unit plan templatekenwoodacademy.enschool.org/ourpages/auto/2014/9/8... · Web view2014. 9....

Kenwood Academy: Curriculum Map 2014-2015TeacherFirst and Last Name Anton, Fatima

Del Rio, EmmanuelMcDonnell, BernadetteMcEvoy-Hein, JeffreyRoach, GinnaWidell, Elizabeth

Course Advanced Algebra with Trig

Subject Area Mathematics

Grade Level 11th grade

UnitsCalendarUnit 1 Title Functions and Their Inverses Dates (school calendar weeks) September 2 – September 22 (15 days)Unit 2 Title Quadratic and Square Root FunctionsDates (school calendar weeks) September 23 – November 18 (37 days)Unit 3 Title Systems of EquationsDates (school calendar weeks) November 19 – December 19 (20 days)Unit 4 Title Power Functions and Rational Functions Dates (school calendar weeks) January 5 – January 14 (8 days)Unit 5 Title Polynomial and Composite Functions Dates (school calendar weeks) January 14 – January 29 (9 days including finals)Unit 6 Title ACT Review Dates (school calendar weeks) February 2 – March 2 (20 days)Unit 7 Title Exponential and Logarithmic FunctionsDates (school calendar weeks) March 3 – April 17 (27 days)Unit 8 Title Trigonometric Functions Dates (school calendar weeks) April 20 – June 16 (41 days including finals)

Unit 1 Summary + Curriculum AlignmentUnit Title Functions and Their InversesMajor Topics

Function Parent Functions: Linear, Quadratic, Exponential, and Absolute Value Inverse of a Relation & Linear, Quadratic, and Exponential Functions

Description of Primary Performance Task

NOTE: One task per unit

The task requires students to analyze a situation, describe the appropriate function for the situation using multiple representations, and make connections among the representations. The task provides an opportunity to compare various types of functions.

Common Core Standard(s) Related to Task

Number and QuantityN-Q.01Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.N-Q.02Define appropriate quantities for the purpose of descriptive modeling.Functions

FunctionsF-BF.04Find inverse functions.

a. Solve an equation of the form f(x) = c for a simple function fthat has an inverse and write an expression for the inverse. Forexample, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1.b. (+) Verify by composition that one function is the inverse ofanother.c. (+) Read values of an inverse function from a graph or a table,given that the function has an inverse.d. (+) Produce an invertible function from a non-invertible functionby restricting the domain.

F-LE.01Distinguish between situations that can be modeled with linear functions and with exponential functions.

a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

F-LE.03Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

CRS Supporting Skills

College Bound Level 1 (16-19)PSDA: Read tables and graphs

Level 2 (20-23)PSDA: Translate from one representation of data to another (e.g., a bar graph to a circle graph)EEI: Solve routine first degree equationsGR: Locate points in the coordinate plane

F: Evaluate quadratic functions, expressed in function notation, at integer values

Level 3 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equations, Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions), GR: Match linear graphs with their equations.F: Evaluate polynomial functions, expressed in function notation, at integer values

Pre-Accelerated Level 1 (20-23)PSDA: Translate from one representation of data to another (e.g., a bar graph to a circle graph)EEI: Solve routine first degree equationsGR: Locate points in the coordinate planeF: Evaluate quadratic functions, expressed in function notation, at integer values


Level 3 (28-32):PSDA: Interpret and use information from figures, tables, and graphsEEI: Write expressions, equations, or inequalities for common algebra settings, Manipulate expressions and equations GR: Interpret and use information from graphs in the coordinate planeF: Evaluate composite functions at integer values

Honors Level 1 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equations, Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions), GR: Match linear graphs with their equations.F: Evaluate polynomial functions, expressed in function notation, at integer values

Level 2 (28-32)PSDA: Interpret and use information from figures, tables, and graphsEEI: Write expressions, equations, or inequalities for common algebra settings, Manipulate expressions and equations GR: Interpret and use information from graphs in the coordinate planeF: Evaluate composite functions at integer values

Level 3 (33-36)PSDA: Analyze and draw conclusions based on information from figures, tables and graphs.EEI: Write equations and inequalities that require planning, manipulating, and/or

solvingGR: Analyze and draw conclusions based on information from graphs in the coordinate plane, Identify characteristic of graphs based on a set of conditions or on a general equation such as y=ax2+cF: Write an expression for the composite of two simple functions

Interdisciplinary Integrations /Thematic Connections

In this unit, students will see the connection to problems of motion in science (physics) when they will study inverse functions.

Assessment

Diagnostic/ Pre-Assessment

College Bound Unit 1 Diagnostic on CRS 16-19

Pre-Accelerated Unit 1 Diagnostic on CRS 20-23

Honors Unit 1 Diagnostic on CRS 24-27

Formative

College Bound Homework, Exit Tickets, Classwork, Bell Ringers, Quizzes, Calculator Activities, Performance TaskPre-Accelerated

Honors

Summative

College Bound Unit 1ExamI. Multiple Choice (ACT Style)II. Free Response

Pre-Accelerated

Honors

Supplementary Text

Glencoe Algebra II Pearson Algebra 2 – Common Core

Framing QuestionsEssential Question(s)

How can you model data with a Linear, Quadratic, Exponential, and Absolute Value function?What is the relationship between a function and its inverse?Is the inverse of a function always a function?

