Beginning of 1 Quarter Unit 1: Linear Equations, Inequalities, …images.pcmac.org/Uploads/MCPSS/MobileCounty/Departments... · 2013-10-10 · or Infinite Algebra 2.1 Week 4 Sept

MOBILE COUNTY PUBLIC SCHOOLS

DIVISION OF CURRICULUM & INSTRUCTION

HIGH SCHOOL PACING GUIDE AT A GLANCE

FALL SEMESTER 2013-14

ALGEBRA 2

May 2013 Page 1 of 15

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Resource Materials

Website Lesson/Activities

WEEK Standards/Objectives First Quarter (44 days)

Dates:

Taught Tested

20

22

23

29

Dana Center Tasks

“Summer Business”

“Function

Transformations”

MAPS Tasks

“Modeling Situations”

Illuminations Tasks

“Shrinking Candles”

www.kutasoftware.com or Infinite Algebra 2

Week

1

Aug

19 - 23

Beginning of 1st Quarter

Unit 1: Linear Equations, Inequalities,

and Graphing

Create equations and inequalities in one variable and use them

to solve problems. Include equations arising from linear and

quadratic functions, and simple rational and exponential

functions. [A-CED1]

Represent constraints by equations or inequalities, and by

systems of equations and/or inequalities, and interpret

solutions as viable or nonviable options in a modeling context.

[A-CED3]

Rearrange formulas to highlight a quantity of interest, using

the same reasoning as in solving equations. [A-CED4]

Relate the domain of a function to its graph and, where

applicable, to the quantitative relationship it describes.*

[F-IF5]

EOC:

Linear Functions

Graph and solve compound inequalities

Graph systems of linear inequalities (linear

programming)

Solve systems of equations with three variables

http://www.kutasoftware.com/





ALGEBRA 2


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Dates:

Taught Tested

20

22

23

29

Dana Center Tasks

“Summer Business”

“Function

Transformations”

MAPS Tasks

“Modeling Situations”

Illuminations Tasks

“Shrinking Candles”

www.kutasoftware.com or Infinite Algebra 2

Week 2

Aug.

26 - 30

Create equations and inequalities in one variable and use

them to solve problems. Include equations arising from

linear and quadratic functions, and simple rational and

exponential functions. [A-CED1]



solutions as viable or nonviable options in a modeling

context. [A-CED3]

Rearrange formulas to highlight a quantity of interest, using

the same reasoning as in solving equations. [A-CED4]



[F-IF5]

EOC:

Linear Functions

Graph and solve compound inequalities

Graph systems of linear inequalities (linear

programming)

Solve systems of equations with three variables






ALGEBRA 2


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WEEK Standards/Objectives First Quarter

Dates:

Taught Tested

7

8

9

10

11

22

26

TeachEngineering

Task “Close Enough”

www.kutasoftware.com

or Infinite Algebra 2

Week 3

Sept.

3 - 6

(4 days)

Unit 2: Matrices & Solving Systems

Use matrices to represent and manipulate data, e.g., to

represent payoffs or incidence relationships in a network.

(Use technology to approximate roots.) [N-VM6]

(+) Multiply matrices by scalars to produce new matrices,

e.g., as when all of the payoffs in a game are doubled.

[N-VM7]

(+) Add, subtract, and multiply matrices of appropriate

dimensions. [N-VM8]

(+) Understand that, unlike multiplication of numbers, matrix

multiplication for square matrices is not a commutative

operation, but still satisfies the associative and distributive

properties. [N-VM9]

(+) Understand that the zero and identity matrices play a role

in matrix addition and multiplication similar to the role of 0

and 1 in the real numbers. The determinant of a square matrix

is nonzero if and only if the matrix has a multiplicative

inverse. [N-VM10]



solutions as viable or nonviable options in a modeling

context. [A-CED3]

(+) Find the inverse of a matrix if it exists and use it to solve

systems of linear equations (using technology for matrices of

dimension 3 × 3 or greater). [A-REI9]

EOC:

Linear Functions

Solve systems of equations with 3 variables

Number Sense, Quadratic Functions, and Matrices

Use matrices to organize data and solve problems






ALGEBRA 2


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Dates:

Taught Tested

4

6

20

27

28

29

30

30b

34

HRW Ch 1 “Project: Investigating

Water Flow”

MAP Task “Forming Quadratics”

Illuminations Task

“Egg Launch Contest”


or Infinite Algebra 2.1

Week 4

Sept.

