook page 491, # 77)

Earth Science

Richter Scale

32

Given the graph of a function, identify the parent function.

Given the graph of a function, identify the transformations that map the preimage to the image in order to determine the equation of the image.

Using a transformational approach, write the equation of a function given its graph.

The student will investigate and analyze

functions algebraically and graphically.

Key concepts include

a) domain and range,

including limited and

discontinuous domains and

ranges; b) zeros; c) x ­ and y ­intercepts; d) intervals in which a

function is increasing or

decreasing; e) asymptotes; f) end behavior;

ID domain, range, indep/dep variable

SOL A.6

graph linear equations/linear inequal (2 vars)

SOL A.7 investigate/analyze function (linear/quad) families and characteristics (alg/graph) ‐ a) determine relation is function; b) domain/range; c) zeros; d) x‐ and y­intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic)

(Textbook page 491, #s 79­80)

33

Graphing calculators will be used as a

tool to assist in investigation of

functions.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.

Describe restricted/discontinuous domains and ranges.

Given the graph of a function, identify intervals on which the function is increasing and decreasing.

Find the equations of vertical and horizontal asymptotes of functions.

Describe the end behavior of a function.

Investigate exponential and logarithmic functions, using the graphing calculator.

SOL AFDA.1 investigate/analyze function (linear/quad/exp/log) families/characteristics ‐ a) continuity; b) local/abs max/min; c) domain/range; d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes

SOL AFDA.2

use transformations to write equations, given graph of function (linear/quad/exp/log)

SOL AFDA.4

transfer between/analyze mult representations of functions

34

Convert between logarithmic and exponential forms of an equation with bases consisting of natural numbers.

Blooms = Analyze

35

2/17­2/23

Textbook

11­1 11­2 11­3

AII.2 Sequences and Series

The student will investigate and apply

the properties of arithmetic and

geometric sequences and series to solve

real­world problems, including writing

the first n terms, finding the n th term,

and evaluating summation formulas.

Notation will include ∑ and a n .

The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations

to

Distinguish between a sequence and a series.

Generalize patterns in a sequence using explicit and recursive formulas.

Use and interpret the notations ∑, n , n th

term, and a n .

Given the formula, find a n (the n th term) for an arithmetic or a geometric sequence.

Given formulas, write the first n terms and find the sum, S n , of the first n terms of an arithmetic or geometric series.

Given the formula, find the sum of a convergent infinite series.

SOL 7.2

describe/represent arithmetic/geometric sequences using variable expressions

Arithmetic sequence

Arithmetic series Common

difference Geometric

sequence Geometric series Common ratio Infinite Explicit formula Recursive

formula Sigma notation Summation

Carpentry

Vertical supports for a roof (Textbook page 656, #s 65­66) Building Design

“vineyard” design (Textbook page

662, # 6)

Computer

Science

Binary search (Textbook page 671, #s 72­73)

Genealogy

Family Trees (Textbook page 491, #s 79­80)

36

Model real­world situations using sequences and series.

Blooms = Analyze

37

2/24­3/1

Textbook

12­1 12­2 12­3 12­4

AII.12 Permutations

and Combination

s

The student will compute and

distinguish between permutations

and combinations and use

technology for applications.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections, and

representations to

Compare and contrast permutations

and combinations.

Calculate the number of permutations of n objects taken r at a time.

Calculate the number of combinations of n objects taken r at a time.

Use permutations and combinations as counting techniques to solve real­world problems.

Blooms = Analyze

SOL 7.9

investigate/describe the difference between the experimental/theoretical probability SOL 7.10

determine the probability of compound events, Basic Counting Principle SOL 8.12

determine probability of indep/dep events with and without replacement SOL AFDA.6

calculate probabilities a) conditional prob; b) dep/indep events; c) add/mult rules; d) counting techniques (permutations & combinations); Law of Large Numbers

Permutation Combination Factorial

Computer

Science

Passwords (Textbook page

706, #57)

Drama

Assigning roles to a play

(Textbook page 706, #61)

Science

Probability of tree damage

(Textbook page 728, #46)

38

Greene County Public Schools

Algebra II Curriculum & Pacing Guide 2014­2015 Quarter 4 March 14, 2015 – May 27, 2015

Time/Date

s

SOL/Strand Objective/Content/Essential

Questions/Cognitive Level

Vertical

Alignment

Vocabulary Cross­curricular

Connections

3/14­3/23

AII.7a­f Graphing Functions Review

The student will investigate and analyze

functions algebraically and graphically.

Key concepts include

a) domain and range,

including limited and

discontinuous domains and

ranges; b) zeros; c) x ­ and y ­intercepts; d) intervals in which a

function is increasing or

decreasing; e) asymptotes; f) end behavior;

Graphing calculators will be used as a

tool to assist in investigation of

functions.

