Download Pre-Calculus - Lee County School District

THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
Pre-Calculus Honors (1202340)
Adopted Instructional Materials:
1-1
Graphs of Functions
1-2
Polynomial & Rational Functions
Precalculus with Limits, A Graphing Approach
2-1
Trigonometric Functions
2-2
Analytic Trigonometry
Additional Course Information
English Language Development ELD Standards Special
Notes Section:
Teachers are required to provide listening, speaking,
reading and writing instruction that allows English
language learners (ELL) to communicate information,
ideas and concepts for academic success in the content
area of Mathematics. For the given level of English
language proficiency and with visual, graphic, or
interactive support, students will interact with grade
level words, expressions, sentences and discourse to
process or produce language necessary for academic
success. The ELD standard should specify a relevant
content area concept or topic of study chosen by
curriculum developers and teachers which maximizes
an ELL’s need for communication and social skills.
Page 1 of 20
3-1
Trigonometry Applications
3-2
Analytic Geometry
4-1
Limits
4-2
Exponential & Logarithmic Functions
4-3
Sequences & Series
Professional Development






Math Practices by Grade Level
Build Relationships: Teach More Than ‘Just Math’
Sorting Equations Video: Research shows that
formative assessments have a significant impact
on student learning gains. This video is just one
example of using formative assessment to inform
instruction.
CPALMS MFAS Training
Research around formative assessment shows that
students make greater learning gains when they are
accountable for their own learning and the learning
of their peers. The video, Facilitating Peer Learning,
is a good example of a math classroom where
students are engaged with one another.
Five “Key Strategies” for Effective Formative
Assessment
Helpful Websites



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

Khan Academy: Practice by Grade Level Standards
https://www.khanacademy.org/commoncore/m
ap
Shmoop: Math videos
http://www.shmoop.com/video/math-videos
KUTA Software: Test and Worksheet Generator
http://www.kutasoftware.com/
Teaching Channel: Videos and Best Practices
https://www.teachingchannel.org/
Geogebra: Math web applets
https://tube.geogebra.org
Inside Mathematics: Videos and Best Practices
http://www.insidemathematics.org/
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
1-1
Pre-Calculus Honors (1202340)
Adopted Instructional Materials:
Precalculus with Limits, A Graphing Approach
Big Idea: Graphs of Functions
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.F-BF.1: Build a function that models a relationship between two quantities
 MAFS.912.F-BF.1.1: Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a
context.
b. Combine standard function types using arithmetic operations. For example, build a
function that models the temperature of a cooling body by adding a constant function to
a decaying exponential, and relate these functions to the model.
c. 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.
MAFS.912.F-BF.2: Build new functions from existing functions
 MAFS.912.F-BF.2.4: Find inverse functions. 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. For example,
𝑓(𝑥) = 2𝑥 3 or 𝑓(𝑥) = (𝑥 + 1)/(𝑥 − 1) for 𝑥 ≠ 1. Verify by composition that one function
is the inverse of another. Read values of an inverse function from a graph or a table, given
that the function has an inverse. Produce an invertible function from a non-invertible
function by restricting the domain.
MAFS.912.N-CN.3: Use complex numbers in polynomial identities and equations.
 MAFS.912.N-CN.3.9: Know the Fundamental Theorem of Algebra; show that it is true for
quadratic polynomials.
LAFS.1112.SL.1.1: Initiate and participate effectively in a range of
collaborative discussions (one-on-one, in groups, and teacher-led)
with diverse partners on grades 1112 topics, texts, and issues,
building on others ideas and expressing their own clearly and
persuasively.
a. Come to discussions prepared, having read and researched
material under study; explicitly draw on that preparation by
referring to evidence from texts and other research on the
topic or issue to stimulate a thoughtful, well-reasoned
exchange of ideas.
b. Work with peers to promote civil, democratic discussions and
decision-making, set clear goals and deadlines, and establish
individual roles as needed.
c. Propel conversations by posing and responding to questions
that probe reasoning and evidence; ensure a hearing for a full
range of positions on a topic or issue; clarify, verify, or
challenge ideas and conclusions; and promote divergent and
creative perspectives.
d. Respond thoughtfully to diverse perspectives; synthesize
comments, claims, and evidence made on all sides of an
issue; resolve contradictions when possible; and determine
what additional information or research is required to
deepen the investigation or complete the task.
Suggested Mathematical Practice Standards
MAFS.K12.MP.4.1: Model with mathematics.
 What real-world situations could be analyzed and solved by
producing inverse functions?
Page 2 of 20
Updated: June 8, 2016
MAFS.K12.MP.8.1: Look for and express regularity in repeated
reasoning.
 What are the similarities and differences among parent
graphs when applying transformations?
Essential Outcome Question(s)
In what ways can you analyze and describe a function?
Aligned Learning Goals