Unit Content Questions

Can you represent functions algebraically, graphically, numerically and verbally?How do we identify the domain and range of the function?What is the difference between the domain and range of a function versus the domain and range of the problem situation?How do we identify a function using the vertical line test?

Unit 2 Summary + Curriculum AlignmentUnit Title Quadratic and Square Root FunctionsMajor Topics Quadratic Forms

Factoring Completing the Square Solving Quadratic Equations The Quadratic Formula Complex Numbers Graphing Quadratic and Square Root Functions Transforming Quadratic Functions Solving Square Root Equations Algebraically Solving Square RootEquations Graphically



Performance Task 1 (honors) and Task 2 (regulars) on page 266 in Pearson.


FunctionsF-IF.04For 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicityF-IF.05Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.F-IF.07.bGraph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

AlgebraA-CED.01Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A-CED.02Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.A-CED.03Represent 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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.A-REI.02Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.A-REI.11Explain why the <Bx-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.Number and Quantity

N-CN.01Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.N-CN.07

Solve quadratic equations with real coefficients that have complex solutions.CRS Supporting Skills

College Bound Level 1 (16-19)PSDA: Read tables and graphsEEI: Solve one step equations having integer or decimal answersEEI: Combine Like Terms

Level 2 (20-23)PSDA: Translate from one representation of data to another (e.g., a bar graph to a circle graph)EEI: Solve routine first degree equationsEEI: Multiply two binomialsEEI: Perform straightforward word to symbol translationsEEI: Evaluate algebraic expressions by substituting integers for unknown quantitiesGR: Locate points in the coordinate planeF: Evaluate quadratic functions, expressed in function notation, at integer values

Level 3 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equationsEEI: Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions),EEI: Identify solutions to simple quadratic equations EEI: Factor simple quadratics EEI: Add, subtract and multiply binomialsF: Evaluate polynomial functions, expressed in function notation, at integer valuesN: Exhibit some knowledge of the complex numbers N: Work with squares & square roots of numbers N: Determine when an expression is undefined

Pre-Accelerated Level 1 (20-23)PSDA: Translate from one representation of data to another (e.g., a bar graph to a circle graph)EEI: Solve routine first degree equationsEEI: Multiply two binomialsEEI: Perform straightforward word to symbol translationsEEI: Evaluate algebraic expressions by substituting integers for unknown quantitiesGR: Locate points in the coordinate planeF: Evaluate quadratic functions, expressed in function notation, at integer values

Level 2 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equationsEEI: Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions),EEI: Identify solutions to simple quadratic equations EEI: Factor simple quadratics

EEI: Add, subtract and multiply binomialsF: Evaluate polynomial functions, expressed in function notation, at integer valuesN: Exhibit some knowledge of the complex numbers N: Work with squares & square roots of numbers N: Determine when an expression is undefined

Level 3 (28-32):PSDA: Interpret and use information from figures, tables, and graphsEEI: Write expressions, equations, or inequalities for common algebra settingsEEI: Manipulate expressions and equations EEI: Solve quadratic equationsGR: Interpret and use information from graphs in the coordinate planeGR: Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle) F: Evaluate composite functions at integer valuesN: Apply number properties involving even/odd numbers and factors/multiplesN: Multiply two complex numbers

Honors Level 1 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equationsEEI: Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions),EEI: Identify solutions to simple quadratic equations EEI: Factor simple quadratics EEI: Add, subtract and multiply binomialsF: Evaluate polynomial functions, expressed in function notation, at integer valuesN: Exhibit some knowledge of the complex numbers N: Work with squares & square roots of numbers N: Determine when an expression is undefined

Level 2 (28-32):PSDA: Interpret and use information from figures, tables, and graphsEEI: Write expressions, equations, or inequalities for common algebra settingsEEI: Manipulate expressions and equations EEI: Solve quadratic equationsGR: Interpret and use information from graphs in the coordinate planeGR: Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle) F: Evaluate composite functions at integer valuesN: Apply number properties involving even/odd numbers and factors/multiplesN: Multiply two complex numbers

Level 3 (33-36)PSDA: Analyze and draw conclusions based on information from figures, tables and graphs.EEI: Write equations and inequalities that require planning, manipulating, and/or solvingGR: Analyze and draw conclusions based on information from graphs in the coordinate plane

G: Identify characteristic of graphs based on a set of conditions or on a general equation such as y=ax2+c


Students will apply the skills used to solve quadratic functions and use key characteristics of the graphs of quadratic functions to solve various real-world problems in business (revenue prediction) and physics (rocket launch).

Assessment





Formative Homework, Exit Tickets, Classwork, Bell Ringers, Quizzes, Calculator Activities, Performance Task

SummativeUnit 3 Exam

I. Multiple Choice (ACT Style)II. Free Response

Supplementary Text



What are the advantages of a quadratic function in vertex form?

What are the advantages of a quadratic function in standard form?

How is any quadratic function related to the parent quadratic function y = x2?

How are the real solutions of a quadratic equation related to the graph of the related quadratic function?

When you square each side of an equation, is the resulting equation equivalent to the original?


1. Compare and contrast vertex and standard form of a quadratic function. What information does each form give you? Which would you use to graph the function?

