Curriculum Map: Pre-Calculus 2014
Course: Precalculus
Subtopic: Calculus
Grade(s): None specified
Unit: Unit 1: Functions and Their Graphs
Subject: Mathematics
Timeline: 9 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
NATIONAL: US Common Core State Standards (2010)
MA.F-IF.A.1 (Advanced)
Understand that a function from one set (called the domain) to another set (called the
range) assigns to each element of the domain exactly one element of the range. If f is a
function and x is an element of its domain, then f(x) denotes the output of f corresponding
to the input x. The graph of f is the graph of the equation y = f(x).
MA.F-IF.A.2 (Advanced)
Use function notation, evaluate functions for inputs in their domains, and interpret
statements that use function notation in terms of a context.
MA.F-IF.B.4 (Advanced)
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.
MA.F-IF.B.5 (Advanced)
Relate the domain of a function to its graph and, where applicable, to the quantitative
relationship it describes.
MA.F-IF.C.7.A (Advanced) Graph linear and quadratic functions and show intercepts, maxima, and minima.
MA.F-IF.C.7.B (Advanced) Graph square root, cube root, and piecewise-defined functions, including step functions and
absolute value functions.
MA.F-BF.A.1.C (Advanced) Compose functions.
MA.F-BF.B.4.A (Advanced) Solve an equation of the form f(x) = c for a simple function f that has an inverse and write
an expression for the inverse.
Big Ideas: Students will understand that:
You can use numerical, algebraic, and graphical models to solve
problems and represent function as well as translate from one
model to another.
You can determine the domain and range for functions, analyze
function characteristics and represent function transformations
both algebraically and graphically.
You can build new functions from basic functions by adding,
subtracting, multiplying, dividing, and composing functions.
Concepts:Students will know...
Essential Questions:
How do you locate points and find the distance and midpoint
between two points on the Cartesian plane?
How do you identify intercepts and symmetry in order to sketch
graphs of equations?
How do you find the slope of a line and use it to write an
equation for the line?
What are the important defining characteristics and
representations of a function?
How is the graph of a function used to determine the key
elements of that function?
What are the characteristics of the most commonly used
functions in algebra?
How do you write equations and draw graphs for the simple
transformations of a parent function?
How do you combine two parent functions to form a new
function?
What is the inverse of a function, and how do you represent it
graphically and algebraically.
How do you write equations to model real-world data and
identify different models of variation?
Competencies (including Transfer goals):Students will be able
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to independently use their learning to...
Work with rectangular coordinates involving plotting points in
the Cartesian plane, using the Distance and Midpoint formulas,
and modeling and solving real-life problems using the
coordinate plane.
Sketch graphs of equations, identify x- and y-intercepts, using
symmetry to graph equations, writing equations and sketching
graphs of circles, and using graphs of equations to solve real-life
problems.
Write linear equations in two variables and use slope to identify
parallel and perpendicular lines.
Determine whether a relation is a function and find the domains
of functions.
Analyze graphs of functions including the use of the Vertical Line
Test, finding zeroes of functions, and determining relative
minimum and maximums.
Identify parent functions.
Transform functions including using vertical and horizontal
shifts, reflections, and nonrigid transformations to sketch
graphs.
Add, subtract, multiply, and divide functions and find the
composition of functions.
Find inverse functions algebraically and use the Horizontal-Line
Test to determine whether functions are one-to-one.
Use mathematical models for direct, inverse, combined, and
joint variation.
Distance and Midpoint Formulas
Intercepts, symmetry, and slope of graphs
Parent functions
Cartesian Plane
Parallel and perpendicular lines
Linear extrapolation
Funcion, domain, and range
Dependent and independent variables
Vertical and Horizontal Line Test
Zeros of a function
Secant line
Vertical and horizontal shifts/stretches
Composition of functions
Inverse functions
Direct, inverse, and joint variation
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Exit slips
Quizzes
Worksheets
Homework (Bookwork)
Problems done by students on dry-erase boards
Project
Classwork on SmartBoard
Other Evidence (Tests, quizzes, etc)
Stage Three - Learning Plan
Learning Activities:
Learn what functions are and the vocabulary associated with them.
Complete assigned bookwork which includes algebraic and graphical representations along with real world examples of how and when
functions are used.
Making posters of parent functions within a group.
Various activity worksheets which requires students to apply and evaluate the knowledge and skills learned.
Quizzes and tests to have students show mastery of concepts learned.
Flipcharts to show examples of functions and to monitor students’ progress as they learn the topics.
Project using mathematical modeling having students’ research data and find the function to represent the data for their topic. They
will then use their model to predict future values.
