all mathematics courses must incorporate the eight ...images.pcmac.org/uploads/gadsdencounty... ·...

2013-2014 Algebra 2 Honors

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All mathematics courses must incorporate the Eight Mathematical Practice Standards

MACC.K12.MP.1.1 MACC.K12.MP.2.1 MACC.K12.MP.3.1

Make sense of problems and persevere in solving them

Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others

MACC.K12.MP.4.1 MACC.K12.MP.5.1 MACC.K12.MP.6.1

Model with mathematics Use appropriate tools strategically Attend to precision

MACC.K12.MP.7.1 MACC.K12.MP.

Look for and make use of structure

Look for and express regularity in repeated reasoning

Algebra 2 Honors incorporates the following LACC standards These standards can be meet by using essential questions as writing prompts for bellringers, assigning projects which have the students explore a concept and elaborate on it in detail, incorporating new vocabulary and mathematical symbols into

each lesson and having the students make connections to the words and the concepts, classroom discussions, etc

LACC.910.RST.1.3 LACC.910.RST.2.4 LACC.910.RST3.7

LACC.910.RST.1.3: Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.

LACC.910.RST.2.4: Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.

LACC.910.RST.3.7: Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.

LACC.910.SL.1.1 LACC.910.SL.1.2 LACC.910.SL.1.3

LACC.910.RL.1.1: Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

LACC.910.RL.1.2: Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.

LACC.910.RL.1.3: Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme.


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LACC.910.SL.2.4 LACC.910.WHST.1.1 LACC.910.WHST.2.4

LACC.910.RL.2.4: Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone).

LACC.910.WHST.1.1: Write arguments focused on discipline-specific content.

LACC.910.WHST.2.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

LACC.910.WHST.3.9

LACC.910.WHST.3.9: Draw evidence from informational texts to support analysis, reflection, and research.


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COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors

UNIT TITLE: Chapter 1 Expressions, Equations, and Inequalities

UNIT ESSENTIAL QUESTION: How do variables help you model real-world situations? How can you use the properties of real numbers to simplify algebraic expression? How do you solve an equation or inequality? Jeopardy Review Game http://www.avon-schools.org/Page/7739

SEMESTER: 1 Grading Period: 1

CONCEPT CONCEPT CONCEPT

Lesson 1-4 Solving Equations

To solve equations

To solve problems by writing equations

Lesson 1-5 Solving Inequalities

To solve and graph inequalities

To write and solve compound inequalities

Lesson 1-6 Absolute Value Equations and Inequalities

To write and solve equations and inequalities involving absolute value

STANDARD(S) STANDARD(S) STANDARD(S)

MACC.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. MACC.912.A-CED.1.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

MACC.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. MACC.912.F-IF.3.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima

MACC.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. MACC.912.A-SSE.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity

LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION

How can you use the properties of equality and inverse operations to solve equations?

How can you use the properties of inequality to solve inequalities?

Explain why an absolute value equation can have two solutions

VOCABULARY VOCABULARY VOCABULARY Equation Solution of an equation Inverse operations identity Literal equations

Compound inequality Absolute value Extraneous solution

http://www.avon-schools.org/Page/7739


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RESOURCES

Math Worksheets http://www.kutasoftware.com/

http://www.softschools.com/math/works

heets/ http://www.superteacherworksheets.com

http://freemathworksheets.net/

http://www.onlinemathlearning.com/ http://teachnology.com/worksheets/math

Math Lessons and Worksheets http://www.algebrahelp.com/ http://exchange.smarttech.com/index.html

#tab=0 http://www.nctm.org/resources/content.as

px?id=16385 http://www.onlinemathlearning.com/ http://www.sharemylesson.com/ http://teachers.henrico.k12.va.us/math/hcp

salgebra2/ http://worksheets.theteacherscorner.net/

Math Lessons and Worksheets http://www.crctlessons.com/algebra-

lessons.html http://people.hofstra.edu/stefan_Waner/r

ealworld/tut_alg_review/framesA_3B.html https://www.khanacademy.org/ http://www.thatquiz.org/

Math Games http://www.math-play.com/ http://www.onlinemathlearning.com/ http://coolmath.com/ http://www.mathplayground.com/

Additional Information

Cognitive Complexity: Level 1 and Level 2 Recall and Basic Application of Skills & Concepts

Cognitive Complexity: Level 2 Basic Application of Skills & Concepts


http://www.thatquiz.org/


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UNIT TITLE: Chapter 2 Functions, Equations, and Graph

UNIT ESSENTIAL QUESTION: Does it matter which form of a linear euation you use? How do you use transformations to help graph absolute value functions? How can you model data with a linear function?