Identify a variety of functions given a graph or equation, including linear, quadratic, cubic,
rational, square root, exponential, logarithmic, trigonometric, inverse trigonometric,
absolute value, and greatest integer functions

Determine key features of functions, including domain, range, y-intercepts, zeros,
increasing, decreasing, even, odd, and rates of change

Use functions to model real world problems

Identify graphs of parent functions

Identify the transformations of parent functions given an equation or a graph

Use vertical and horizontal shifts, reflections, and nonrigid transformations to graph
functions

Add, subtract, multiply, and divide functions

Find the composition of functions

Write functions as the composition of two functions

Use function compositions to model and solve real-world problems

Find inverse functions both informally and algebraically

Verify whether or not functions are inverses algebraically and from graphs
Page 3 of 20
District Adopted
Materials
Supplemental
Resources
Strategies for
Differentiation
Precalculus w/
Limits
MAFS.912.F-BF.2.4:
Lesson: Invertible
or Not?
INTERVENTION
Section 1.1
MAFS.912.F-BF.1.1:
Parent Functions
Handout
Chapter 1
Sections 2 – 6
Suggested Lesson
Grouping:
Lessons 1 & 2
Lesson 4
Lessons 5 & 6
MAFS.912.F-BF.1.1:
Foldable Parent
Polynomial
Function Behavior
ENRICHMENT
Section 1.7
MAFS.912.F-BF.1.1:
QR Code Scavenger
Hunt
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
1-2
Pre-Calculus Honors (1202340)
Adopted Instructional Materials:
Precalculus with Limits, A Graphing Approach
Big Idea: Polynomial & Rational Functions
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.F-BF.1: Build a function that models a relationship between two quantities
 MAFS.912.F-BF.1.1: Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a
context.
b. Combine standard function types using arithmetic operations. For example, build a
function that models the temperature of a cooling body by adding a constant function to
a decaying exponential, and relate these functions to the model.
c. 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.
MAFS.912.N-CN.1.: Perform arithmetic operations with complex numbers.
 MAFS.912.N-CN.1.3: Find the conjugate of a complex number; use conjugates to find
moduli and quotients of complex numbers.
MAFS.912.A-APR.4: Rewrite rational expressions.
 MAFS.912.A-APR.4.6: Rewrite simple rational expressions in different forms; write
𝑎(𝑥)/𝑏(𝑥) in the form 𝑞(𝑥) + 𝑟(𝑥)/𝑏(𝑥), where 𝑎(𝑥), 𝑏(𝑥), 𝑞(𝑥), and 𝑟(𝑥) are
polynomials with the degree of 𝑟(𝑥) less than the degree of 𝑏(𝑥), using inspection, long
division, or, for the more complicated examples, a computer algebra system.
 MAFS.912.A-APR.4.7: Understand that rational expressions form a system analogous to the
rational numbers, closed under addition, subtraction, multiplication, and division by a
nonzero rational expression; add, subtract, multiply, and divide rational expressions.
MAFS.912.N-CN.3: Use complex numbers in polynomial identities and equations.
 MAFS.912.N-CN.3.9: Know the Fundamental Theorem of Algebra; show that it is true for
quadratic polynomials.
MAFS.912.C.1: Limits and Continuity.
 MAFS.912.C.1.12: Understand and use the Intermediate Value Theorem on a function over
a closed interval.
LAFS.1112.RST.3.7: Integrate and evaluate multiple sources of
information presented in diverse formats and media (e.g.,
quantitative data, video, multimedia) in order to address a
question or solve a problem.
LAFS.1112.WHST.3.9: Draw evidence from informational texts to
support analysis, reflection, and research.
Page 4 of 20
ELD.K12.ELL.MA.1: English language learners communicate
information, ideas and concepts necessary for academic success
in the content area of Mathematics.
Suggested Mathematical Practice Standards
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
 How did you decide how to approach this problem?
MAFS.K12.MP.3.1: Construct viable arguments and critique the
reasoning of others.
 What do you think about _____’s work?
 Is your answer different than ____’s? If so, how?
Updated: June 8, 2016