Materials and Resources:
Textbook (Chapter 1)
SmartBoard
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Unit: Unit 2: Polynomial and Rational Functions
Subject: Mathematics
Timeline: 4 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
NATIONAL: US Common Core State Standards (2010)
MA.F-IF.B.4 (Advanced)
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.
MA.F-IF.C.7.A (Advanced) Graph linear and quadratic functions and show intercepts, maxima, and minima.
MA.F-IF.C.7.B (Advanced) Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
MA.F-IF.C.7.C (Advanced) Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
MA.F-IF.C.7.D (Advanced) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
MA.F-IF.C.8.A (Advanced) Use the process of factoring and completing the square in a quadratic function to show
zeros, extreme values, and symmetry of the graph, and interpret these in terms of a
context.
Big Ideas: Students will understand that:
Essential Questions:
You can identify, analyze, and sketch polynomial functions as
well as solve polynomial equations and inequalities.
You can identify, analyze and sketch power functions.
You can identify, analyze, and sketch rational functions as well
as solve rational equations and inequalities.
Concepts:Students will know...
How do you sketch graphs and write equations for parabolas?
How do you sketch the graphs of polynomial functions?
How do you divide a polynomial by another polynomial and
interpret the result?
How do you find all zeros of a polynomial function?
How do you sketch the graph of the rational function f(x) = N(x)
/ D(x)?
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
Analyze and write quadratic functions in standard form and use
results to find minimum and maximum values in real-life
applications.
Use transformations and find/use the real zeroes of polynomial
functions to sketch their graphs.
Use long division and synthetic division to divide polynomials by
other polynomials.
Use the Fundamental Theorem of Algebra to determine the
number of zeroes of polynomial functions.
Find zeroes of polynomial functions by using various methods
including factoring, Descartes’s Rule of Signas, etc.
Find the domain and vertical/horizontal/slant asymptotes to help
sketch the graphs of rational functions.
Use rational functions to model and solve real-life problems. Quadratic functions
Parabolas
Maximum and Minimums
Intermediate Value Theorem
Leading Coefficient Test
Long Division of Polynomials
Synthetic Division
Remainder Theorem
Fundamental Theorem of Algebra
Rational Zero Test
Linear Factorization Theorem
Descartes' Rule of Signs
Rational Functions
Vertical, Horizontal, and Slant Asymptote
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Exit slips
Quizzes
Worksheets
Homework (Bookwork)
Problems done by students on dry-erase boards
Project
Classwork on SmartBoard
Other Evidence (Tests, quizzes, etc)
Stage Three - Learning Plan
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Learning Activities:
Learn what polynomial and rational functions are and the vocabulary associated with them.
Complete assigned bookwork which includes quadratic and polynomial functions.
Various activity worksheets which requires students to apply and evaluate the knowledge and skills learned.
Quizzes and tests to have students show mastery of concepts learned.
Flipcharts to show examples of polynomial functions and to monitor students’ progress as they learn the topics.
Project modeling quadratic functions and students will use their model to predict values.
Materials and Resources:
Textbook (Chapter 2)
SmartBoard
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Unit: Unit 3: Exponential and Logarithmic Functions
Subject: Mathematics
Timeline: 4 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
NATIONAL: US Common Core State Standards (2010)
MA.F-IF.C.7.E (Advanced) Graph exponential and logarithmic functions, showing intercepts and end behavior, and
trigonometric functions, showing period, midline, and amplitude.
MA.F-IF.C.8.B (Advanced) Use the properties of exponents to interpret expressions for exponential functions.
MA.F-BF.B.5 (Advanced)
Understand the inverse relationship between exponents and logarithms and use this
relationship to solve problems involving logarithms and exponents.
MA.F-LE.A.1.C (Advanced) Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
MA.F-LE.A.2 (Advanced)
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading
these from a table).
MA.F-LE-A.3 (Advanced)
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
MA.F-LE.A.4 (Advanced)
For exponential models, express as a logarithm the solution to ab to the ct power = d
where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using
technology.
Big Ideas: Students will understand that:
Essential Questions:
You can identify, analyze, and graph exponential and logarithmic
functions to form a model of real life situations.
You can convert equations between logarithmic form and
exponential form, evaluate common and natural logarithms, and
graph common and natural logarithmic functions. You can apply the properties of logarithms to evaluate
expressions, graph functions, and solve application problems
using equations.
How do you write and graph exponential functions?
How do you recognize, evaluate, and graph logarithmic
functions?
How do you rewrite logarithmic expressions to simplify or
evaluate them?
How do you solve exponential and logarithmic equations?