Lesson 2-2 Direct Variation

To write and interpret direct variation equations

Lesson 2-3 Linear Functions and Slope-Intercept Form

To graph linear equations

To write equations of lines

Lesson 2-4 More About Linear Equations

To write an equation of a line given its slope and a point on the line

Graph piecewise functions


MACC.912.A-CED.1.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.


MACC.912.F-IF.3.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. MACC.912.F-IF.3.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). MACC.912.F-IF.3.7b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions


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How do you write and interpret direct variation equations?

How would you describe the slope of a line on a coordinate plane?

What can you determine about two lines given their slope?

VOCABULARY VOCABULARY VOCABULARY Direct variation Constant of variations

Slope-InterceptLinear function Linear equation y-intercept x-intercept slope-intercept form

Point-slope form standard form of a linear equation parallel lines perpendicular lines Piecewise function Step function Greatest integer function

RESOURCES Math Resources http://mathforum.org/mbower/johnandb

etty/frame.htm http://mathforum.org/ http://www.purplemath.com/modules/ http://mathwords.com/ http://people.hofstra.edu/stefan_Waner/r

ealworld/tut_alg_review/framesA_3B.html

Math Resources http://www.mathsisfun.com/ http://www.aaamath.com/ http://interactmath.com/Default.aspx http://algebrafunsheets.com/AlgebraII/inde

x.php http://www.mathworksheetsgo.com/sheets

/algebra-2/ http://www.tenmarks.com/

Math Resources https://www.teachingchannel.org/videos http://illuminations.nctm.org/ http://krysstal.com/numbers.html http://www.ic-schools.net/tutorials





http://www.mathworksheetsgo.com/sheets/algebra-2/


http://www.tenmarks.com/


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Lesson 2-5 Using Linear Models

To write linear equations that model real-world data

To make predictions from linear models

Lesson 2-6 Families of Functions

To analyze transformations of functions Lesson 2-7 Absolute Value Functions and Graphs

To graph absolute value functions


MACC.912.F-IF.2.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

MACC.912.F-BF.2.3: 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.

MACC.912.F-BF.2.3: 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.


How do you model a real-world situation with linear equations?

How do you use parent functions to graph transformations?

What does the absolute value functions represent?

VOCABULARY VOCABULARY VOCABULARY

Scatter plot correlation line of best fit Correlation coefficient

Parent function Transformation Translation Reflection Vertical stretch Vertical compression

Absolute value function Axis of symmetry Vertex


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RESOURCES


http://www.softschools.com/math/worksh

eets/ http://www.superteacherworksheets.com




#tab=0 http://www.nctm.org/resources/content.a

spx?id=16385 http://www.onlinemathlearning.com/ http://www.sharemylesson.com/ http://teachers.henrico.k12.va.us/math/hc

psalgebra1/ http://worksheets.theteacherscorner.net/



ealworld/tut_alg_review/framesA_3B.html https://www.khanacademy.org/







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CONCEPT

Lesson 2-8 Two-Variable Inequalities To graph two-variable inequalities

STANDARD(S)


LESSON ESSENTIAL QUESTION

How do you graph an inequality?

VOCABULARY

Linear inequality Boundary Half-plane Test point

RESOURCES








http://teachnology.com/worksheets/math


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UNIT TITLE: Chapter 3 Linear Systems

UNIT ESSENTIAL QUESTION: How does representing functions graphically help you solve a system of equations? How does writing equivalent equations help solve a system of equations? How are the properties of equality used in the matrix solution of a system of equations?



Lesson 3-1 Solving Systems Using Tables and Graphs

To solve a linear system using a graph or a table

Lesson 3-2 Solving Systems Algebraically

To solve linear systems algebraically Lesson 3-3 Systems of Inequalities

To solve systems of linear inequalities



MACC.912.A-REI.3.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

MACC.912.A-REI.4.12: Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.


How do you solve a system of equation by graphing?

How do you solve a system of equation algebraically?

How do you solve a system of inequalities?