MAFS.912.C.1.13: Understand and apply the Extreme Value Theorem: If 𝑓(𝑥) is continuous
over a closed interval, then f has a maximum and a minimum on the interval.
MAFS.912.A-APR.3: Use polynomial identities to solve problems.
 MAFS.912.A-APR.3.5: Know and apply the Binomial Theorem for the expansion of (𝑥 + 𝑦)𝑛
in powers of 𝑥 and 𝑦 for a positive integer n, where 𝑥 and 𝑦 are any numbers, with
coefficients determined for example by Pascal’s Triangle.
Essential Outcome Question(s)
What tools can help identify the zeros of a polynomial function?
How are various polynomial theorems helpful in solving problems?
Aligned Learning Goals
District Adopted
Materials

Analyze quadratic functions and use key features to solve real-world problems

Use transformations to sketch the graph of a polynomial function

Determine the end behavior of a polynomial function

Understand and define zeros of a function

Identify the zeros of a factored polynomial function and use them to sketch the graph the
function

Divide polynomials using long division and synthetic division to find the zeros of a
polynomial function

Apply the Remainder Theorem when dividing polynomials

Apply the Rational Zero Test and Descartes’s Rule of Signs to find zeros of a polynomial
function

Apply the Fundamental Theorem of Algebra to determine the number of zeros of a
polynomial function

Use various methods to find all the zeros, including rational and complex zeros, of a
polynomial function

Understand and use the Intermediate Value Theorem on a function over a closed interval

Understand and use the Extreme Value Theorem

Add, subtract, multiply, and divide complex numbers

Find the conjugate of a complex number
Page 5 of 20
Precalculus with
Limits
Chapter 2
Sections 2 – 5
Chapter 8
Section 4
Supplemental
Resources
Strategies for
Differentiation
MAFS.912.N-CN.1.3:
Complex Numbers
Maze
INTERVENTION
Polynomial Review
Materials
ENRICHMENT
Lessons 6 & 7
Lesson 8
MAFS.C.1.13:
Extreme Value
Theorem
Suggested Lesson
Grouping:
Ch. 2
Lessons 1 & 4
Lesson 2
Lesson 3
Lesson 5
Ch. 8
Lesson 4
Updated: June 8, 2016

Find complex solutions of quadratic equations

Use the Binomial Theorem to calculate binomial coefficients

Use binomial coefficients to write binomial expansions

Use Pascal’s Triangle to calculate binomial coefficients
Formative Assessment Options:
MAFS.9.12.A-APR.3.4:
Performance Task Trina’s Triangles
Page 6 of 20
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
2-1
Pre-Calculus Honors (1202340)
Adopted Instructional Materials:
Precalculus with Limits, A Graphing Approach
Big Idea: Trigonometric Functions
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.F-TF.1: Extend the domain of trigonometric functions using the unit circle
 MAFS.912.F-TF.1.1: Understand radian measure of an angle as the length of the arc on the
unit circle subtended by the angle; Convert between degrees and radians.
 MAFS.912.F-TF.1.2: Explain how the unit circle in the coordinate plane enables the
extension of trigonometric functions to all real numbers, interpreted as radian measures of
angles traversed counterclockwise around the unit circle.
 MAFS.912.F-TF.1.3: 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.
 MAFS.912.F-TF.1.4: Use the unit circle to explain symmetry (odd and even) and periodicity
of trigonometric functions.
MAFS.912.F-TF.2: Model periodic phenomena with trigonometric functions.
 MAFS.912.F-TF.2.5: Choose trigonometric functions to model periodic phenomena with
specified amplitude, frequency, and midline.
 MAFS.912.F-TF.2.6: Understand that restricting a trigonometric function to a domain on
which it is always increasing or always decreasing allows its inverse to be constructed.
 MAFS.912.F-TF.2.7: 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.
MAFS.912.G-SRT.3: Define trigonometric ratios and solve problems involving right triangles
 MAFS.912.G-SRT.3.8: Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
LAFS.1112.RST.1.3: Follow precisely a complex multistep
procedure when carrying out experiments, taking measurements,
or performing technical tasks; analyze the specific results based on
explanations in the text.
LAFS.1112.SL.2.4: Present information, findings, and supporting
evidence, conveying a clear and distinct perspective, such that
listeners can follow the line of reasoning, alternative or opposing
perspectives are addressed, and the organization, development,
substance, and style are appropriate to purpose, audience, and a
range of formal and informal tasks.
ELD.K12.ELL.MA.1: English language learners communicate
information, ideas and concepts necessary for academic success in
the content area of Mathematics.
Suggested Mathematical Practice Standards
MAFS.K12.MP.1.1: Make sense of problems and persevere in
solving them.
 What is this problem asking?
 Could someone else understand how to solve the problem
based on your explanation?
MAFS.K12.MP.4.1: Model with mathematics.
 Does your solution make sense?
 What do you know about the situation already?
Essential Outcome Question(s)
In what ways are trigonometric functions useful?
In what ways can you determine the measure of a central angle?
Page 7 of 20
Updated: June 8, 2016
Aligned Learning Goals