How do you use exponents and logarithms to model a variety of
situations?
Concepts:Students will know...
Exponential Functions
Natural Base e
Logarithmic and Natural Logarithmic Functions
One-to-One Property
Change of Base Formula
Properties of Logarithms
Exponential Growth and Decay
Gaussian Model
Logistic Growth Model
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
Recognize, evaluate, and graph exponential functions with base
a and base e.
Recognize, evaluate, and graph logarithmic and natural
logarithmic functions.
Use properties of logarithms to evaluate, rewrite, expand, or
condense logarithmic expressions.
Solve exponential and logarithmic equations.
Use exponential growth and decay functions to model and solve
real-life problems.
Use logarithmic functions to model and solve real-life problems.
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Exit slips
Quizzes
Worksheets
Homework (Bookwork)
Problems done by students on dry-erase boards
Project
Classwork on SmartBoard
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Other Evidence (Tests, quizzes, etc)
Stage Three - Learning Plan
Learning Activities:
Learn what exponential and logarithmic functions are and the vocabulary associated with them.
Complete assigned bookwork which includes exponential and logarithmic functions.
Making posters of exponential and logarithmic functions within a group.
Various activity worksheets which requires students to apply and evaluate the knowledge and skills learned.
Quizzes and tests to have students show mastery of concepts learned.
Flipcharts to show examples of exponential/logarithmic functions and to monitor students’ progress as they learn the topics.
Project using compound interest to show exponential growth.
Materials and Resources:
Textbook (Chapter 3)
SmartBoard
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Unit: Unit 4: Trigonometry
Subject: Mathematics
Timeline: 6 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
NATIONAL: US Common Core State Standards (2010)
MA.F-TF.A.1 (Advanced)
Understand radian measure of an angle as the length of the arc on the unit circle subtended
by the angle.
MA.F-TF.A.2 (Advanced)
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.
MA.F-TF.A.3 (Advanced)
Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3,
pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for
pi–x, pi+x, and 2pi–x in terms of their values for x, where x is any real number.
MA.F-TF.A.4 (Advanced)
Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric
functions.
MA.F-TF.B.6 (Advanced)
Understand that restricting a trigonometric function to a domain on which it is always
increasing or always decreasing allows its inverse to be constructed.
MA.F-TF.B.7 (Advanced)
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.
MA.F-TF.C.8 (Advanced)
Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin(theta),
cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the
angle.
MA.F-TF.C.9 (Advanced)
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to
solve problems.
Big Ideas: Students will understand that:
You can define the six trigonometric functions as well as solve
and apply problems involving the trigonometric functions of real
numbers and the properties of the sine and cosine as periodic
functions.
You can generate and analyze the graphs of the 6 trigonometric
functions and explore various transformations of these graphs.
You can relate the concept of inverse functions to trigonometric
functions.
Concepts:Students will know...
Angles
Radian and Degree Measures
Arc Length
Area of a Sector of a Circle
Unit Circle
Trigonometric Functions
Even and Odd Functions
Trigonometric Identities
Reference Angles
Trigonometric Functions of Real Numbers
Sine and Cosine Curves
Amplitude and Period
Mathematical Modeling
Reciprocal Functions
Damped Trigonometric Graphs
Inverse Trigonometric Functions
Harmonic Motion
Essential Questions:
How do you describe angles and angular movement?
How do you evaluate trigonometric functions by using the unit
circle?
How do you use trigonometry to find unknown side lengths and
angles in right triangles?
How do you evaluate trigonometric functions of any angle?
How do you sketch the graphs of sine and cosine functions?
How do you sketch the graphs of other trigonometric functions?
How do you evaluate and graph the inverses of trigonometric
functions?
How do you use trigonometric functions to solve real-life
problems?
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
Describe angles, use radian and degree measures, and use
angles to model and solve real-life problems.
Identify a unit circle and describe its relationship to real
numbers.
Evaluate trigonometric functions using the unit circle.
Use a calculator to evaluate trigonometric functions.
Use the fundamental trigonometric identities and use
trigonometric functions to model and solve real-life problems.
Evaluate trigonometric functions of any angle and of real
numbers.
Sketch the graphs of basic sine and cosine functions and sketch
translations of sine and cosine graphs.
Sketch the graphs of tangent, cotangent, secant, and cosecant
functions.
Evaluate and graph the inverse sine function and other inverse
trigonometric functions.
Evaluate the composition of trigonometric functions.
Solve real-life problems involving right triangles, directional
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bearings, and harmonic motion.