VOCABULARY VOCABULARY VOCABULARY System of equations Linear system solution of a system inconsistent system consistent system independent system dependent system

Equivalent system Systems of linear inequalities


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Cognitive Complexity: Level 1 Recall Cognitive Complexity: Level 2 Basic Application of Skills & Concepts


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CONCEPT CONCEPT

Lesson 3-4 Linear Programming

To solve problems using linear programming

Lesson 3-5 Systems with Three Variables

To solve systems in three variables using elimination

To solve systems in three variables using substitution

STANDARD(S) STANDARD(S)

MACC.912.A-CED.1.3: 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.

MACC.912.A-REI.3.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION

How do you solve real-world problems involving multiple linear relationships?

How do you solve systems of three equations in three variables?

VOCABULARY VOCABULARY

Constraints Linear programming feasible region Objective function

RESOURCES










Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cognitive Complexity: Level 1: Recall


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UNIT TITLE: Chapter 4 Quadratic Functions and Equations

UNIT ESSENTIAL QUESTION: What are the advantages of a quadratic function in vertex form or standard form? How is any quadratic function related to the parent quadratic function? How are the real solutions of a quadratic equation related to the graph of the related quadratic function? Jeopardy Review Game http://www.avon-schools.org/Page/7739



Lesson 4-1 Quadratic Functions and Transformations

To identify and graph quadratic functions

Lesson 4-2 Standard Form of a Quadratic Function

To graph quadratic functions written in standard form

Lesson 4-3 Modeling with Quadratic Functions

To model data with quadratic functions


MACC.912.F-BF.2.3: 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. MACC.912.F-IF.3.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima

MACC.912.A-CED.1.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MACC.912.F-IF.3.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima

MACC.912.F-IF.2.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes


How is any quadratic related to the parent quadratic function?

What useful information does the graph of a quadratic equation give you?

How would you describe three noncollinear points if with no two are in line vertically?

http://www.avon-schools.org/Page/7739


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Parabola Quadratic function Vertex form axis of symmetry vertex of a parabola minimum value Maximum value

Standard form





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Lesson 4-4 Factoring Quadratic Expressions

To find common and binomial factors of quadratic expressions

To factor special quadratic expressions

Lesson 4-5 Quadratic Equations

To solve quadratic equations by factoring

To solve quadratic equations by graphing

Lesson 4-6 Completing the Square

To solve equations by completing the square

To rewrite functions by completing the square


MACC.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it. MACC.912.A-SSEE.2.3a: Factor a quadratic expression to reveal the zeros of the function it defines

MACC.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. MACC.912.A-APR.2.3: 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. MACC.912.F-IF.3.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima

MACC.912.A-REI.4b: 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. MACC.912.A-SSE.2.3b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.


How do you factor quadratic trinomials into products of two binomials?

How do you solve a quadratic equation by finding the zeros?

What does completing a perfect square trinomial allow you to do?


Factoring Greatest common factor (GCF) of an expression Perfect square trinomial difference of two squares

Zero of a function Zero-product property

Completing the Square


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RESOURCES
















Cognitive Complexity: Level 1 and Level 2 Recall and Basic Application of Skills & Concepts



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Lesson 4-7 The Quadratic Formula

To solve quadratic equations using th Quadratic Formula

To determine the number of solutions by using the discriminant

Lesson 4-8 Complex numbers

To identify, graph, and perform operations with complex numbers

To find complex number solutions of quadratic equations

Lesson 4-9 Quadratic Systems

To solve and graph systems of linear and quadratic equations

To solve and graph systems of quadratic inequalities


MACC.912.A-REI.4b: 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.

MACC.912.N-CN.1.1: 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. MACC.912.N-CN.1.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. MACC.912.N-CN.3.7: Solve quadratic equations with real coefficients that have complex solutions. MACC.912.N-CN.3.8: Extend polynomial identities to the complex numbers.

MACC.912.A-CED.1.3: 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. MACC.912.A-REI.3.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically MACC.912.A-REI.4.11: 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.


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How do you use the quadratic equation to solve quadratic in standard form?

What are the complex numbers based on? How is solving systems involving quadratic equations similar to systems involving linear equations?