2. How do you write the transformed equation based on the parent function?3. How do we use the parameters a, b, c and m to graph a transformation of a parent function?4. How do you describe a transformation in terms of horizontal and vertical shifts and vertical

stretches and shrinks?5. Why might you factor a quadratic equation? What does the Zero-Product Property tell you

about the factors?6. What information does the discriminant give you about the number and type of solutions to

a quadratic equation?7. When is a complex number the solution to a quadratic equation?8. Compare and contrast factoring, completing the square, and using the Quadratic Formula to

solve a quadratic equation. Under what circumstances would you use each one?9. How can you describe the domain and range of a square root function?10. How is a square root function transformed?

Unit 3 Summary + Curriculum AlignmentUnit Title Systems of EquationsMajor Topics Determine solutions for linear systems by graphing with and without calculators.

Determine solutions for linear systems by algebraically. Solve non-linear systems by graphing.



Fencing Source: Balanced Assessment Materials from Mathematics Assessment Project

http://map.mathshell.org/materials/download.php?fileid=1086)


AlgebraA-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A-CED.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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. A-CED.4.Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify the solution method.A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A-REI.5.Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.


College Bound Level 1 (16-19)PSDA: Read tables and graphs

Level 2 (20-23)PSDA: Translate from one representation of data to another (e.g., a bar graph to a circle graph)EEI: Solve routine first degree equationsGR: Locate points in the coordinate planeF: Evaluate quadratic functions, expressed in function notation, at integer values

Level 3 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equations, Write expressions,

equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions), GR: Match linear graphs with their equations.F: Evaluate polynomial functions, expressed in function notation, at integer values



Level 3 (28-32):PSDA: Interpret and use information from figures, tables, and graphsEEI: Write expressions, equations, or inequalities for common algebra settings, Manipulate expressions and equations; Find solutions to systems of linear equationsGR: Interpret and use information from graphs in the coordinate planeF: Evaluate composite functions at integer values

Honors Level 1 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equations, Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions), GR: Match linear graphs with their equations.F: Evaluate polynomial functions, expressed in function notation, at integer values

Level 2 (28-32)PSDA: Interpret and use information from figures, tables, and graphsEEI: Write expressions, equations, or inequalities for common algebra settings, Manipulate expressions and equations; Find solutions to systems of linear equationsGR: Interpret and use information from graphs in the coordinate planeF: Evaluate composite functions at integer values

Level 3 (33-36)PSDA: Analyze and draw conclusions based on information from figures, tables and graphs.EEI: Write equations and inequalities that require planning, manipulating, and/or solvingGR: Analyze and draw conclusions based on information from graphs in the coordinate plane, Identify characteristic of graphs based on a set of conditions or on a general equation such as y=ax2+cF: Write an expression for the composite of two simple functions

Interdisciplina Students will apply the skills used to solve systems of equations in a chemistry problem to determine the exact

ry Integrations /Thematic Connections

quantities of mixtures. Also, students will solve problems involving finance and revenue using systems of equations.

Assessment






SummativeUnit 4Exam


Supplementary Text



What is meant by the solution of a linear system?What types of problems can be solved using linear systems?How can a graphing calculator be used to solve systems of equations and non-linear systems?


1. What do you look for to determine whether to use elimination, substitution or graphing to solve a linear system?

2. What are the three different possible solutions for a linear system?3. What determines whether two systems are equivalent?

Unit 4 Summary + Curriculum AlignmentUnit Title Power Functions and Rational FunctionsMajor Topics Rational Exponents & Radicals

Simplifying Expressions Solving Rational Exponent Equations Adding & Subtracting Rational Functions Multiplying & Dividing Rational Functions



Delia and Kari have the same size bathroom. It takes Delia 3 hours longer to finish tiling her bathroom than Kari. If they work together it takes them 2 hours to lay the tiles per bathroom. How long does it take Kari to lay the tiles in her bathroom by herself? How long does it take Delia to finish her bathroom if she works alone? Show your work.


FunctionsF-IF.04For 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicityF-IF.05Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

AlgebraA-APR.06Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.A-APR.07(+) 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.A-REI.02Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.A-CED.01Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A-CED.03Represent 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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

Number and QuantityN-CN.01Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.N-CN.07

Solve quadratic equations with real coefficients that have complex solutions.CRS College Bound Level 1 (16-19)

Supporting Skills

EEI: Solve one-step equations having integer or decimal answers; Combine like terms

Level 2 (20-23)EEI: Solve routine first degree equations; Multiply two binomialsF: Evaluate quadratic functions, expressed in function notation, at integer values

Level 3 (24-27)EEI: Solve real-world problems using first-degree equations, Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions), Identify solutions to simple quadratic equations; Add, subtract, and multiply polynomials; Factor simple quadraticsF: Evaluate polynomial functions, expressed in function notation, at integer valuesN: Determine when an expression is undefined

Pre-Accelerated Level 1 (20-23)EEI: Solve routine first degree equations; Multiply two binomialsF: Evaluate quadratic functions, expressed in function notation, at integer values

Level 2 (24-27)EEI: Solve real-world problems using first-degree equations, Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions), Identify solutions to simple quadratic equations; Add, subtract, and multiply polynomials; Factor simple quadraticsF: Evaluate polynomial functions, expressed in function notation, at integer valuesN: Determine when an expression is undefined; Exhibit some knowledge of the complex numbers.