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Exit slips
Quizzes
Worksheets
Homework (Bookwork)
Problems done by students on dry-erase boards
Project
Classwork on SmartBoard
Other Evidence (Tests, quizzes, etc)
Stage Three - Learning Plan
Learning Activities:
Learn what trigonometric functions are and the vocabulary associated with them.
Complete assigned bookwork which includes trigonometric functions.
Making posters of trigonometric functions within a group.
Various activity worksheets which requires students to apply and evaluate the knowledge and skills learned.
Quizzes and tests to have students show mastery of concepts learned.
Flipcharts to show examples of trigonometric functions and to monitor students’ progress as they learn the topics.
Unit circle project.
Materials and Resources:
Textbook (Chapter 4)
SmartBoard
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Unit: Unit 5: Analytic Trigonometry
Subject: Mathematics
Timeline: 4 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
NATIONAL: US Common Core State Standards (2010)
MA.F-TF.C.8 (Advanced)
Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin(theta),
cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the
angle.
MA.F-TF.C.9 (Advanced)
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to
solve problems.
Big Ideas: Students will understand that:
Essential Questions:
You can use the fundamental identities to simplify trigonometric
expressions and solve trigonometric equations.
You can determine whether an equation is an identity and
confirm identities analytically.
Concepts:Students will know...
How do you rewrite trigonometric expressions in order to
simplify and evaluate functions?
How do you verify a trigonometric identity?
How do you solve trigonometric equations written in quadratic
form or containing more than one angle?
How do you simplify expressions and solve equations that
contain sums or differences of angles?
How do you rewrite trigonometric expressions that contain
functions of multiple or half-angles, or functions that involve
squares or products of trigonometric expressions.
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
Recognize and write the fundamental trigonometric identities.
Use the fundamental trigonometric identities to evaluate
trigonometric functions, simplify trigonometric expressions, and
rewrite trigonometric expressions.
Verify trigonometric identities.
Use standard algebraic techniques to solve trigonometric
equations.
Solve trigonometric equations of quadratic type and
trigonometric equations involving multiple angles.
Use inverse trigonometric functions to solve trigonometric
equations.
Use sum and difference formulas to evaluate trigonometric
functions, verify identities, and solve trigonometric equations.
Use multiple-angle, power-reducing, half-angle, product-to-sum,
sum-to-product formulas to rewrite and evaluate trigonometric
functions.
Use trigonometric formulas to rewrite real-life models.
Fundamental Trigonometric Identities
Verifying Trigonometric Identities
Solving Trigonometric Equations
Sum and Difference Formulas
Multiple-Angle Formulas
Power-Reducing Formulas
Half-Angle Formulas
Sum-to-Product Formula
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Exit slips
Quizzes
Worksheets
Homework (Bookwork)
Problems done by students on dry-erase boards
Project
Classwork on SmartBoard
Other Evidence (Tests, quizzes, etc)
Stage Three - Learning Plan
Learning Activities:
Learn what trigonometric identities are and the vocabulary associated with them.
Complete assigned bookwork which includes trigonometric identities and equations.
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Various activity worksheets which requires students to apply and evaluate the knowledge and skills learned.
Quizzes and tests to have students show mastery of concepts learned.
Flipcharts to show examples of trigonometric identities and to monitor students’ progress as they learn the topics.
Materials and Resources:
Textbook (Chapter 5)
SmartBoard
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Unit: Unit 6: Additional Topics in Trigonometry
Subject: Mathematics
Timeline: 2 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
Big Ideas: Students will understand that:
Essential Questions:
You can apply the law of sines and law of cosines and use these
to solve real-world problems.
Concepts:Students will know...
How do you use trigonometry to solve and find the areas of
oblique triangles?
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
Law of Sines
Area of an Oblique Triangle
Law of Cosines
Heron's Area Formula
Use the Law of Sines to solve oblique triangles (AAS, ASA, or
SSA).
Find the areas of oblique triangles.
Use the Law of Sines to model and solve real-life problems.
Use the Law of Cosines to solve oblique triangles (SSS or SAS).
Use the Law of Cosines to model and solve real-life problems.
Use Heron’s Area Formula to find the area of a triangle.
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Exit slips
Quizzes
Worksheets
Homework (Bookwork)
Problems done by students on dry-erase boards
Project
Classwork on SmartBoard
Other Evidence (Tests, quizzes, etc)
Stage Three - Learning Plan
Learning Activities:
Learn what the Law of Sines and Cosines are and the vocabulary associated with them.
Complete assigned bookwork which includes Law of Sines and Cosines.
Various activity worksheets which requires students to apply and evaluate the knowledge and skills learned.
Quizzes and tests to have students show mastery of concepts learned.