Describe angles using appropriate vocabulary

Understand and use both degrees and radians to measure central angles

Solve real-world problems involving central angles, arcs, and sectors

Model converting between degrees and radians

Identify a unit circle and describe its relationship to real numbers

Determine the value of basic trigonometric functions using right triangle geometry

Evaluate trigonometric functions using the unit circle and a calculator

Use domain and period to evaluate sine and cosine functions

Solve real-world right triangle problems using trigonometric ratios

Explain how the unit circle in the coordinate plane enables the extension of trigonometric
functions to all real numbers

Use the unit circle to find trigonometric values in both mathematical and real-world
contexts

Identify and use trigonometric identities to solve problems

Find reference angles

Evaluate trigonometric functions of angles and real numbers

Sketch the graphs of sine, cosine, and tangent functions, including understanding and
applying transformations in both mathematical and real-world contexts

Sketch the graphs of cotangent, secant, and cosecant functions, applying transformations
in both mathematical and real-world contexts

Explain how restricting the domain of the graph of a trigonometric function allows for the
inverse to be constructed and use inverse functions to solve problems

Evaluate and graph inverse trigonometric functions

Evaluate the composition of trigonometric functions

Solve real-world problems involving right triangles using trigonometric functions and the
Pythagorean Theorem
Page 8 of 20
District Adopted
Materials
Supplemental
Resources
Strategies for
Differentiation
Precalculus with
Limits
MAFS.912.F-TF.1.1:
Lesson: Radians vs.
Degrees
INTERVENTION
Right Triangle
Review Material
MAFS.912.F-TF.1.4:
Lesson: Graphs
from the Unit Circle
Lesson 4.8, pp 329-31
Chapter 4
Omit Harmonic
Motion
Suggested Lesson
Grouping:
Lessons 1 & 2
Lessons 3 & 4
Lessons 5 & 6
Lesson 7
Lesson 8
EXTENSION
MAFS.912.F-TF.2.5:
Lesson: Ferris
Wheel and Periodic
Motion
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
2-2
Pre-Calculus Honors (1202340)
Adopted Instructional Materials:
Precalculus with Limits, A Graphing Approach
Big Idea: Analytic Trigonometry
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.F-TF.2: Model periodic phenomena with trigonometric functions.
 MAFS.912.F-TF.2.7: 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.
MAFS.912.F-TF.3: Prove and apply trigonometric identities.
 MAFS.912.F-TF.3.8: Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to
calculate trigonometric ratios.
 MAFS.912.F-TF.3.9: Prove the addition and subtraction, half-angle, and double-angle
formulas for sine, cosine, and tangent and use these formulas to solve problems.
MAFS.912.G-SRT.3: Define trigonometric ratios and solve problems involving right triangles
 MAFS.912.G-SRT.3.8: Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
MAFS.912.A-APR.3: Use polynomial identities to solve problems.
 MAFS.912.A-APR.3.4: Prove polynomial identities and use them to describe numerical
relationships. For example, the polynomial identity (𝑥 2 + 𝑦 2 )2 = (𝑥 2 − 𝑦 2 ) 2 + (2𝑥𝑦)2
can be used to generate Pythagorean triples.
LAFS.1112.WHST.2.4: Produce clear and coherent writing in which
the development, organization, and style are appropriate to task,
purpose, and audience.
ELD.K12.ELL.MA.1: English language learners communicate
information, ideas and concepts necessary for academic success in
the content area of Mathematics.
Suggested Mathematical Practice Standards
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
 Explain how you know that a given trig equation models the
given real-world situation.
MAFS.K12.MP.5.1: Use appropriate tools strategically.
 What methods can be used to solve trigonometric equations?
Essential Outcome Question(s)
How are trigonometric identities used to solve problems?
Aligned Learning Goals