Level 3 (28-32):EEI: Write expressions, equations, or inequalities for common algebra settings, Manipulate expressions and equations GR: Interpret and use information from graphs in the coordinate planeN: Apply rules of exponents; Multiply two complex numbers

Honors Level 1 (24-27)EEI: Solve real-world problems using first-degree equations, Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions), Identify solutions to simple quadratic equations; Add, subtract, and multiply polynomials; Factor simple quadraticsF: Evaluate polynomial functions, expressed in function notation, at integer valuesN: Determine when an expression is undefined; Exhibit some knowledge of the complex numbers.

Level 2 (28-32):EEI: Write expressions, equations, or inequalities for common algebra settings, Manipulate expressions and equations GR: Interpret and use information from graphs in the coordinate planeN: Apply rules of exponents; Multiply two complex numbers

Level 3 (33-36)EEI: Write equations and inequalities that require planning, manipulating, and/or

solvingN: Apply properties of complex numbers


Students will apply the skills learned in this unit to solve problems related to Physics (Electrical Current) and Music (Harmonic Mean).

Assessment








Supplementary Text



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?

What kinds of asymptotes are possible for rational functions?

Are irrational expression and its simplified form equivalent?


1. When you simplify rational expressions, why must you include any restrictions on the domain of the original expression, even when there are not restrictions on the simplified form?

2. How are operations with rational expressions like operations with fractions? How are they different?

What are the steps in solving a rational equation algebraically?

Unit 5 Summary + Curriculum AlignmentUnit Title Polynomial and Composite Functions Major Topics Composing Functions

Monomials Polynomials Dividing Polynomials

Factoring PolynomialsDescription of Primary Performance Task


In this performance task, the student must model the problem situation both algebraically & graphically. The student must also determine key features of the polynomial's graph that has meaning in the context of the problem situation.


AlgebraA-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomialsA-APR.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)A-APR.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.A-APR.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.1

FunctionsF-IF-2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.F-IF-4For 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.F-IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.F-BF.1c Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

CRS College Bound Level 1 (16-19)

Supporting Skills

EEI: Solve one-step equations having integer or decimal answers; Combine Like Terms; Substitute whole numbers for unknown quantities to evaluate expressions; Read tables and graphs

Level 2 (20-23)PSDA: Translate from one representation of data to another (e.g., a bar graph to a circle graph)EEI: Solve routine first degree equations; Evaluate algebraic expressions by substituting integers for unknown quantities; Multiply two binomials F: Evaluate quadratic functions, expressed in function notation, at integer values



Level 2 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equations, Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions);Add, subtract, and multiply polynomialsF: Evaluate polynomial functions, expressed in function notation, at integer valuesN: Work with squares and square roots of numbers; Work problems involving positive integer exponents; Work with cubes and cube roots of numbers; Determine when an expression is undefined

Level 3 (28-32):PSDA: Interpret and use information from figures, tables, and graphsEEI: Write expressions, equations, or inequalities for common algebra settings, Manipulate expressions and equations GR: Interpret and use information from graphs in the coordinate planeF: Evaluate composite functions at integer valuesN: Apply rules of exponents

Honors Level 1 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equations, Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions); Add, subtract, and multiply polynomialsF: Evaluate polynomial functions, expressed in function notation, at integer valuesN: Work with squares and square roots of numbers; Work problems involving positive integer exponents; Work with cubes and cube roots of numbers; Determine when an expression is

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Level 3 (33-36)PSDA: Analyze and draw conclusions based on information from figures, tables and graphs.EEI: Write equations and inequalities that require planning, manipulating, and/or solvingGR: Analyze and draw conclusions based on information from graphs in the coordinate plane; Identify characteristic of graphs based on a set of conditions or on a general equation such as y=ax2+cF: Write an expression for the composite of two simple functions

N: Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers; apply properties of complex numbers.


Students will apply the skills learned in this unit to solve problems related to Engineering (building design) and Business (sales).

Assessment








Supplementary Text



What does the degree of a polynomial tell you about it’s 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?


1. What is the relationship between the degree of a polynomial and the number of real zeros it has?

2. What is the relationship between the degree of a polynomial function and the number of local extreme values of the function?

3. How can we describe the end behavior of polynomials of odd and even degree?4. What is a monomial and how is it related to binomials, trinomials, etc?5. Do we always employ the sametechnique for multiplying polynomials together?

6. When do we use FOIL?7. How can factoring polynomials help us?8. What is the GCF of a polynomial?9. What does it mean for a polynomial to be written in standard form?10. In what ways can polynomials model real-life situations?11. How do we use special products tomultiply polynomials?12. What is factoring?13. How can we evaluate compositions of functions for different values in the domain?

Is the composition of functions commutative?

Unit 6 Summary + Curriculum AlignmentUnit Title ACT ReviewMajor Topics Adding, Subtracting and Multiplying Matrices

Finding the Determinant of a Square Matrix Writing the Equation of a Circle Solving for one variable Midpoint & Distance Formula Percents, Averages and Probability Word Problems Abs. Value Equations Solving Inequalities Slope, Equations of Line Pythagorean Theorem Right Triangle Trig Plane & Coordinate Geometry Area & Volume



Full Length Math Practice ACT


Number and QuantityN-VM.7.(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.N-VM.8. (+) Add, subtract, and multiply matrices of appropriate dimensions.

N-VM.9.(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a

commutative operation, but still satisfies the associative and distributive properties.

AlgebraA-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A-CED.4.Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify the solution method.A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

FunctionsF-IF-2. Use function notation, evaluate functions for inputs in their domains, and interpretstatements that use function notation in terms of a context.