Quadratic formula Discriminant

Imaginary unit imaginary number complex number pure imaginary number complex number plane absolute value of a complex number complex conjugates

Systems of quadratic inequalities

RESOURCES

Math Resources http://mathforum.org/mbower/johnandbe

tty/frame.htm http://mathforum.org/ http://www.purplemath.com/modules/ http://mathwords.com/ http://people.hofstra.edu/stefan_Waner/r


Math Resources http://www.mathsisfun.com/ http://www.aaamath.com/ http://interactmath.com/Default.aspx http://algebrafunsheets.com/AlgebraII/ind

ex.php





Cognitive Complexity: Level 2 and Level 3 Basic Application of Skills & Concepts and Strategic Thinking & Complex Reasoning


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UNIT TITLE: Chapter 5 Polynomials and Polynomial Functions

UNIT ESSENTIAL QUESTION: What does the degree of a polynomial function tell you about its related polynomial function? For a polynomial function, how are factors, zeros, and x-intercepts related? For a polynomial equation, how are factors and roots related?



Lesson 5-1 Polynomial Functions

To classify polynomials

To graph polynomial functions and describe end behavior

Lesson 5-2 Polynomials, Linear, Factors, and Zeros

To analyze the factored form of a polynomial

To write a polynomial function from its zero

Lesson 5-3 Solving Polynomial Equations

To solve polynomial equations by factoring

To solve polynomial equations by graphing


MACC.912.A-SSE.1.1a: Interpret parts of an expression, such as terms, factors, and coefficients MACC.912.F-IF.3.7c: Graph polynomial functions, identify zeros and asymptotes when suitable factorizations are available, and showing end behavior

MACC.912.F-IF.3.7c: Graph polynomial functions, identify zeros and asymptotes when suitable factorizations are available, and showing end behavior MACC.912.A-SSE.2.3c: Use the properties of exponents to transform expressions for exponential functions.

MACC.912.A-REI.4.11: 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.


How can you know the “behaviors” of a polynomial by looking at its algebraic form?

How can the zeros of a polynomial function help you fact the polynomial, graph the function, and solve the related polynomial equation?

How do you solve polynomial functions by graphing and factoring?


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VOCABULARY VOCABULARY VOCABULARY Monomial Degree of a monomial Polynomial Degree of a polynomial Polynomial function Standard form of a polynomial function turning point end behavior

Factor theorem multiple zero multiplicity relative maximum relative minimum

Sum of cubes Difference of cubes

RESOURCES Math Worksheets

http://www.kutasoftware.com/

http://www.softschools.com/math/worksheets/

http://www.superteacherworksheets.com
















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Lesson 5-4 Dividing Polynomials

To divide polynomials using long division

To divide polynomials using synthetic division

Lesson 5-5 Theorems About Roots of Polynomial Equations

To solve equations using the Rational Root Theorem

To use the Conjugate Root Theorem

Lesson 5-6 The Fundamental Theorem of Algebra

To use the Fundamental Theorem of Algebra to solve polynomial equations with complex solutions


MACC.912.A-APR.2.2: 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).

MACC.912.N-CN.3.7: Solve quadratic equations with real coefficients that have complex solutions.

MACC.912.N-CN.3.7: Solve quadratic equations with real coefficients that have complex solutions. MACC.912.N-CN.3.8: Extend polynomial identities to the complex numbers. MACC.912.N-CN.3.9: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.


How is dividing whole numbers using long division similar to dividing polynomials with long division?

How do you use the Rational Root Theorem and Conjugate Root Theorems to solve equations?

How can the degree of a polynomial equation help you determine how many roots the equation has?


Synthetic Division Remainder Theorem

Rational Root Theorem Conjugate Root Theorem Descartes’ Rule of Signs

Fundamental Theorem of Algebra


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RESOURCES





ex.php



Cognitive Complexity: Level 1: Recall Cognitive Complexity: Level 1: Recall Cognitive Complexity: Level 1: Recall


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Lesson 5-7 The Binomial Theorem

To expand a binomial using Pascal's Triangle

To use the Binomial Theorem

Lesson 5-8 Polynomial Models in the Real World

To fit data to linear, quadratic, cubic, or quartic models

Lesson 5-9 Transforming Polynomial Functions

To apply transformations to graphs of polynomials


MACC.912.A-APR.3.5: Know and apply the Binomial Theorem for the expansion of (x+y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

MACC.912.F-IF.2.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

MACC.912.F-BF.2.3: 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.


How can you use Pascal's Triangle and the Binomial Theorem to expand polynomials?

How do you analyze data to determine the type of polynomial function it represents?