9 - 13

Unit 3: Quadratics Solve quadratic equations with real coefficients that have

complex solutions. [N-CN7]

(+) Know the Fundamental Theorem of Algebra; show that it is

true for quadratic polynomials. [N-CN9]

Create equations and inequalities in one variable and use them to

solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential

functions. [A-CED1]

Explain why the x-coordinates of the points where the graphs of

the equations y = f(x) and y = g(x) intersect are the solutions of

the equation f(x) = g(x); find the solutions approximately, e.g.,

using technology to graph the functions, make tables of values, or

find successive approximations. Include cases where f(x) and/or

g(x) are linear, polynomial, rational, absolute value, exponential,

and logarithmic functions.* [A-REI11]

Create graphs of conic sections, including parabolas, hyperbolas,

ellipses, circles, and degenerate conics, from second-degree

equations. [AL]


applicable, to the quantitative relationship it describes.* [F-IF5]

Graph functions expressed symbolically, and show key features

of the graph, by hand in simple cases and using technology for

more complicated cases.* [F-IF7]

Graph polynomial functions, identifying zeros when suitable

factorizations are available, and showing end behavior. [F-IF7c]

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x),

f(kx), and f(x + k) for specific values of k (both positive and

negative); find the value of k given the graphs. Experiment with

cases and illustrate an explanation of the effects on the graph

using technology. Include recognizing even and odd functions

from their graphs and algebraic expressions for them. [F-BF3]

Lessons: 1.1 – 1.4

EOC:


Graph and solve quadratic equations and inequalities

Determine number and type of roots for a quadratic

equations

Determine domain and range of a quadratic function

Identify, graph, determine the characteristics of, and

write equations of circles and parabolas






ALGEBRA 2


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Dates:

Taught Tested

1

2

3

4

5

20

25

27

HRW Ch 1 “Project: Investigating

Water Flow”

MAP Task “Forming Quadratics”

Illuminations Task

“Egg Launch Contest”


or Infinite Algebra 2.1

Week 5

Sept.

16 - 20

Know there is a complex number i such that i2 = –1, and every

complex number has the form a + bi with a and b real.

[N-CN1]

Use the relation i2 = –1 and the commutative, associative, and

distributive properties to add, subtract, and multiply complex

numbers. [N-CN2]

(+) Find the conjugate of a complex number; use conjugates to

find moduli and quotients of complex numbers. [N-CN3]

Solve quadratic equations with real coefficients that have

complex solutions. [N-CN7] (+) Extend polynomial identities to the complex numbers.

Example: Rewrite x2 + 4 as (x + 2i)(x – 2i). [N-CN8]




functions. [A-CED1]

Recognize when the quadratic formula gives complex

solutions, and write them as a ± bi for real numbers a and b.

[A-REI4b] Explain why the x-coordinates of the points where the graphs

of the equations y = f(x) and y = g(x) intersect are the solutions

of the equation f(x) = g(x); find the solutions approximately,

e.g., using technology to graph the functions, make tables of

values, or find successive approximations. Include cases where

f(x) and/or g(x) are linear, polynomial, rational, absolute value,

exponential, and logarithmic functions.* [A-REI11]

Lessons: 1.5, 1.6, 1.8, 1.9

EOC:


Graph and solve quadratic equations and inequalities

Determine number and type of roots for a quadratic

equation

Graph and solve systems of quadratic inequalities

Manipulate complex numbers






ALGEBRA 2


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Dates:

Taught Tested

13

15

16

17

19

30

30b

34

HRW Ch 2 “Project: Playing the

Game”

HRW Ch 2 “Problem Solving

Workshop Sheet”

Week 6

Sept.

23 - 27

Unit 4: Polynomials Use the structure of an expression to identify ways to rewrite

it. [A-SSE2]

Understand 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. [A-APR1]

Know and apply the Remainder Theorem: For a polynomial

p(x) and a number a, the remainder on division by x – a is

p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

[A-APR2]

Identify zeros of polynomials when suitable factorizations are

available, and use the zeros to construct a rough graph of the

function defined by the polynomial. [A-APR3]

Rewrite 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, long division, or for the more

complicated examples, a computer algebra system. [A-APR6]

Graph functions expressed symbolically, and show key

features of the graph, by hand in simple cases and using

technology for more complicated cases.* [F-IF7]

Graph polynomial functions, identifying zeros when suitable

factorizations are available, and showing end behavior.