SOL 7.12

represent relationships with tables, graphs, rules, and words SOL 8.14

make connections between any two representations (tables, graphs, words, rules) SOL 8.17

ID domain, range, indep/dep variable

Parent Function Family of

Functions Absolute value

function Quadratic Function Square Root

Function Cubic Function Cube Root

Function Radical Function Rational Function Exponential

Function Logarithmic

Function

39

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.

Describe restricted/discontinuous domains and ranges.

Given the graph of a function, identify intervals on which the function is increasing and decreasing.

Find the equations of vertical and horizontal asymptotes of functions.

Describe the end behavior of a function.

Investigate exponential and logarithmic functions, using the graphing calculator.

Blooms = Analyze

SOL A.7 investigate/analyze function (linear/quad) families and characteristics (alg/graph) ‐ a) determine relation is function; b) domain/range; c) zeros; d) x‐ and y­intercepts; e) find values of funct for elements in domain; f) make connect between/among mult repres of funct (concrete/verbal/ numeric/graphic/algebraic)

SOL AFDA.1 investigate/analyze function (linear/quad/exp/log) families/characteristics ‐ a) continuity; b) local/abs max/min; c) domain/range;

Transformation of Functions

Dilation Refection Translation(vertica

l and horizontal) Vertex Domain Range Zeroes of

functions x and y­intercepts End behavior Increasing

intervals Decreasing

intervals Axis of symmetry Asymptote Discontinuity Continuous

function Discontinuous

function

40

d) zeros; e) intercepts; f) intervals inc/dec; g) end behaviors; h) asymptotes SOL AFDA.4

transfer between/analyze mult representations of functions (alg formulas/graphs/tables/ words)

41

3/24­4/6

Textbook

10­7

AII.5 Non­Linear Systems

The student will solve nonlinear

systems of equations, including

linear­quadratic and

quadratic­quadratic, algebraically

and graphically. Graphing

calculators will be used as a tool to

visualize graphs and predict the

number of solutions.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections,

and representations to

Predict the number of solutions to a

nonlinear system of two equations.

Solve a linear­quadratic system of two equations algebraically and graphically.

Solve a quadratic­quadratic system of two equations algebraically and graphically.

Blooms = Apply

SOL 7.15

a) solve one‐step inequalities; b) graph solutions on number line SOL 8.15

b) solve two‐step linear inequalities and graph results on number line; c) ID properties of operations used to solve SOL A.5

solve multistep linear inequ (2 vars) ‐ a) solve multistep linear inequal (alg/graph); b) justify steps used in solving inequal; c) solve real‐world problems involving inequal; d) solve systems of inequal SOL AFDA.5

determine opt values in problem situations by identifying constraints/using linear programming techniques

Solution Root Nonlinear systems of

equations Linear­quadratic

system Quadratic­quadratic

system

Communications

Range of radio station

(Textbook page 636, #59)

Earth Science

Using a seismograph and system of equation to locate epicenter (Textbook page 634, example 4)

42

4/7­4/22

Textbook

7­7 12­7

AII.11 Normal

Distribution and Z­Scores

The student will identify properties

of a normal distribution and apply

those properties to determine

probabilities associated with areas

under the standard normal curve.

The student will use problem solving,

mathematical communication,

mathematical reasoning, connections, and

representations to

Identify the properties of a normal

probability distribution.

Describe how the standard deviation and the mean affect the graph of the normal distribution.

Compare two sets of normally distributed data using a standard normal distribution and z­scores.

Represent probability as area under the curve of a standard normal probability distribution.

Use the graphing calculator or a standard normal probability table to

SOL 5.16

a) describe mean/median/mode; b) describe mean as fair share; c) find the mean/median/mode/range; d) describe range as measure of variation SOL 6.15

a) describe mean as balance point; b) decide which measure of center is appropriate SOL A.9

given a set of data, interpret variation in real‐world contexts/calculate/interpret mean absolute deviation/stand dev/zscores SOL AFDA.7

analyze norm distrib ‐ a) characteristics of normally distrib data; b) percentiles; c)

Normal distribution curve

Mean Area under a curve Normal probability

distribution Percentile Population Standard deviation Z­score

Biology

Heights of adult women

(Textbook page 750, #44­46)

Manufacturing

Life expectancy of light bulb

(Textbook page 750, #41­43)

Business

Wait time (Textbook page 750, #38­40)

43

determine probabilities or percentiles based on z­scores.

Blooms = Evaluate

normalizing data, using z‐scores; d) area under std norm curve/probability

44

4/25­5/13

AII.1­AII.12

Review of all SOL concepts.

45