How do you apply transformations to graphs of polynomials?

VOCABULARY VOCABULARY VOCABULARY Expand Pascal's Triangle Binomial Theorem

Power function Constant of proportionality


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RESOURCES



















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UNIT TITLE: Chapter 6 Radical Functions and Rational Exponents

UNIT ESSENTIAL QUESTION: To simplify the nth root of an expression, what must be true about the expression? When you square each side of an equation, is the resulting equation equivalent to the original? How are a function and its inverse function related? SEMESTER: 1 Grading Period: 2


Lesson 6-1 Roots and Radical Expressions

To find nth roots

Lesson 6-2 Multiplying and Dividing Radical Expressions

To multiply and divide radical Expressions

Lesson 6-3 Binomial Radical Expressions

To add and subtract expressions


MACC.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it.

MACC.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it. MACC.912.A-APR.4.7: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

MACC.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it. MACC.912.A-APR.4.7: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.


How are powers and roots related?

How can you simplify a radical expression? Do the properties of real numbers apply to radicals? If so which ones and why?

VOCABULARY VOCABULARY VOCABULARY nth root Principal root Radicand Index

Simplest form of a radical Rationalize the denominator

Like radicals


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Cognitive Complexity: Level 2: Basic Application of Skills & Concepts




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Lesson 6-4 Rational Exponents

To simplify expressions with rational exponents

Lesson 6-5 Solving Square Root and Other Radical Equations

To solve square root and other radical equations

Lesson 6-6 Function Operations

To add, subtract, multiply, and divide functions

To find the composite of two functions


MACC.912.N-CN.1.1: 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.

MACC.912.N-CN.1.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

MACC.912.A-REI.1.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

MACC.912.A-CED.1.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

MACC.912.F-BF.1.1: Write a function that describes a relationship between two quantities.


How can you write radical expression in an equivalent form using fractional exponents?

How do you get an extraneous solution when solving a square root equation?

What is the difference between performing simple operations of functions and real numbers?


Rational exponent

Radical equation Square root equation

Composite function


28

RESOURCES
















Cognitive Complexity: Level 1 and Level 3 Recall and Strategic Thinking & Complex Reasoning

Cognitive Complexity: Level 3 Strategic Thinking & Complex Reasoning


29

CONCEPT CONCEPT

Lesson 6-7 Inverse Relations and Functions

To find the inverse of a relation or function

Lesson 6-8 Graphing Radical Functions

To graph square root and other radical functions


MACC.912.F-BF.2.4: Find inverse functions.

MACC.912.F-IF.3.7b: Graph square root, cubic root, and peicewise-defined functions, including step functions and absolute value functions

MACC.912.F-IF.3.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.


Will the inverse of a function always be a function?

How are square root functions and quadratic functions related?


Inverse relation Inverse function One-to-one function

Radical function Square root function

RESOURCES

Math Resources

http://mathforum.org/mbower/johnandbetty/frame.htm

http://mathforum.org/

http://www.purplemath.com/modules/

http://mathwords.com/

http://people.hofstra.edu/stefan_Waner/realworld/tut_alg_review/framesA_3B.html

Math Resources

http://www.mathsisfun.com/

http://www.aaamath.com/

http://interactmath.com/Default.aspx

http://algebrafunsheets.com/AlgebraII/index.php





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UNIT TITLE: Chapter 7 Exponential and Logarithmic Functions

UNIT ESSENTIAL QUESTION: How do you model a quantity that changes regularly over time by the same percentage? How are exponents and logarithms related? How are exponential functions and logarithmic functions related? SEMESTER: 2 Grading Period: 3


Lesson 7-1 Exploring Exponential Models

To model exponential growth and decay

Lesson 7-2 Properties of exponential functions

To explore the properties of functions of the form y = abx

To graph exponential functions that have base e

Lesson 7-3 Logarithmic Functions as Inverses

To write and evaluate logarithmic expressions

To graph logarithmic functions


MACC.912.A-CED.1.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MACC.912.F-IF.3.7e: Graph exponential and logarithmic functions, showing intercepts and end behaviors, and trigonometric functions, showing period, midline, and amplitude

MACC.912.F-IF.3.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. MACC.912.F-IF.3.7e: Graph exponential and logarithmic functions, showing intercepts and end behaviors, and trigonometric functions, showing period, midline, and amplitude

MACC.912.F-IF.3.7e: Graph exponential and logarithmic functions, showing intercepts and end behaviors, and trigonometric functions, showing period, midline, and amplitude MACC.912.F-BF.2.4: Find inverse functions.