[F-IF7c] Identify the effect on the graph of replacing f(x) by f(x) + k, k

f(x), f(kx), and f(x + k) for specific values of k (both positive

and negative); find the value of k given the graphs. Experiment

with cases and illustrate an explanation of the effects on the

graph using technology. Include recognizing even and odd

functions from their graphs and algebraic expressions for

them. [F-BF3]

Lessons: 2.1, 2.2, 2.4, 2.5, and 2.6

EOC:

Polynomial Functions

Evaluate, simplify, and factor polynomial expressions

Find minimum and maximum values, domain, and range

of polynomial functions, both graphically and

algebraically

Recognize connections among zeros, x-intercepts,

factors, and solutions of polynomial equations





ALGEBRA 2


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Dates:

Taught Tested

12

12a

12b

24

29

30

30a

33

33a

34

35

35a

HRW Ch 3 “Project: Walk This

Way”

HRW Ch 3 “Review Games and

Activities”


Workshop Sheet”

Week 7

Sept. 30 -

Oct. 4

Unit 5: Radical & Rational Exponents

Interpret expressions that represent a quantity in terms of its

context.* [A-SSE1]

Interpret parts of an expression such as terms, factors, and

coefficients. [A-SSE1a]

Interpret complicated expressions by viewing one or more of

their parts as a single entity. [A-SSE1b]

Solve simple rational and radical equations in one variable,

and give examples showing how extraneous solutions may

arise. [AL]



[F-IF5] Graph functions expressed symbolically, and show key



Graph square root, cube root, and piecewise-defined functions,

including step functions and absolute value functions. [F-IF7b] Write a function that describes a relationship between two

quantities.* [F-BF1]

Combine standard function types using arithmetic operations.

[F-BF1b]

Identify the effect on the graph of replacing f(x) by f(x) + k, k


and negative); find the value of k given the graphs. Experiment

with cases and illustrate an explanation of the effects on the

graph using technology. Include recognizing even and odd

functions from their graphs and algebraic expressions for

them. [F-BF3] Find inverse functions. [F-BF4]

Solve an equation of the form f(x) = c for a simple function f

that has an inverse, and write an expression for the inverse.

[F-BF4a]

Lessons: 3.1 – 3.6

EOC:

Non-polynomial Functions

Manipulate and evaluate radical expressions; solve

rational and radical equations





ALGEBRA 2


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Dates:

Taught Tested

20

30

30c

31

33

33a

36

HRW Ch 4 (1) “Project: ”


Activities”


Workshop Sheet”

Dana Center Tasks

“Bighorn Sheep”

“Equal Salaries for

Equal Work?”

Week 8

Oct.

7 - 11

Unit 6: Logarithms & Exponentials




functions. [A-CED1]

Graph functions expressed symbolically, and show key



Graph exponential and logarithmic functions, showing

intercepts and end behavior, and trigonometric functions,

showing period, midline, and amplitude. [F-IF7e]

Write a function defined by an expression in different but

equivalent forms to reveal and explain different properties of

the function. [F-IF8] Write a function that describes a relationship between two

quantities.* [F-BF1]

Combine standard function types using arithmetic operations.

[F-BF1b] For exponential models, express as a logarithm the solution to

abct = d where a, c, and d are numbers, and the base b is 2, 10,

or e; evaluate the logarithm using technology. [F-LE4]

Lessons: 4.1 – 4.7

EOC:


Convert between logarithmic and exponential equations;

graph each

Week 9

Oct.

14 - 18

EQT Review

EQT





ALGEBRA 2


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WEEK Standards/Objectives Second Quarter (40 days)

Dates:

Taught Tested

15

20

21

24

29

34

HRW Ch 5 “Project: The Ideal

Container”


Activities”


Workshop Sheet”

Dana Center Task

“You’re Toast, Dude!”