Flipcharts to show examples of the Law of Sines and Cosines along with Heron’s Formula and to monitor students’ progress as they
learn the topics.
Materials and Resources:
Textbook (Chapter 6)
WhiteBoard
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Unit: Unit 7: Sequences and Series
Subject: Mathematics
Timeline: 4 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
NATIONAL: US Common Core State Standards (2010)
MA.F-BF.A.2 (Advanced)
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Big Ideas: Students will understand that:
Essential Questions:
You can describe a sequence as a function where the domain is
the set of natural numbers.
You can represent sequences and series using various notations.
You can discover and justify the formula for a finite arithmetic
series.
You can discover and justify the formulas for finite and infinite
geometric series.
Concepts:Students will know...
How do you represent a sequence of numbers or the sum of a
sequence?
How do you find the nth term or partial sum of an arithmetic
sequence?
How do you find terms and sums of geometric sequences?
How do you use mathematical induction to find and prove
formulas for sums of sequences and series?
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
Sequences
Factorial Notation
Summation Notation
Properties of Sums
Series
Arithmetic Sequences
Sum of a Finite Arithmetic Sequence
Geometric Sequences
Sum of a Finite Geometric Sequence
Geometric Series
Mathematical Induction
Pattern Recognition
Sums of Powers of Integers
Finite Differences
Use sequence notation to write the terms of sequences.
Use factorial notation and summation notation to write sums.
Find the sums of series.
Recognize, write, and find the nth terms of arithmetic
sequences.
Find nth partial sums of arithmetic sequences.
Recognize, write, and find the nth terms of geometric
sequences.
Find the sum of a finite and infinite geometric series.
Use mathematical induction to prove statements involving a
positive integer n.
Use pattern recognition and mathematical induction to write a
formula for the nth term of a sequence.
Find the finite differences of sequences.
Use the Binomial Theorem to calculate binomial coefficients.
Use Pascal’s Triangle to calculate binomial coefficients.
Use binomial coefficients to write binomial expansions.
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Exit slips
Quizzes
Worksheets
Homework (Bookwork)
Problems done by students on dry-erase boards
Project
Classwork on SmartBoard
Other Evidence (Tests, quizzes, etc)
Stage Three - Learning Plan
Learning Activities:
Learn what arithmetic sequences and partial sums are and geometric sequences and series are and the vocabulary associated with
them.
Complete assigned bookwork which includes arithmetic sequences and geometric sequences and series.
Various activity worksheets which requires students to apply and evaluate the knowledge and skills learned.
Quizzes and tests to have students show mastery of concepts learned.
Flipcharts to show examples of the arithmetic sequences and geometric sequences and series and to monitor students’ progress as they
learn the topics.
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Materials and Resources:
Textbook (Chapter 9)
SmartBoard
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Unit: Unit 8: Topics in Analytic Geometry
Subject: Mathematics
Timeline: 3 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
Big Ideas: Students will understand that:
Essential Questions:
You can analysis of lines with trigonometry and a distance
formula.
You can solve problems involving conic sections, eventually
classifying a conic by its equation in general form.
Concepts:Students will know...
How do you find the angle of inclination of a line and the
distance between a point and a line?
How do you recognize each conic section and solve problems
involving parabolas?
How do you solve problems involving ellipses?
How do you solve problems involving hyperbolas and classify a
conic section on the basis of its general equation?
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
Inclination of a Line
Angle Between Two Lines
Distance Between a Point and a Line
Conics
Parabolas
Ellipses
Eccentricity
Hyperbolas
Asymptotes of a Hyperbola
General Equations of Conics
Find the inclination of a line and the distance between a point
and a line.
Recognize a conic as the intersection of a plane and a doublenapped cone.
Write equations of parabolas in standard form and graph
parabolas.
Write equations of ellipses in standard form and graph ellipses.
Find eccentricities of ellipses.
Write equations of hyperbolas in standard form.
Find asymptotes of and graph hyperbolas.
Classify conics from their general equations.
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Exit slips
Quizzes
Worksheets
Homework (Bookwork)
Problems done by students on dry-erase boards
Project
Classwork on SmartBoard
Other Evidence (Tests, quizzes, etc)
Stage Three - Learning Plan
Learning Activities:
Learn what conic sections are and the vocabulary associated with them.
Complete assigned bookwork which includes finding the inclination of a line and solving problems using conic sections.
Various activity worksheets which requires students to apply and evaluate the knowledge and skills learned.
Quizzes and tests to have students show mastery of concepts learned.
Flipcharts to show examples of the conic sections and to monitor students’ progress as they learn the topics.
Materials and Resources:
Textbook (Chapter 10)
SmartBoard
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