Understand and write fundamental trigonometric identities, including reciprocal identities,
quotient identities, Pythagorean identities, cofunction identities, and even and odd
identities
District Adopted
Materials
Supplemental
Resources
Strategies for
Differentiation
Precalculus with
Limits
MAFS.912.F-TF.2.7:
Shmoop: Solving
Trig Equations
INTERVENTION
Trigonometry
Review Work
Chapter 5
Page 9 of 20
Updated: June 8, 2016

Use trigonometric identities to evaluate trigonometric functions and simplify/rewrite
trigonometric expressions

Use various methods to prove trigonometric identities by manipulating trigonometric
expressions with Pythagorean identities

Prove the Pythagorean identity (sin 𝜃)2 + (cos 𝜃)2 = 1 and use it to calculate
trigonometric ratios

Solve equations involving trigonometry in mathematical contexts

Use inverse trigonometric functions to find solutions to trigonometric equations modeling
real-world problems

Prove the sum and difference identities for sine, cosine, and tangent

Prove the double-angle and half-angle identities for sine, cosine, and tangent

Use the sum and difference identities and the double-angle and half-angle identities to
rewrite expressions and solve problems
Page 10 of 20
MAFS.912.T-TF.3.8:
Lesson Videos
MAFS.912.F-TF.3.9:
Shmoop: Verifying
Trig Equations
MAFS.912.F-TF.3.9:
I Have Who Has Trig
Identities
MAFS.912.F-TF.3.9:
Trig Function Maze
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
3-1
Pre-Calculus Honors (1202340)
Adopted Instructional Materials:
Precalculus with Limits, A Graphing Approach
Big Idea: Trigonometry Applications
Standards
Math Content Standards
MAFS.912.N-CN.1.: Perform arithmetic operations with complex numbers.
 MAFS.912.N-CN.1.3: Find the conjugate of a complex number; use conjugates to find
moduli and quotients of complex numbers.
MAFS.912.N-CN.2: Represent complex numbers and their operations on the complex plane.
 MAFS.912.N-CN.2.4: Represent complex numbers on the complex plane in rectangular and
polar form (including real and imaginary numbers), and explain why the rectangular and
polar forms of a given complex number represent the same number.
 MAFS.912.N-CN.2.5: Represent addition, subtraction, multiplication, and conjugation of
complex numbers geometrically on the complex plane; use properties of this
representation for computation. For example, (1 + 3 i) = 8 because (1 + 3 i) has modulus 2
and argument 120.
MAFS.912.N-VM.1: Represent and model with vector quantities.
 MAFS.912.N-VM.1.1: Recognize vector quantities as having both magnitude and direction.
Represent vector quantities by directed line segments, and use appropriate symbols for
vectors and their magnitudes (e.g., v, |v|, ||v||, v).
 MAFS.912.N-VM.1.2: Find the components of a vector by subtracting the coordinates of
an initial point from the coordinates of a terminal point.
 MAFS.912.N-VM.1.3: Solve problems involving velocity and other quantities that can be
represented by vectors.
MAFS.912.N-VM.2: Perform operations on vectors.
 MAFS.912.N-VM.2.4: Add and subtract vectors. Add vectors end-to-end, component-wise,
and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is
typically not the sum of the magnitudes. Given two vectors in magnitude and direction
form, determine the magnitude and direction of their sum. Understand vector subtraction
v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w
and pointing in the opposite direction. Represent vector subtraction graphically by
connecting the tips in the appropriate order, and perform vector subtraction componentwise.
Page 11 of 20
Suggested Literacy & English Language Standards
LAFS.1112.SL.1.2: Integrate multiple sources of information
presented in diverse formats and media (e.g., visually,
quantitatively, orally) in order to make informed decisions and
solve problems, evaluating the credibility and accuracy of each
source and noting any discrepancies among the data.
LAFS.1112.SL.1.3: Evaluate a speaker’s point of view, reasoning,
and use of evidence and rhetoric, assessing the stance, premises,
links among ideas, word choice, points of emphasis, and tone
used.
Suggested Mathematical Practice Standards
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
 What do you notice about…?
MAFS.K12.MP.6.1: Attend to precision.
 What labels should you use to accurately represent the
problem?
Updated: June 8, 2016