F-IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★

GeometryG-SRT.8.Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★G-GPE.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.G-GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.★


College Bound Level 1 (16-19) BOA: Solve routine one-step arithmetic problems (using whole numbers, fractions, and decimals) such as single-step percent; Solve some routine two-step arithmetic problemsPSDA: Calculate the average of a list of numbers; Calculate the average, given the number of data values and the sum of the data values; Read tables and graphs; Perform computations on data from tables and graphs; Use the relationship between the probability of an event and the probability of its complementN: Recognize one-digit factors of a numberEEI: Substitute whole numbers for unknown quantities to evaluate expressions; Solve one-step equations having integer or decimal answers; Combine like terms (e.g., 2x + 5x)GR: Locate points on the number line and in the first quadrantPPF: Exhibit some knowledge of the angles associated with parallel linesM: Compute the perimeter of polygons when all side lengths are given; Compute the area of rectangles when whole number dimensions are given

Level 2 (20-23)BOA:Solve routine two-step or three-step arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, and computing with a given averagePSDA:Calculate the missing data value, given the average and all data values but one; Translate from one representation of data to another (e.g., a bar graph to a circle graph); Determine the probability of a simple event; Exhibit knowledge of simple counting techniquesN: Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor EEI: Evaluate algebraic expressions by substituting integers for unknown quantities; Add and subtract simple algebraic expressions; Solve routine first-degree equations; Perform straightforward word-to-symbol translations; Multiply two binomials*GR: Locate points in the coordinate plane; Comprehend the concept of length on the number line*; Exhibit knowledge of slope*PPF: Find the measure of an angle using properties of parallel lines; Exhibit knowledge

of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°)

M:Compute the area and perimeter of triangles and rectangles in simple problems; Use geometric formulas when all necessary information is givenF: Evaluate quadratic functions, expressed in function notation, at integer values

Level 3 (24-27)BOA: Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour)PSDA: Calculate the average, given the frequency counts of all the data values; Manipulate data from tables and graphs; Compute straightforward probabilities for common situations; Use Venn diagrams in counting*N:Find and use the least common multiple; Order fractions; Work with numerical factors; Work with scientific notation; Work with squares and square roots of numbers; Work problems involving positive integer exponents*EEI:Solve real-world problems using first-degree equations; Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions); Identify solutions to simple quadratic equations; Add, subtract, and multiply polynomials*; Factor simple quadratics (e.g., the difference of squares and perfect square trinomials)*; Solve first-degree inequalities that do not require reversing the inequality sign*GR: Identify the graph of a linear inequality on the number line*; Determine the slope of a line from points or equations*; Match linear graphs with their equations*; Find the midpoint of a line segment*PPF: Use several angle properties to find an unknown angle measure; Recognize Pythagorean triples*; Use properties of isosceles triangles*M:Compute the area of triangles and rectangles when one or more additional simple steps are required; Compute the area and circumference of circles after identifying necessary information; Compute the perimeter of simple composite geometric figures with unknown side lengthsF: Evaluate polynomial functions, expressed in function notation, at integer values

Pre-Accelerated Level 1 (20-23)BOA: Solve routine two-step or three-step arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, and computing with a given averagePSDA: Calculate the missing data value, given the average and all data values but one; Translate from one representation of data to another (e.g., a bar graph to a circle graph); Determine the probability of a simple event; Exhibit knowledge of simple counting techniquesN: Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor EEI: Evaluate algebraic expressions by substituting integers for unknown quantities; Add and subtract simple algebraic expressions; Solve routine first-degree equations; Perform straightforward word-to-symbol translations; Multiply two binomials*GR: Locate points in the coordinate plane; Comprehend the concept of length on the number line*; Exhibit knowledge of slope*PPF: Find the measure of an angle using properties of parallel lines; Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°)

M:Compute the area and perimeter of triangles and rectangles in simple problems;

Use geometric formulas when all necessary information is givenF: Evaluate quadratic functions, expressed in function notation, at integer values

Level 2 (24-27)BOA: Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour)PSDA: Calculate the average, given the frequency counts of all the data values; Manipulate data from tables and graphs; Compute straightforward probabilities for common situations; Use Venn diagrams in counting*N:Find and use the least common multiple; Order fractions; Work with numerical factors; Work with scientific notation; Work with squares and square roots of numbers; Work problems involving positive integer exponents*EEI:Solve real-world problems using first-degree equations; Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions); Identify solutions to simple quadratic equations; Add, subtract, and multiply polynomials*; Factor simple quadratics (e.g., the difference of squares and perfect square trinomials)*; Solve first-degree inequalities that do not require reversing the inequality sign*GR: Identify the graph of a linear inequality on the number line*; Determine the slope of a line from points or equations*; Match linear graphs with their equations*; Find the midpoint of a line segment*PPF: Use several angle properties to find an unknown angle measure; Recognize Pythagorean triples*; Use properties of isosceles triangles*M:Compute the area of triangles and rectangles when one or more additional simple steps are required; Compute the area and circumference of circles after identifying necessary information; Compute the perimeter of simple composite geometric figures with unknown side lengthsF: Evaluate polynomial functions, expressed in function notation, at integer values; Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths†