GA Dept. of Ed. Tasks

“Rational Function

Characteristics”

“Graphing Rational

Functions”

“Finding Horizontal

Asymptote”

“Inverse of a Rational

Function”

“Partial Fraction

Decomposition”

Week 10

Oct

22 - 25

(4 days)

Teacher Workday

Beginning of 2nd

Quarter

EXPLORE/PLAN

Unit 7: Rational Functions









Create equations in two or more variables to represent

relationships between quantities; graph equations on

coordinate axes with labels and scales. [A-CED2]



arise. [A-REI2]



[F-IF5] Identify the effect on the graph of replacing f(x) by f(x) + k, k


and negative); find the value of k given the graphs.

Experiment with cases and illustrate an explanation of the

effects on the graph using technology. Include recognizing

even and odd functions from their graphs and algebraic

expressions for them. [F-BF3]

Lessons: 5.2 – 5.5

EOC:




of polynomial expressions



algebraically

Recognize connections among zeros, x-intercepts, factors,

and solutions of polynomial equations





ALGEBRA 2


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Dates:

Taught Tested

15

20

21

24

29

34

HRW Ch 5 “Project: The Ideal

Container”


Activities”


Workshop Sheet”

Dana Center Task

“You’re Toast, Dude!”


“Rational Function

Characteristics”

“Graphing Rational

Functions”

“Finding Horizontal

Asymptote”

“Inverse of a Rational

Function”

“Partial Fraction

Decomposition”

Week 11

Oct 28

-

Nov 1

Parenting Day









Create equations in two or more variables to represent

relationships between quantities; graph equations on

coordinate axes with labels and scales. [A-CED2]



arise. [A-REI2]



[F-IF5] Identify the effect on the graph of replacing f(x) by f(x) + k, k


and negative); find the value of k given the graphs.

Experiment with cases and illustrate an explanation of the

effects on the graph using technology. Include recognizing

even and odd functions from their graphs and algebraic

expressions for them. [F-BF3]

Lessons: 5.2 – 5.7

EOC:




of polynomial expressions



algebraically

Recognize connections among zeros, x-intercepts,

factors, and solutions of polynomial equations





ALGEBRA 2


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Dates:

Taught Tested

37

38

39

40

41

42

43

44

45

46

Dana Center Tasks

“Gamers”

“Rock, Paper, Scissors”

“How Odd . . .”

Holt McDougal

Geometry

“Ch 13.1 Permutations

and Combinations”

“Ch 13.2 Technology

Lab”

“Ch 13.2 Lab –

Exploring

Probability Data”

“Ch 13.2 Connection:

Sampling”

Week 12

Nov

4 - 8

Unit 8: Probability

(+) Use probabilities to make fair decisions (e.g., drawing by

lots, using a random number generator). [S-MD6]

(+) Analyze decisions and strategies using probability concepts

(e.g., product testing, medical testing, pulling a hockey goalie at

the end of a game). [S-MD7]

Describe events as subsets of a sample space (the set of

outcomes), using characteristics (or categories) of the

outcomes, or as unions, intersections, or complements of other

events (“or,” “and,” “not”). [S-CP1]

Understand the conditional probability of A given B as P(A and

B)/P(B), and interpret independence of A and B as saying that

the conditional probability of A given B is the same as the

probability of A, and the conditional probability of B given A is

the same as the probability of B. [S-CP3]

Construct and interpret two-way frequency tables of data when

two categories are associated with each object being classified.

Use the two-way table as a sample space to decide if events are

independent and to approximate conditional probabilities.

[S-CP4]

Recognize and explain the concepts of conditional probability

and independence in everyday language and everyday

situations. [S-CP5]

Find the conditional probability of A given B as the fraction of

B’s outcomes that also belong to A, and interpret the answer in

terms of the model. [S-CP6]

Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B),

and interpret the answer in terms of the model. [S-CP7]

(+) Apply the general Multiplication Rule in a uniform

probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and

interpret the answer in terms of the model. [S-CP8]

(+) Use permutations and combinations to compute

probabilities of compound events and solve problems. [S-CP9]

Holt McDougal Geometry Textbook Lessons: 13.1 – 13.5

EOC:

Probability, Sequences, and Series

Use counting techniques to solve problems





ALGEBRA 2


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Dates:

Taught Tested

14

HRW Ch 7 “Project: Investigate

the Fibonacci

Numbers”


Activities”


Workshop Sheet”