MAFS.912.N-VM.2.5: Multiply a vector by a scalar.
a. Represent scalar multiplication graphically by scaling vectors and possibly reversing
their direction; perform scalar multiplication component-wise, e.g., as c
=
.
b. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the
direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c >
0) or against v (for c < 0).
MAFS.912.G-SRT.4: Apply trigonometry to general triangles.
 MAFS.912.G-SRT.4.10: Prove the Laws of Sines and Cosines and use them to solve
problems.
 MAFS.912.G-SRT.4.11: Understand and apply the Law of Sines and the Law of Cosines to
find unknown measurements in right and non-right triangles (e.g., surveying problems,
resultant forces).
 MAFS.912.G-SRT.4.9: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by
drawing an auxiliary line from a vertex perpendicular to the opposite side.
Essential Outcome Question(s)
How can vectors be used in real-world problem solving?
Aligned Learning Goals

Prove the Laws of Sines and Cosines

Understand and apply the Law of Sines and the Law of Cosines to find unknown
measurements in right and non-right triangles
1
𝑎𝑏 sin 𝐶
2

Derive the formula 𝐴 =

Recognize, understand, and use symbols and vocabulary associated with vectors, including
magnitude and direction

Represent vectors using sketches, symbols, rectangular components, and in terms of
magnitude and direction

Add and subtract vectors, adding end-to-end, component-wise, and by the parallelogram
rule

Multiply a vector by a scalar

Calculate magnitudes for vectors, sums of vectors, and scalar multiples of vectors
Page 12 of 20
for the area of a triangle
District Adopted
Materials
Supplemental
Resources
Strategies for
Differentiation
Precalculus with
Limits
MAFS.912.G-SRT.4.11:
When To Use The Law
of Sines
INTERVENTION
Trigonometry
Review Work
Chapter 6
MAFS.912.G-SRT.4.11:
Law of Sines Ambiguity
MAFS.912.N-VM.1.1:
Lesson: Vectors: Tip to
Tail
MAFS.912.N-VM.1.3:
Lesson: Amusement
Park Physics
MAFS.N-CN.1.3:
Lesson: Can You Hear
Me Now? Dividing
Complex Numbers
Updated: June 8, 2016

Solve real-world applications of velocity and other quantities that can be modeled by
vectors

Plot complex numbers in the complex plane

Find the absolute value of complex numbers

Write the trigonometric form of complex numbers

Perform operations with complex numbers written in trigonometric form

Convert complex numbers from rectangular form to polar form and vice versa

Explain how a complex number in polar form and rectangular form represent the same
number