Level 3 (28-32)BOA: Solve word problems containing several rates, proportions, or percentagesPSDA: Calculate or use a weighted average; Interpret and use information from figures, tables, and graphs; Apply counting techniques; Compute a probability when the event and/or sample space are not given or obviousN: Apply number properties involving prime factorization; Apply number properties involving even/odd numbers and factors/multiples; Apply number properties involving positive/negative numbers; Apply rules of exponents; Multiply two complex numbers†EEI: Manipulate expressions and equations; Write expressions, equations, and inequalities for common algebra settings; Solve linear inequalities that require reversing the inequality sign; Solve absolute value equations; Solve quadratic equations; Find solutions to systems of linear equationsGR: Interpret and use information from graphs in the coordinate plane; Match number line graphs with solution sets of linear inequalities; Use the distance formula; Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point; Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle)†PPF:Apply properties of 30°-60°-90°, 45°-45°-90°, similar, and congruent triangles; Use the Pythagorean theoremM:Use relationships involving area, perimeter, and volume of geometric figures to

compute another measureF:Evaluate composite functions at integer values†; Apply basic trigonometric ratios to solve right-triangle problems†

Honors Level 1 (24-27)BOA: Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour)PSDA: Calculate the average, given the frequency counts of all the data values; Manipulate data from tables and graphs; Compute straightforward probabilities for common situations; Use Venn diagrams in counting*N:Find and use the least common multiple; Order fractions; Work with numerical factors; Work with scientific notation; Work with squares and square roots of numbers; Work problems involving positive integer exponents*EEI:Solve real-world problems using first-degree equations; Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions); Identify solutions to simple quadratic equations; Add, subtract, and multiply polynomials*; Factor simple quadratics (e.g., the difference of squares and perfect square trinomials)*; Solve first-degree inequalities that do not require reversing the inequality sign*GR: Identify the graph of a linear inequality on the number line*; Determine the slope of a line from points or equations*; Match linear graphs with their equations*; Find the midpoint of a line segment*PPF: Use several angle properties to find an unknown angle measure; Recognize Pythagorean triples*; Use properties of isosceles triangles*M:Compute the area of triangles and rectangles when one or more additional simple steps are required; Compute the area and circumference of circles after identifying necessary information; Compute the perimeter of simple composite geometric figures with unknown side lengthsF: Evaluate polynomial functions, expressed in function notation, at integer values; Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths†

Level 2(28-32)BOA: Solve word problems containing several rates, proportions, or percentagesPSDA: Calculate or use a weighted average; Interpret and use information from figures, tables, and graphs; Apply counting techniques; Compute a probability when the event and/or sample space are not given or obviousN: Apply number properties involving prime factorization; Apply number properties involving even/odd numbers and factors/multiples; Apply number properties involving positive/negative numbers; Apply rules of exponents; Multiply two complex numbers†EEI: Manipulate expressions and equations; Write expressions, equations, and inequalities for common algebra settings; Solve linear inequalities that require reversing the inequality sign; Solve absolute value equations; Solve quadratic equations; Find solutions to systems of linear equationsGR: Interpret and use information from graphs in the coordinate plane; Match number line graphs with solution sets of linear inequalities; Use the distance formula; Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point; Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle)†PPF: Apply properties of 30°-60°-90°, 45°-45°-90°, similar, and congruent triangles; Use the Pythagorean theorem

M:Use relationships involving area, perimeter, and volume of geometric figures to compute another measureF: Evaluate composite functions at integer values†; Apply basic trigonometric ratios to solve right-triangle problems†

Level 3 (33-36)BOA: Solve complex arithmetic problems involving percent of increase or decrease and problems requiring integration of several concepts from pre-algebra and/or pre-geometry (e.g., comparing percentages or averages, using several ratios, and finding ratios in geometry settings)

PSDA: Distinguish between mean, median, and mode for a list of numbers; Analyze and draw conclusions based on information from figures, tables, and graphs; Exhibit knowledge of conditional and joint probability

N: Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers; Exhibit knowledge of logarithms and geometric sequences; Apply properties of complex numbers

EEI: Write expressions that require planning and/or manipulating to accurately model a situation; Write equations and inequalities that require planning, manipulating, and/or solving; Solve simple absolute value inequalities

GR: Match number line graphs with solution sets of simple quadratic inequalities; Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax2 + c; Solve problems integrating multiple algebraic and/or geometric concepts; Analyze and draw conclusions based on information from graphs in the coordinate plane

PPF: Draw conclusions based on a set of conditions; Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas; Use relationships among angles, arcs, and distances in a circle

M: Use scale factors to determine the magnitude of a size change; Compute the area of composite geometric figures when planning or visualization is required

F: Write an expression for the composite of two simple functions†; Use trigonometric concepts and basic identities to solve problems†; Exhibit knowledge of unit circle trigonometry†; Match graphs of basic trigonometric functions with their equations


Students will apply the skills learned in this unit to solve problems related to Business (sales) and Technology (computer chip design).

Assessment Diagnostic/ Pre-Assessment







Supplementary Text



How can you use a matrix to organize data?

How do you write equation of a circle?

Does it matter which form of a linear equation you use?

How can you model data with a linear function?

How can you find slope from points, equations, and graphs?

How do you solve absolute value equations?

How do you evaluate functions using function notation?Unit Content Questions

1. How do you add, subtract, and multiply matrices?2. How do you find determinant of a matrix?3. How can slope and y-intercept be determined from data, graphs, and equations?4. How do you write equations of different lines?5. How do you evaluate absolute value expressions?6. How can you find percentages and averages?7. How do you find the distance & midpoint between two points?8. How do you find the missing side of a right triangle?9. How do you find missing angle or side of any triangle?10. How do you identify the radius and center of a circle?11. How do you identify and calculate special angle pairs?12. How do you find the area and volume of a given shape?