Noyce Foundation

Task “Growing Staircases”

Week 13

Nov

12 - 15

(4 days)

Veteran’s Day

Unit 9: Series & Sequences

Derive the formula for the sum of a finite geometric series

(when the common ratio is not 1), and use the formula to solve

problems.* [A-SSE4]

Lessons: 7.1 – 7.5

EOC:

Probability, Sequences, and Series

Use sequences and series to solve problems

EOC

EOC

EOC

EOC

HRW Ch 9 “Project: Model

Harmonic Motion”

HRW Ch 10 “Project: Construct

Triangles”


Activities”


Activities”


Workshop Sheet”


Workshop Sheet”

Dana Center Task “Satellite”

Week 14

Nov

18 - 22

Unit 10: Trigonometry

Understand radian measure of an angle as the length of the arc

on the unit circle subtended by the angle. [F-TF1]

Explain how the unit circle in the coordinate plane enables the

extension of trigonometric functions to all real numbers,

interpreted as radian measures of angles traversed

counterclockwise around the unit circle. [F-TF2]

Define the six trigonometric functions using ratios of the sides

of a right triangle, coordinates on the unit circle, and the

reciprocal of other functions. [AL]

Choose trigonometric functions to model periodic phenomena

with specified amplitude, frequency, and midline.* [F-TF5]

Lessons: 9.1 – 9.3, 10.1 – 10.2

EOC:


Graph and determine domain, range, amplitude and

period of cosine and sine functions





ALGEBRA 2


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Dates:

Taught Tested

EOC

EOC

EOC

EOC

HRW Ch 9 “Project: Model

Harmonic Motion”

HRW Ch 10 “Project: Construct

Triangles”


Activities”


Activities”


Workshop Sheet”


Workshop Sheet”

Dana Center Task “Satellite”

Week 15

Nov

25 - 26

(2 days)

Thanksgiving Holiday

Understand radian measure of an angle as the length of the arc

on the unit circle subtended by the angle. [F-TF1]

Explain how the unit circle in the coordinate plane enables the

extension of trigonometric functions to all real numbers,

interpreted as radian measures of angles traversed

counterclockwise around the unit circle. [F-TF2]

Define the six trigonometric functions using ratios of the sides

of a right triangle, coordinates on the unit circle, and the

reciprocal of other functions. [AL]

Choose trigonometric functions to model periodic phenomena

with specified amplitude, frequency, and midline.* [F-TF5]

EOC:


Graph and determine domain, range, amplitude and

period of cosine and sine functions





ALGEBRA 2


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Dates:

Taught Tested

28 HRW Ch 8 “Project: Construct a

Hyperbola”


Activities”


Workshop Sheet”


“Getting to Know Conic

Sections Learning

Task”

“Circles Learning Task”

“Parabolas Learning

Task”

“Is It Really an Ellipse

Learning Task”

“Hyperbolas Learning

Task”

Week 16

Dec

2 - 6

Unit 11: Conics

Create graphs of conic sections, including parabolas,

hyperbolas, ellipses, circles, and degenerate conics, from

second-degree equations.

Lessons: 8.2 – 8.5

EOC:


write equations of circles and parabolas (ellipses and

hyperbolas)





ALGEBRA 2


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Resource Materials



Dates:

Taught Tested

HRW Ch 8 “Project: Construct a

Hyperbola”


Activities”


Workshop Sheet”


“Getting to Know Conic

Sections Learning

Task”

“Circles Learning Task”

“Parabolas Learning

Task”

“Is It Really an Ellipse

Learning Task”

“Hyperbolas Learning

Task”

Week 17

Dec

9 - 13

Create graphs of conic sections, including parabolas,

hyperbolas, ellipses, circles, and degenerate conics, from

second-degree equations.

Lessons: 8.6, 9.5, 9.6

EOC:



write equations of circles and parabolas (ellipses and

hyperbolas)


Use law of cosines and law of sines

TASK/EQT Review Week 18

Dec

16 - 20

End of Quarter

Complete quarterly TASK

Documents

Beginning of 1 Quarter Unit 1: Linear Equations, Inequalities, …images.pcmac.org/Uploads/MCPSS/MobileCounty/Departments... · 2013-10-10 · or Infinite Algebra 2.1 Week 4 Sept