all mathematics courses must incorporate the eight ...images.pcmac.org/uploads/gadsdencounty... ·...
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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.
2013-2014 Algebra 2 Honors
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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.
2013-2014 Algebra 2 Honors
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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
2013-2014 Algebra 2 Honors
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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
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
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COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors
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?
SEMESTER: 1 Grading Period: 1
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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-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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LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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
Additional Information
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
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CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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
2013-2014 Algebra 2 Honors
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RESOURCES
Math Worksheets http://www.kutasoftware.com/
http://www.softschools.com/math/worksh
eets/ 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.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/
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/
Math Games http://www.math-play.com/ http://www.onlinemathlearning.com/ http://coolmath.com/ http://www.mathplayground.com/
Additional Information
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
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CONCEPT
Lesson 2-8 Two-Variable Inequalities To graph two-variable inequalities
STANDARD(S)
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.
LESSON ESSENTIAL QUESTION
How do you graph an inequality?
VOCABULARY
Linear inequality Boundary Half-plane Test point
RESOURCES
Math Worksheets http://www.kutasoftware.com/
http://www.softschools.com/math/worksh
eets/ http://www.superteacherworksheets.com
http://freemathworksheets.net/
http://www.onlinemathlearning.com/ http://teachnology.com/worksheets/math
Additional Information
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
10
COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors
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?
SEMESTER: 1 Grading Period: 1
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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-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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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
2013-2014 Algebra 2 Honors
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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
Math Resources https://www.teachingchannel.org/videos http://illuminations.nctm.org/ http://krysstal.com/numbers.html http://www.ic-schools.net/tutorials
Additional Information
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 1 Recall Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
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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
Math Lessons and Worksheets http://www.algebrahelp.com/ http://exchange.smarttech.com/index.html
#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/
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/
Math Games http://www.math-play.com/ http://www.onlinemathlearning.com/ http://coolmath.com/ http://www.mathplayground.com/
Additional Information
Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning
Cognitive Complexity: Level 1: Recall
2013-2014 Algebra 2 Honors
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COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors
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
SEMESTER: 1 Grading Period: 1
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
2013-2014 Algebra 2 Honors
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VOCABULARY VOCABULARY VOCABULARY
Parabola Quadratic function Vertex form axis of symmetry vertex of a parabola minimum value Maximum value
Standard form
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
Math Resources https://www.teachingchannel.org/videos http://illuminations.nctm.org/ http://krysstal.com/numbers.html http://www.ic-schools.net/tutorials
Additional Information
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
15
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
VOCABULARY VOCABULARY VOCABULARY
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
2013-2014 Algebra 2 Honors
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RESOURCES
Math Worksheets http://www.kutasoftware.com/
http://www.softschools.com/math/worksh
eets/ 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.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/
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/
Math Games http://www.math-play.com/ http://www.onlinemathlearning.com/ http://coolmath.com/ http://www.mathplayground.com/
Additional Information
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 1 and Level 2 Recall and Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
17
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
2013-2014 Algebra 2 Honors
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LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
VOCABULARY VOCABULARY VOCABULARY
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
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/ind
ex.php
Math Resources https://www.teachingchannel.org/videos http://illuminations.nctm.org/ http://krysstal.com/numbers.html http://www.ic-schools.net/tutorials
Additional Information
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 1: Recall
Cognitive Complexity: Level 2 and Level 3 Basic Application of Skills & Concepts and Strategic Thinking & Complex Reasoning
2013-2014 Algebra 2 Honors
19
COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors
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?
SEMESTER: 1 Grading Period: 2
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
2013-2014 Algebra 2 Honors
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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
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
salgebra1/ 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/
Math Games http://www.math-play.com/ http://www.onlinemathlearning.com/ http://coolmath.com/ http://www.mathplayground.com/
Additional Information
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
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CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
VOCABULARY VOCABULARY VOCABULARY
Synthetic Division Remainder Theorem
Rational Root Theorem Conjugate Root Theorem Descartes’ Rule of Signs
Fundamental Theorem of Algebra
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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
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/ind
ex.php
Math Resources https://www.teachingchannel.org/videos http://illuminations.nctm.org/ http://krysstal.com/numbers.html http://www.ic-schools.net/tutorials
Additional Information
Cognitive Complexity: Level 1: Recall Cognitive Complexity: Level 1: Recall Cognitive Complexity: Level 1: Recall
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CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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
Math Worksheets http://www.kutasoftware.com/
http://www.softschools.com/math/worksh
eets/ 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.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/
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/
Math Games http://www.math-play.com/ http://www.onlinemathlearning.com/ http://coolmath.com/ http://www.mathplayground.com/
Additional Information
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 Basic Application of Skills & Concepts
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25
COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors
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
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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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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
Math Resources https://www.teachingchannel.org/videos http://illuminations.nctm.org/ http://krysstal.com/numbers.html http://www.ic-schools.net/tutorials
Additional Information
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
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CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
VOCABULARY VOCABULARY VOCABULARY
Rational exponent
Radical equation Square root equation
Composite function
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RESOURCES
Math Worksheets http://www.kutasoftware.com/
http://www.softschools.com/math/worksh
eets/ 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.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/
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/
Math Games http://www.math-play.com/ http://www.onlinemathlearning.com/ http://coolmath.com/ http://www.mathplayground.com/
Additional Information
Cognitive Complexity: Level 1: Recall
Cognitive Complexity: Level 1 and Level 3 Recall and Strategic Thinking & Complex Reasoning
Cognitive Complexity: Level 3 Strategic Thinking & Complex Reasoning
2013-2014 Algebra 2 Honors
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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
STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
Will the inverse of a function always be a function?