Find products and quotients of complex numbers in polar form and represent them
geometrically on the complex plane
Page 13 of 20
MAFS.912.N-VM.2.4:
Online Game: Vector
Island
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
3-2
Pre-Calculus Honors (1202340)
Adopted Instructional Materials:
Precalculus with Limits, A Graphing Approach
Big Idea: Analytic Geometry
Standards
Math Content Standards
MAFS.912.G-GPE.1: Translate between the geometric description and the equation for a
conic section.
 MAFS.912.G-GPE.1.1: Derive the equation of a circle of given center and radius using the
Pythagorean Theorem; complete the square to find the center and radius of a circle given
by an equation.
 MAFS.912.G-GPE.1.2: Derive the equation of a parabola given a focus and directrix.
 MAFS.912.G-GPE.1.3: Derive the equations of ellipses and hyperbolas given the foci and
directrices.
Suggested Literacy & English Language Standards
LAFS.1112.WHST.1.1: Write arguments focused on disciplinespecific content.
a. Introduce precise, knowledgeable claim(s), establish the
significance of the claim(s), distinguish the claim(s) from
alternate or opposing claims, and create an organization that
logically sequences the claim(s), counterclaims, reasons, and
evidence.
b. Develop claim(s) and counterclaims fairly and thoroughly,
supplying the most relevant data and evidence for each while
pointing out the strengths and limitations of both claim(s) and
counterclaims in a discipline-appropriate form that anticipates
the audiences knowledge level, concerns, values, and possible
biases.
c. Use words, phrases, and clauses as well as varied syntax to link
the major sections of the text, create cohesion, and clarify the
relationships between claim(s) and reasons, between reasons
and evidence, and between claim(s) and counterclaims.
d. Establish and maintain a formal style and objective tone while
attending to the norms and conventions of the discipline in
which they are writing.
e. Provide a concluding statement or section that follows from or
supports the argument presented.
Suggested Mathematical Practice Standards
MAFS.K12.MP.7.1: Look for and make use of structure.
 How does simplifying this equation relate to…?
Page 14 of 20
Updated: June 8, 2016
Essential Outcome Question(s)
What are similarities and differences among the equations of conic sections and the graphs of conic sections?
Aligned Learning Goals

Understand and use vocabulary associated with conic sections

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

Derive the equation of a parabola given a focus and directrix

Derive the equations of ellipses and hyperbolas given the foci and directrices

Find asymptotes of and graph hyperbolas

Find eccentricities of ellipses

Analyze and graph equations of circles, ellipses, parabolas, identifying key features

Identify conics sections from equations

Solve real-world problems involving conic sections

Classify conics from their general equations
Page 15 of 20
District Adopted
Materials
Supplemental
Resources
Precalculus with
Limits
MAFS.912.G-GPE.1.2:
Chapter 9
Sections 1 – 3
Lesson: Intro to
Conic Sections
Hands-On
Strategies for
Differentiation
ENRICHMENT
Pg. 663: Rotations
Lessons 4, 5, 6, & 7
Conic Sections Extra
Practice
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
4-1
Pre-Calculus Honors (1202340)
Adopted Instructional Materials:
Precalculus with Limits, A Graphing Approach
Big Idea: Limits and an Introduction into Calculus
Standards
Math Content Standards
MAFS.912.C.1: Limits and Continuity.
 MAFS.912.C.1.1: Understand the concept of limit and estimate limits from graphs and
tables of values.
 MAFS.912.C.1.2: Find limits by substitution.
 MAFS.912.C.1.3: Find limits of sums, differences, products, and quotients.
 MAFS.912.C.1.4: Find limits of rational functions that are undefined at a point.
 MAFS.912.C.1.5: Find one-sided limits.
 MAFS.912.C.1.9: Understand continuity in terms of limits.
 MAFS.912.C.1.10: Decide if a function is continuous at a point.
 MAFS.912.C.1.11: Find the types of discontinuities of a function.
Suggested Literacy & English Language Standards
LAFS.1112.RST.2.4: Determine the meaning of symbols, key terms,
and other domain-specific words and phrases as they are used in a
specific scientific or technical context relevant to grades 1112 texts
and topics.
ELD.K12.ELL.SI.1: English language learners communicate for
social and instructional purposes within the school setting.
Suggested Mathematical Practice Standards
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
Essential Outcome Question(s)
What methods can be used to find the limit of a function?
Aligned Learning Goals

Understand and explain the concept of a limit

Estimate limits of functions at both a fixed point and at infinity

Determine if limits of a function exists

Use properties of limits and direct substitution to evaluate limits

Evaluate one-sided limits of functions

Understand and explain continuity in terms of limits

Decide if a function is continuous at a point

Find limits of sums, differences, products, and quotients
Page 16 of 20
District Adopted
Materials
Supplemental
Resources
Precalculus with
Limits
MAFS.912.C.1.1:
Lesson: Leap Frog
Limits Review Game
Chapter 11
Sections 1, 2, & 4
MAFS.912.C.1.11:
Types of
Discontinuity
Limits
Video Series
Strategies for
Differentiation
MAFS.912.C.1.1:
Shmoop: Graphing
and Visualizing
Limits
MAFS.912.C.1.1-4:
Worksheet Practice
on Limits
Updated: June 8, 2016