Unit 7 Summary + Curriculum AlignmentUnit Title Exponential and Logarithmic Functions Major Topics Modeling an Exponential Function.

Number “e” and Continuous Compound Interest. Transforming Exponential Functions. Basics of Logarithms. Properties of Logarithms. Natural Logs and Change of Base. Solving Exponential Equations Analytically Solving Exponential and Logarithmic Equations Graphically Modeling and Solving Compound Interest Equations



The performance task, “ Graduation Present” will ask the students to use the compound interest equations to answer a question about saving money. The students will need to usegraphs and tables to illustrate and support their answers. The students will also be asked to illustrate their solutions algebraically and to provide an explanation about how a graphing calculator could be used to justify or verify their solution.


FunctionsF-IF.05Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.F-IF.07.eGraph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.F-IF.08.bUse the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.F-BF.04(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.F-BF.05(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.F-LE.04For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.F-LE.05Interpret the parameters in a linear or exponential function in terms of a context.

AlgebraA-CED.01Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A-CED.02

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.A-CED.03Represent 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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.A-REI.01Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A-REI.11Explain why the <Bx-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.A-SSE.03.cUse the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.


College Bound Level 1 (16-19)PSDA: Read tables and graphsEEI: Solve one-step equations having integer or decimal answers, Combine Like Terms, Substitute whole numbers for unknown quantities to evaluate expressions

Level 2 (20-23)PSDA: Translate from one representation of data to another (e.g., a bar graph to a circle graph)EEI: Solve routine first degree equations, Evaluate algebraic expressions by substituting integers for unknown quantities, Add and subtract simple algebraic expressionsGR: Locate points in the coordinate plane,Translate from one representation of data to another F: Evaluate quadratic functions, expressed in function notation, at integer values

Level 3 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equations, Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions), GR: Manipulate data from tables and graphs.F: Evaluate polynomial functions, expressed in function notation, at integer valuesN: Work problems involving positive integer exponentsN: Determine when an expression is undefined

Pre-Accelerated Level 1 (20-23)PSDA: Translate from one representation of data to another (e.g., a bar graph to a circle graph)EEI: Solve routine first degree equations, Evaluate algebraic expressions by substituting integers for unknown quantities, Add and subtract simple algebraic expressionsGR: Locate points in the coordinate plane,Translate from one representation of data to

another F: Evaluate quadratic functions, expressed in function notation, at integer values

Level 2 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equations, Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions), GR: Manipulate data from tables and graphs.F: Evaluate polynomial functions, expressed in function notation, at integer valuesN: Work problems involving positive integer exponentsN: Determine when an expression is undefined


Honors Level 1 (24-27)PSDA: Manipulate data from tables and graphsEEI: Solve real-world problems using first-degree equations, Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions), GR: Manipulate data from tables and graphs.F: Evaluate polynomial functions, expressed in function notation, at integer valuesN: Work problems involving positive integer exponentsN: Determine when an expression is undefined


Level 3 (33-36)PSDA: Analyze and draw conclusions based on information from figures, tables and graphs.EEI: Write equations and inequalities that require planning, manipulating, and/or solving, Write expressions that require planning and/or manipulating to accurately model a situationGR: Analyze and draw conclusions based on information from graphs in the coordinate plane, Identify characteristic of graphs based on a set of conditions or on a general equation such as y=ax2+cN: Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers, Exhibit knowledge of logarithms and geometric sequences


Students will apply the skills learned in this unit to solve problems related to Biology (population growth) and Physical Science (magnitude of earthquakes).

Assessment








Supplementary Text



How are exponents and logarithms related?

How are exponential functions and logarithmic functions related?

How do you model a quantity that changes regularly over time by the same percentage?

Why are logarithms important?

How would you describe the relationship between exponential and logarithmic functions?

What is the best method for solving an exponential equation with a variable exponent? Can you determine the strengths and weaknesses of using a specific method given a certain situation?

What is the difference between growth and decay? How do you determine the rate of growth or decay given an equation or situation?

What is the difference between a common logarithm and a natural logarithm?


1. How do we develop exponential models based upon repeated multiplication from tabular data?

2. How do you describe the graph of exponential functions based on parameter changes of the parent function?

3. How do we find a function that models a set of exponential data points? 4. How do we demonstrate an understanding of the number e based on limits from graphs and

tables? 5. How do we use exponential functions to model and solve problems involving both

exponential growth and decay?6. How do we solve problems involving continuously compounding interest rates?7. How do you apply the inverse relationship between exponential and logarithmic functions?8. How do you convert between exponential and logarithmic forms of an expression?9. How do we identify the domain and range of logarithmic functions?10. How do we use properties of logarithms to rewrite and solve problems?11. How do we formulate exponential and logarithmic equations and inequalities to answer

questions about problem situations?12. How do you solve exponential and logarithmic equations and inequalities by graphing,

tabular, and analytical methods?