How can repeated multiplication with a function be represented?

Explain what the factor a does to the graph of y =

abx. If the exponential function y = bx is one-to-one, then what is it’s inverse?


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VOCABULARY VOCABULARY VOCABULARY Exponential function Exponential growth Exponential decay Asymptote Growth factor Decay factor

Natural base exponential function Continuously compounded interest

Logarithm Logarithmic function Common Logarithm Logarithmic Scale




















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Lesson 7-4 Properties of Logarithms

To use the properties of logarithms

Lesson 7-5 Exponential and Logarithmic Equations

To solve exponential and logarithmic equations

Lesson 7-6 Natural Logarithms

To evaluate and simplify natural logarithmic expressions

To solve equations using natural logarithms


MACC.912.F-LE.1.4: 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.




How are the properties of logarithms related to the properties of exponents?

How do you use logarithms to solve exponential equations and vice versa?

How are the natural logarithmic functions related to their inverse?


Change of Base Formula Exponential equation Logarithmic equation

Natural logarithmic function

RESOURCES

Math Resources






Math Resources
















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UNIT TITLE: Chapter 8 Rational Functions

UNIT ESSENTIAL QUESTION: Are two quantities inversely proportional if an increase in one corresponds to a decrease in the other? What kinds of asymptotes are possible for a rational function? Are a rational expression and its simplified form equivalent?



Lesson 8-1 Inverse Variation

To recognize and use inverse variation

To use joint and other variations

Lesson 8-2 The Reciprocal Function Family

To graph reciprocal functions

To graph translations of reciprocal functions

Lesson 8-3 Rational Functions and Their Graphs

To identify properties of rational functions

To graph rational functions



MACC.912.F-BF.2.3: 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. MACC.912.A-CED.1.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

MACC.912.A-APR.2.3: 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. MACC.912.F-BF.1.1b: Combine standard function types using arithmetic operations


What is an inverse variation and how is it used?

What do the transformations of the parent reciprocal function include?

Explain what happens to the graph of a function if it has a polynomial in its denominator.


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VOCABULARY VOCABULARY VOCABULARY Inverse variation Combined Variation Joint variation

Reciprocal function Branch

Rational function Continuous graph Discontinuous graph Point of discontinuity Removable discontinuity Non-removable discontinuity


















Cognitive Complexity: Level 1 and Level 2: Recall and Basic Application of Skills & Concepts



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Lesson 8-4 Rational Expressions

To simplify rational expressions

To multiply and divide rational expressions

Lesson 8-5 Adding and Subtracting Rational Expressions

To add and subtract rational expressions

Lesson 8-6 Solving Rational Equations

To solve rational equations

To use rational equations to solve problems


MACC.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it MACC.912.A-SSE.1.1a: Interpret complicated expressions by viewing one or more of their parts as a single entity

MACC.912.A-APR.4.7: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

MACC.912.A-APR.4.7: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.


How is multiplying and dividing fractions similar to multiplying and dividing rational expressions?

How is adding and subtracting fractions similar to adding and multiplying rational expressions?

How do you approach solving and equation containing rational expressions? Can there be extraneous solutions?


Rational expression Simplest form

Complex fraction

Rational equation


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RESOURCES

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Math Resources
















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UNIT TITLE: Chapter 9 Sequences and Series

UNIT ESSENTIAL QUESTION: How can you represent the terms of a sequence explicitly? How can you represent them recursively? What are equivalent explicit and recursive definitions for an arithmetic sequence? How can you model a geometric sequence? How can you model its sum?



Lesson 9-1 Mathematical Patterns

To identify mathematical patterns found in a sequence

To use a formula to find the nth term of a sequence

Lesson 9-2 Arithmetic sequences

To define, identify, and apply arithmetic sequences

Lesson 9-3 Geometric Sequences

To define, identify, and apply arithmetic sequences


MACC.912.F-BF.1.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. MACC.912.A-SSE.2.4: 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

MACC.912.F-BF.1.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. MACC.912.F-IF.1.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.



How do you relate numbers in a list if there is a pattern?

How can you build an arithmetic sequence? How can you build a geometric sequence?