Find limits of rational functions that are undefined at a point

Find limits of sequences
Page 17 of 20
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
4-2
Pre-Calculus Honors (1202340)
Adopted Instructional Materials:
Precalculus with Limits, A Graphing Approach
Big Idea: Exponential and Logarithmic Functions
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.F-BF.1: Build a function that models a relationship between two quantities.
 MAFS.912.F-BF.1.1: Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a
context.
b. Combine standard function types using arithmetic operations. For example, build a
function that models the temperature of a cooling body by adding a constant function
to a decaying exponential, and relate these functions to the model.
c. 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.
MAFS.912.F-BF.2: Build new functions from existing functions.
 MAFS.912.F-BF.2.5 - Understand the inverse relationship between exponents and
logarithms and use this relationship to solve problems involving logarithms and exponents.
LAFS.910.WHST.3.9: Draw evidence from informational texts to
support analysis, reflection, and research.
ELD.K12.ELL.MA.1: English language learners communicate
information, ideas and concepts necessary for academic success in
the content area of Mathematics.
Suggested Mathematical Practice Standards
MAFS.K12.MP.4.1: Model with mathematics.
 What other ways could you use to model the situation
mathematically?
MAFS.K12.MP.7.1: Look for and make use of structure.
 How can you use what you know to explain why this works?
Essential Outcome Question(s)
How can the properties of exponential and logarithmic expressions be used to solve equations?
Aligned Learning Goals

Understand and graph exponential functions

Understand and graph logarithmic functions

Use the properties of logarithms to expand and condense logarithmic expressions

Use the One-to-One Property and properties of exponentials and logarithmic expressions
to solve exponential and logarithmic equations
Page 18 of 20
District Adopted
Materials
Supplemental
Resources
Precalculus with
Limits
Log Review Jigsaw
Puzzle
Chapter 3
Sections 1 – 4
Worksheet Practice
on Exponential and
Logarithmic
Functions
Strategies for
Differentiation
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
4-3
Pre-Calculus Honors (1202340)
Adopted Instructional Materials:
Precalculus with Limits, A Graphing Approach
Big Idea: Sequences and Series
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.A-APR.3: Use polynomial identities to solve problems.
 MAFS.912.A-APR.3.4: Prove polynomial identities and use them to describe numerical
relationships. For example, the polynomial identity (𝑥 2 + 𝑦 2 )2 = (𝑥 2 − 𝑦 2 ) 2 + (2𝑥𝑦)2
can be used to generate Pythagorean triples.
 MAFS.912.A-APR.3.5: Know and apply the Binomial Theorem for the expansion of
(𝑥 + 𝑦)𝑛 in powers of 𝑥 and 𝑦 for a positive integer n, where 𝑥 and 𝑦 are any numbers,
with coefficients determined for example by Pascal’s Triangle.
MAFS.912.F-BF.1: Build a function that models a relationship between two quantities.
 MAFS.912.F-BF.1.2 - Write arithmetic and geometric sequences both recursively and with
an explicit formula, use them to model situations, and translate between the two forms.
LAFS.910.WHST.3.9: Draw evidence from informational texts to
support analysis, reflection, and research.
ELD.K12.ELL.MA.1: English language learners communicate
information, ideas and concepts necessary for academic success in
the content area of Mathematics.
ELD.K12.ELL.SI.1: English language learners communicate for
social and instructional purposes within the school setting.
Suggested Mathematical Practice Standards
MAFS.K12.MP.4.1: Model with mathematics.
 What other ways could you use to model the situation
mathematically?
 What connections can you make between different
representations of the situation?
MAFS.K12.MP.7.1: Look for and make use of structure.
 How can you use what you know to explain why this works?
 What patterns do you see?
Essential Outcome Question(s)
What methods can be used to find the sums of series of numbers?
Page 19 of 20
Updated: June 8, 2016
Aligned Learning Goals

Understand and write explicit and recursive formulas from given sequences

Understand summation notation, and use it to find sums of series

Find the nth term of arithmetic or geometric sequences

Find the sum of finite arithmetic or geometric series

Find the sum of infinite geometric series
Page 20 of 20
District Adopted
Materials
Supplemental
Resources
Precalculus with
Limits
Worksheet Practice
on Sequences &
Series
Strategies for
Differentiation
Chapter 8
Sections 1 – 3
Updated: June 8, 2016