Unit 8 Summary + Curriculum AlignmentUnit Title Trigonometric Functions Major Topics Characteristics of Periodic Functions

Angles in Standard Position Coterminal& Reference Angles Unit Circle Evaluating Trigonometric Values of Special Angles Parent Sine and Cosine Graph Transformations & Translations of Sine & Cosine Functions Parent Tangent Graph & Transformations Inverse Notation. Evaluating Inverse Trig Functions Compositions of Inverse Trig Functions

Graphing Inverse Trig FunctionsDescription of Primary Performance Task


The performance task will require the student to write a sine, cosine and tangent function given the amplitude and period. The student will also be asked to determine the possibility of transforming the graphs of tangent and secant functions given the horizontal and vertical shifts. Additionally, the student must be to successfully describe the relationship between reciprocal trig functions.


FunctionsF-TF.1.Understand radian measure of an angle as the length of the arc on the unitcircle subtended by the angle.F-TF.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.F-TF.3.(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π – x, π + x, and 2π – x in terms of their values for x, where x is any real number.F-TF.4.(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.F-TF.5.Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.F-TF.6.(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.F-TF.7.(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.


College Bound Level 1 (16-19) BOA: Solve routine one-step arithmetic problems (using whole numbers, fractions, and decimals) such as single-step percent; Solve some routine two-step arithmetic problems

PSDA: Read tables and graphs; Perform computations on data from tables and graphs; EEI: Substitute whole numbers for unknown quantities to evaluate expressions; Solve one-step equations having integer or decimal answers; Combine like terms (e.g., 2x + 5x)

Level 2 (20-23)PSDA: Translate from one representation of data to another (e.g., a bar graph to a circle graph); EEI: Evaluate algebraic expressions by substituting integers for unknown quantitiesGR: Locate points in the coordinate plane; PPF: Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°)

Level 3 (24-27)BOA: Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour)PSDA: Manipulate data from tables and graphsF: Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths†

Pre-Accelerated Level 1 (20-23)PSDA: Translate from one representation of data to another (e.g., a bar graph to a circle graph); EEI: Evaluate algebraic expressions by substituting integers for unknown quantitiesGR: Locate points in the coordinate plane; PPF: Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°)

Level 2 (24-27)BOA: Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour)PSDA: Manipulate data from tables and graphsF: Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths†

Level 3 (28-32)PSDA:Interpret and use information from figures, tables, and graphs; EEI: Manipulate expressions and equations; Write expressions, equations, and inequalities for common algebra settings; GR: Interpret and use information from graphs in the coordinate plane; PPF: Apply properties of 30°-60°-90°, 45°-45°-90°, similar, and congruent triangles; Use the Pythagorean theoremM:Use relationships involving area, perimeter, and volume of geometric figures to compute another measureF: Evaluate composite functions at integer values†; Apply basic trigonometric ratios to solve right-triangle problems†

Honors Level 1 (24-27)BOA: Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour)PSDA: Manipulate data from tables and graphsF: Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths†

Level 2 (28-32)PSDA:Interpret and use information from figures, tables, and graphs; EEI: Manipulate expressions and equations; Write expressions, equations, and inequalities for common algebra settings; GR: Interpret and use information from graphs in the coordinate plane; PPF: Apply properties of 30°-60°-90°, 45°-45°-90°, similar, and congruent triangles; Use the Pythagorean theoremM:Use relationships involving area, perimeter, and volume of geometric figures to compute another measureF: Evaluate composite functions at integer values†; Apply basic trigonometric ratios to solve right-triangle problems†

Level 3 (33-36)PSDA: Analyze and draw conclusions based on information from figures, tables, and graphs;

EEI: Write expressions that require planning and/or manipulating to accurately model a situation; Write equations and inequalities that require planning, manipulating, and/or solving

GR: Solve problems integrating multiple algebraic and/or geometric concepts; Analyze and draw conclusions based on information from graphs in the coordinate plane

PPF: Draw conclusions based on a set of conditions; Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas; Use relationships among angles, arcs, and distances in a circle

F: Use trigonometric concepts and basic identities to solve problems†; Exhibit knowledge of unit circle trigonometry†; Match graphs of basic trigonometric functions with their equations


Students will apply the skills learned in this unit to solve problems related to Biology (DNA Strands) and Physical Science (Tidal Waves).

Assessment






SummativeUnit 9Exam


Supplementary Text


Framing Questions

Essential Question(s)

How can you model periodic behavior?

If you know the value sin(x), how can you find cos(x), tan(x), csc(x), sec(x), cot(x)?

How do the trig functions relate to the trig ratios for a right triangle?

How can you transform the sine, cosine, and tangent graphs?

How can you define the inverse trigonometric functions and their graphs?

Explain how you can apply understanding of periodicity to find solution sets?

How can you apply trigonometric inverses and their properties to solve and analyze problem situations?


1. How can you determine if a function is periodic?2. If you were asked to graph a cosine function, what would be the first step?3. How is graphing transformations of trigonometric functions like graphing transformations of

other functions you have studied? How is it different?4. Explain how one can determine the period, frequency, and amplitude of periodic functions

(as well as symmetry where appropriate).5. How can you translate between symbolic and graphical representations of abstract periodic

functions?6. How do you generate the graphs of the sine, cosine, and tangent parent functions?7. How can you transform the sine, cosine, and tangent graphs?8. How can you define what a radian is and how it relates to the unit circle?9. How can you place angles of rotation in standard position and find coterminal angles?10. How can we solve trigonometric equations using graphs and tables?11. How can you algebraically solve trigonometric equations using inverse trigonometric

functions?

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