VOCABULARY VOCABULARY VOCABULARY Sequence Term of a sequence Explicit formula Recursive formula

Arithmetic sequence Common difference Arithmetic mean

Geometric sequence Common ratio Geometric mean


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39

CONCEPT CONCEPT

Lesson 9-4 Arithmetic Series

To define arithmetic series and find their sums

Lesson 9-5 Geometric Series

To define geometric series and find their sums


MACC.912.F-BF.1.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. MACC.912.F-IF.1.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.



How can you find the sum of a finite arithmetic sequence if you know two terms and the total numbers of terms?

How can you find the sum of a finite geometric sequence if you know the first term, the number of terms, and the common ratio?


Series Finite series Infinite series Arithmetic series Limits

Geometric series Converge Diverge


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RESOURCES





ex.php http://www.mathworksheetsgo.com/sheet

s/algebra-2/ http://www.tenmarks.com/








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UNIT TITLE: Chapter 10 Quadratic Relations and Conic Sections

UNIT ESSENTIAL QUESTION: What is the intersection of a cone and a plane parallel to a line along the side of the cone?



Lesson 10-1 Exploring Conic Sections

To graph and identify conic sections

Lesson 10-2 Parabolas

To write the equation of a parabola and to graph parabolas

Lesson 10-6 Translating Conic Sections

To write the equation of a translated conic section

To identify a translated conic section from an equation


MACC.912.G-GPE.1.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. MACC.912.G-GPE.1.2: Derive the equation of a parabola given a focus and directrix. MACC.912.G-GPE.1.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

MACC.912.G-GPE.1.2: Derive the equation of a parabola given a focus and directrix.

MACC.912.G-GPE.1.2: Derive the equation of a parabola given a focus and directrix.


Identify the four types of curves known as conic sections. Identify the distinct shape and properties of each.

How are the focus and directrix related? How would you write the equation of a translated conic section?


42

VOCABULARY VOCABULARY VOCABULARY Conic section

Focus of a parabola Directrix Focal length
















Cognitive Complexity: Level 2 and Level 3: Basic Application of Skills & Concepts and Strategic Thinking & Complex Reasoning





43


UNIT TITLE: Chapter 11 Probability and Statistics

UNIT ESSENTIAL QUESTION: What is the difference between a permutation and a combination? What is the difference between experimental and theoretical probability? How are measures of central tendency difference from standard deviation?



Lesson 11-1 Permutations and Combinations

To count permutations

To count combinations

Lesson 11-2 Probability

To find the probability of an event using theoretical, experimental, and simulation methods

Lesson 11-3 Probability of Multiple Events

To find the probability of event A and B

To find the probability of event A or B


MACC.912.S-CP.2.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

MACC.912.S-IC.1.2: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation

MACC.912.S-CP.1.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. MACC.912.S-CP.1.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. MACC.912.S-CP.2.7: 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.


How can you use multiplication to quickly count the number of ways certain things can happen?

Explain the different ways to find probability of an event?

How do you find the probability of two events occurring together?


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VOCABULARY VOCABULARY VOCABULARY Fundamental counting principle Permutation N factorial combination

Experimental probability Simulation Sample space Equally likely outcomes Theoretical probability

Dependent events Independent events Mutually exclusive events

RESOURCES Math Resources






Math Resources
















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Lesson 11-4 Conditional Probability

To find conditional probabilities

To use tables and tree diagrams to determine conditional probabilities

Lesson 11-5 Probability Models

To use probabilities to make fair decisions and analyze decisions

Lesson 11-6 Analyzing Data

To calculate measures of central tendency

To draw and interpret box-and-whisker plots


MACC.912.S-CP.1.3: 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. MACC.912.S-CP.1.4: 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. MACC.912.S-CP.1.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. MACC.912.S-CP.2.6: 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. MACC.912.S-CP.2.8: 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.

MACC.912.S-MD.2.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). MACC.912.S-MD.2.7: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game) LACC.910.SL.1.3: Evaluate s speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence

MACC.912.S-MD.2.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). MACC.912.S-MD.2.7: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a gam


46


When does conditional probability exist? How can you use probability models to analyze situations and make decisions?

Depending on what characteristics you want to study, how can you describe and compare sets of data?


Conditional probability Contingency table

Probability model

Measure of central tendency Mean Median Mode Bimodal Outlier Range of a set of data Quartile Interquartile range Box-and-whisker plot percentile

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Lesson 11-7 Standard Deviation

To find the standard deviation and variance of a set of values

To apply standard deviation and variance

Lesson 11-8 Samples and Surveys

To identify sampling methods

To recognize bias in samples and surveys

Lesson 11-9 Binomial Distributions

To binomial probabilities and to use binomial distributions


MACC.912.S-IC.2.6: Evaluate reports based on data. MACC.912.S-ID.1.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

MACC.912.S-IC.1.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. MACC.912.S-IC.2.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. MACC.912.S-IC.2.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. MACC.912.S-IC.2.6: Evaluate reports based on data.

MACC.912.S-CP.2.9: Use permutations and combinations to compute probabilities of compound events and solve problems.


What does the standard deviation measure and how is it used?

What kind of statistical information can you collect about a population by studying a sample of the population?

How can you use binomial probabilities in situations involving two possible outcomes?


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Measure of variation Variance Standard deviation

Population Sample Convenience sample Self-selected sample Systematic sample Random sample Bias Observational bias Observational study Controlled experiment survey

Binomial experiment Binomial probability Binomial theorem

RESOURCES





ex.php http://www.mathworksheetsgo.com/sheet

s/algebra-2/ http://www.tenmarks.com/










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CONCEPT CONCEPT

Lesson 11-10 Normal Distributions

To use a normal distibution Use unions, intersections, or complements

to describe the set of outcomes

Apply the Addition Rule


MACC.912.S-ID.1.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

MACC.912.S-CP.1.1: 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”). MACC.912.S-CP.2.7: 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.


Why do many common statistics gathered from samples in the natural world tend to have a normal distribution about their mean?

How would you describe a set of outcomes using unions, intersections, or complements? How do you apply the Addition Rule?


Discrete probability distribution Continuous probability distribution Normal distribution


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51


UNIT TITLE: Chapter 13 Trigonometry

UNIT ESSENTIAL QUESTION: How can you model periodic behavior? (Common Core does not require N-VM to be taught in Algebra 2, therefore, Chapter 12 is optional)



Lesson 13-1 Exploring Periodic Data

To identify cycles and periods of periodic functions

To find the amplitude of periodic functions

Lesson 13-2 Angles and the Unit Circle

To work with angles in standard position

To find coordinates of points on the unit circle

Lesson 13-3 Radian Measure

To use radian measure for angles

To find the length of an arc of a circle


MACC.912.F-IF.2.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

MACC.912.F-TF.1.2: 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.

MACC.912.F-TF.1.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.


What is periodic behavior? Give an example.

Explain what the input and output are and how they are related.

How do you find the arc of a circle?

VOCABULARY VOCABULARY VOCABULARY Periodic function cycle period amplitude

Standard position Initial side Terminal side Coterminal angles Unit circle Cosine of θ Sine of θ

Central angle Intercepted arc radian


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53


Lesson 13-4 The Sine Function

To identify properties of the sine function

To graph since curves

Lesson 13-5 The Cosine Function

To graph and write cosine functions

To solve trigonometric equations

Lesson 13-6 The Tangent Function

To graph the tangent function


MACC.912.F-TF.1.2: 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.

MACC.912.F-TF.2.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. MACC.912.F-IF.2.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship

MACC.912.F-IF.3.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude MACC.912.F-TF.1.2: 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.


What are the properties of the sine function?

What can you tell me about each and every point along the unit circle?

Explain what a tangent function is?


Sine function Sine curve

Cosine function

Tangent of θ Tangent function


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Math Resources
















55


Lesson 13-7 Translating Sine and Cosine Functions

To graph translations of trigonometric functions

To write equations of translations

Lesson 13-8 Reciprocal Trigonometric Functions

To evaluate reciprocal trigonometric functions

To graph reciprocal trigonometric functions

Lesson 14-1 Trigonometric Identities

To verify trigonometric identities


MACC.912.F-IF.3.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude MACC.912.F-TF.2.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

MACC.912.F-IF.3.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude

MACC.912.F-TF.3.8: Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.


How is translating periodic functions similar to translating other functions?

What are the reciprocals of cosine, sine, and tangent? How are the found?

How can you write trigonometric expressions in various equivalent forms using the six basic trigonometric functions?


Phase shift

Cosecant Secant cotangent

Trigonometric identity


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