How are square root functions and quadratic functions related?
VOCABULARY VOCABULARY
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
Additional Information
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
30
COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors
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
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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
RESOURCES Math Worksheets
http://www.kutasoftware.com/
http://www.softschools.com/math/worksheets/
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
salgebra1/ 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/
Math Games http://www.math-play.com/ http://www.onlinemathlearning.com/ http://coolmath.com/ http://www.mathplayground.com/
Additional Information
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
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CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
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.
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
VOCABULARY VOCABULARY VOCABULARY
Change of Base Formula Exponential equation Logarithmic equation
Natural logarithmic 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
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
Additional Information
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
33
COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors
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?
SEMESTER: 2 Grading Period: 3
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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-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
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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
RESOURCES Math Worksheets
http://www.kutasoftware.com/
http://www.softschools.com/math/worksheets/
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 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 1 and Level 2: Recall and Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
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CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
VOCABULARY VOCABULARY VOCABULARY
Rational expression Simplest form
Complex fraction
Rational equation
2013-2014 Algebra 2 Honors
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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
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
Additional Information
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
37
COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors
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?
SEMESTER: 2 Grading Period: 3
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
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
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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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RESOURCES Math Worksheets
http://www.kutasoftware.com/
http://www.softschools.com/math/worksheets/
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 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
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
STANDARD(S) STANDARD(S)
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.
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
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
VOCABULARY VOCABULARY
Series Finite series Infinite series Arithmetic series Limits
Geometric series Converge Diverge
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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
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/ind
ex.php http://www.mathworksheetsgo.com/sheet
s/algebra-2/ http://www.tenmarks.com/
Additional Information
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
41
COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors
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?
SEMESTER: 2 Grading Period: 4
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
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VOCABULARY VOCABULARY VOCABULARY Conic section
Focus of a parabola Directrix Focal length
RESOURCES Math Worksheets
http://www.kutasoftware.com/
http://www.softschools.com/math/worksheets/
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 2 and Level 3: Basic Application of Skills & Concepts and Strategic Thinking & Complex Reasoning
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
43
COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors
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?
SEMESTER: 2 Grading Period: 4
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
2013-2014 Algebra 2 Honors
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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
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
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
Additional Information
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 1 and Level 2: Recall and Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
45
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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
2013-2014 Algebra 2 Honors
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LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
VOCABULARY VOCABULARY VOCABULARY
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
RESOURCES
Math Worksheets http://www.kutasoftware.com/
http://www.softschools.com/math/worksh
eets/ 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.a
spx?id=16385 http://www.onlinemathlearning.com/ http://www.sharemylesson.com/ http://teachers.henrico.k12.va.us/math/hc
psalgebra2/ 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 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2 and Level 3: Basic Application of Skills & Concepts and Strategic Thinking & Complex Reasoning
Cognitive Complexity: Level 2 and Level 3: Basic Application of Skills & Concepts and Strategic Thinking & Complex Reasoning
2013-2014 Algebra 2 Honors
47
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
2013-2014 Algebra 2 Honors
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VOCABULARY VOCABULARY VOCABULARY
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
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
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/ind
ex.php http://www.mathworksheetsgo.com/sheet
s/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
Additional Information
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 1 and Level 2: Recall and Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
49
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
STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
VOCABULARY VOCABULARY
Discrete probability distribution Continuous probability distribution Normal distribution
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RESOURCES
Math Worksheets http://www.kutasoftware.com/
http://www.softschools.com/math/worksh
eets/ 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.a
spx?id=16385 http://www.onlinemathlearning.com/ http://www.sharemylesson.com/ http://teachers.henrico.k12.va.us/math/hc
psalgebra2/ 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 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 1 and Level 2: Recall and Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
51
COURSE CODE: 1200340 COURSE NAME: Algebra 2 Honors
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)
SEMESTER: 2 Grading Period: 4
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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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RESOURCES Math Worksheets
http://www.kutasoftware.com/
http://www.softschools.com/math/worksheets/
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 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 1: Recall
2013-2014 Algebra 2 Honors
53
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
VOCABULARY VOCABULARY VOCABULARY
Sine function Sine curve
Cosine function
Tangent of θ Tangent function
2013-2014 Algebra 2 Honors
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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
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
Additional Information
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
2013-2014 Algebra 2 Honors
55
CONCEPT CONCEPT CONCEPT
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
STANDARD(S) STANDARD(S) STANDARD(S)
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.
LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION LESSON ESSENTIAL QUESTION
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?
VOCABULARY VOCABULARY VOCABULARY
Phase shift
Cosecant Secant cotangent
Trigonometric identity
2013-2014 Algebra 2 Honors
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RESOURCES
Math Worksheets http://www.kutasoftware.com/
http://www.softschools.com/math/worksh
eets/ 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.a
spx?id=16385 http://www.onlinemathlearning.com/ http://www.sharemylesson.com/ http://teachers.henrico.k12.va.us/math/hc
psalgebra2/ 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 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts