Horizontal Curriculum Map by 3-Week Block
Standards
1B
1A
Block
Topic(s)/
Essential
Question(s)
COURSE:__Precalculus________________
Content/Materials
How do you
complete
1.1.1, 1.1.2, 1.1.3, 1.1.4.1.2.1,1.2.1,
transformations of
1.2.2, 1.3.1, 1.3.2, 1.4.1, 1.4.2
parents and other
Closure
graphs? How do you Transformations of Parent Graphs; Basic
use function
Inverses and Function Operations;
operations to
Transformation of Non-Parent Graphs;
combine expressions?
Point-Slope Form of a Line; Law of
How does the point- Sines; Law of Cosines; Radian Measure;
slope form a line?
and Common Angles in the Unit Circle
What are the Laws of
Sines and Cosines?
How do you use
radians to measure
angles?
How are functions
constructed when
using more than one
equation? How do
you find the sum of
sequences? How do
you find the are of a
curve using
rectangles and
trapezoids? How do
you develop
summation notation?
2.1.1, 2.1.2,2.2.1, 2.2.2, 2.3.1,
2.3.2. 2.3.3, 2.3.4, 2.3.5, 2.3.6,
2.3.7, 2.3.8
closure
Piecewise Functions; Shifting Piecewise
Functions; Periodic Functions; Summation
Notation and Area Under a Curve. The
major idea of the chapter is finding the area
under a curve.
Assessments
Using the assessment
bank: 1.1 1, 5,
1.1.2 4,
1.1.3 5
1.1.4 3
Review: Exponents,
Converting between
radical and exponential
expressions, degrees,
minutes and seconds,
Right triangles.
Participation quiz 1.2.2
Half from previous
chapter
2.1.1 3
2.1.2 2
2.2.1 4
2.2 5
2.3 2, 9, 12
Unit Word: 3
Review concepts include:
factoring, rational
exponents, addition
rational expressions,
multiplying rational
expressions
Academic
Vocabulaty
Function, Domain,
range, parent graphs,
transformation,
shifting functions,
stretching functions,
inverse of a function,
non-parent
functions, point
slope, laws of sines,
laws of cosines,
radians. Coterminal,
Sierpinksi Triangle
Piecewise functions,
intuitive notion of
continuity,
horizontal and
vertival shifts of
piecewise functions,
periodic functions,
sigma notation, area
under curve, leftendpoint rectangles,
right endpoint
rectangles,
trapezoids, midpoint
rectangles, shifting
areas, area as a
function
Standards
1C
Block
Topic(s)/
Essential
Question(s)
How and why do you
shift graphs? What
are equivalent
transformations?
How do you apply
exponential functions
to model real-world
situations? What is a
log functions, its
graphs and
properties?
Content/Materials
Assessments
3.1.1, 3.1.2, 3.1.3, 3.2.1, 3.2.2, 3.2.3,
3.3.1 Chapter Closure
Horizontal and Vertical Stretches;
Applications of Exponential Functions;
Stretching Exponential Functions;
Inverse Functions; Logs as Inverse
Exponentials; Graphing Log Functions;
Laws of Logarithms and Solving
Exponential Equations
Participation quiz 3.2.2
Half from previous
chapter
From assessment bank
3.1.1 5
3.1.2 6
3.1.3 5
3.2.1 4
3.2.2 1
3.2.3 4
3.1.1 3
Bigger problems 1 – 3
Review concepts include
finding roots and
simplifying complex
fractions and equations
Academic
Vocabulaty
Function
transformations,
applications of
exponential
functions, equivalent
transformations,
equivalent
transformations,
inverse functions,
vertical line test,
Standards
2B
2A
Block
Topic(s)/
Essential
Question(s)
How do you use unit
circle to find exact
values of trig
functions? How do
you graph sinusoidal
functions? What are
reciprocal
trigonometric
functions, Secant,
Cosecant, and
cotangent? How do
you simplify and
verify expressions?
What is modeling
using periodic
functions?
How do you sketch
and simplify rational
functions? How do
you solve problems
involving direct and
inverse variations?
What is continuity?
What happens to
limits as x goes to
infinity? How do
you model using
periodic functions?
Content/Materials
4.1.1, 4.1.2, 4.1.3, 4.2.1, 4.2.2, 4.2.3,
4.2.4, 4.3.1 4.3.2
Special Angles in the Unit Circle; Sine
and Cosine in the Unit Circle; Graphs of
Sine and Cosine; Reciprocal Trig
Functions; Simplifying Trig
Expressions; Frequency of Sine and
Cosine Graphs; Verifying Trig
Identities; Applications of Trig
Functions; and Graphical Addition
(chapter 4 moves into the next block)
5.1.1, 5.1.2, 5.1.3, 5.2.1, 5.2.2, 5.2.3,
5.2.4, 5.2.5
Inverse and Direct Variation;
Transformations of Rational Functions;
Graphing Reciprocals of Functions;
Introduction to Limits; Working With
One-Sided Limits; Continuity - Formal
Definition and Piecewise Functions and
Limits.
Chapter closure
Assessments
Participation quiz 4.2.2
Half from previous
chapter
4.1.3 1,2
4.2.1 5
4.2.3 2, 4
Application question 2.
Review radical
expressions
Participation quiz 5.2.3
Half from previous
chapters
From chapter assessment
5.1.1 4,5
5.1.2 5, 6
5.1.3 2
5.2.2 2,3
5.2.3 2
5.2.5 1-3
challenge problems 2-4
review concepts include
simplifying complicated
rational expressions, and
solving equations with
radicals
Academic
Vocabulaty
logarithms, laws of
logarithms, LN vs
LOG
Pythagorean identity
trigonometric ratios,
five point method,
angular frequency,
modeling with
periodic functions
Direct and Inverse
Variation,
transforming ration
functions, limits,
one-sided limits,
continuous function,
piecewise functions
and limits
Topic(s)/
Essential
Question(s)
Content/Materials
2C
How do I solve for
trigonometric
equations? What is
the SSA case of a
triangle? How do I
solve for it? How do
I use the angle sum
and difference
formulas and doubleangle formulas?
6.1.1, 6.1.2, 6.1.3, 6.1.4, 6.2.1, 6.2.2,
6.2.3, 6.3.1, 6.3.2, 6.4.1, 6.4.1 Solving
Trig Equations; Inverse Sine and Cosine;
The Ambiguous Case of the Law of
Sines; Graphs of Tangent and Inverse
Tangent; Graphing
y = a sin ( b(x - h) ) + k ; Angle Sum and
Difference Formulas; Modeling With
Periodic Functions; Double- and HalfAngle Formulas; and Solving More
Complex Trig Equations.
Chapter Closure
3A
Standards
Participation quiz 7.2.2
Increasing and
Half from previous
decreasing functions,
chapters
concavity, even and
From assessment bank
odd functions,
Why is it important
7.1.1 4,5
substitutions,
to use the appropriate 7.1.1, 7.1.2, 7.2.1, 7.2.2, 7.2.3, 7.3.1, 7.3.3
7.1.2 3-5
polynomial division,
language when
7.2.1 1-5
arithmetic series,
Describing Functions: Increasing,
setting up math
7.2.2
1,
2
geometric series,
Decreasing, Concavity; Odd and Even
problems? How do
7.2.3 4
Pascal’s triangle,
Functions; Setting up Word Problems;
Using “u” Substitution; Polynomial
you set up complex
7.2.4 1-3
binomial
Division;
The
Binomial
Formula
and
word problems?
7.3.1 4
expressions,
Pascal’s Triangle; Adding Arithmetic Series;
How do you use
7.3.2 1, 5-7
binomial
Adding
Geometric
Series;
and
Binomial
Pascal’s Triangle to
7.3.3 4, 5
probabilities
Probability
expand binomials?
Challenge problems 1 – 3
Review topics include
completing the square and
solving inequalities
Block
Assessments
Participation quiz 6.2.2,
Half from previous
chapters
6.1.1 2
6.1.2 3
6.1.3 3,5
6.1.4 1
6.2.2 1,2
6.2.3 3 – 5
6.3.2 1-3
Academic
Vocabulaty
Inverse sine, inverse
cosine, tangent,
inverse tangent,
angle sum, double
and half angle
formulas
Standards
3B
Content/Materials
How do you find
limits to infinite and
at points? How do
you determine if a
graph has an
asymptote or a hole?
How do you use
limits to find sums of
infinite geometric
series? What the
harmonic series?
What is the Fibonacci
sequence?
8.1.1, 8.1.2, 8.1.3, 8.1.4, 8.2.1, 8.2.2, 8.2.3,
8.2.4, 8.4.5, 8.5.6
Limits at Infinity; Limits of Rational
Functions (at infinity); Recursive
Sequences; Limits of Rational Functions (at
a point); The Number e; Applications of e;
Infinite Geometric Series and Proof by
Mathematical Induction.
3C
Block
Topic(s)/
Essential
Question(s)
How do you calculate
the rate of change?
How do you know
what equation to use
when? How do you
estimate the
instantaneous rates of
change? What is the
relationship between
velocity and
distance?
9.1.1, 9.1.2, 9.1.3, 9.1.4, 9.2.1, 9.2.2, 9.3.1,
9.3.2, 9.3.3. 9.3.4. 9.3.5
Rates of Change From Data; Slopes and
Rates of Change; Average Velocity and
Rates of Change; Finding Slope at a Point;
Slopes of Secant and Tangent Lines;
Velocity and Position Graphs; Finding
Instantaneous Velocity; Finding Slope
Functions; The Definition of a Derivative
and Slope and Area Under a Curve
Assessments
Academic
Vocabulaty
Participation quiz: 8.2.2
Half from previous
chapters,
8.1.1 1, 2
8.1.2 1, 3
8.1.3 1
8.2.1 1
8.2.2 1, 3, 4
8.2.3 1. 2
8.2.4 1, 3, 5
review topics include
writing repeating
decimals as fractions
Dominant terms,
limits to infinite,
holes, asymptotes,
squeeze method, e.
infinite geometric
series, harmonic
series, Fibonacci
series, induction
Participation quiz 9.2.2
half from previous
chapters
9.1.2 1,2, 4
9.1.4 2, 3, 7
9.2.2 1-3
9.3.1 1, 2
9.3.3 1-4
9.3.4 1, 4
9.3.5 1-5
rates of change,
slope and rates of
change, AROC,
IROC, Secant line vs
tangent line, velocity
and position graphs,
derivative
Standards
4A
How do you define
vectors in standard
and component form?
When do you use
vectors? How does
this relate to physics?
How can you use
parametric equations
to solve real world
problems?
4B
Block
Topic(s)/
Essential
Question(s)
How can you plot
points and graph
equations using polar
and rectangular
equations? What are
the various families
of polar functions?
What is DeMoivre’s
Theorem? How can
you use it to find the
powers and the roots
of complex numbers?
Content/Materials
10.1.1, 10.1.2, 10.1.3, 10.1.4, 10.2.1, 10.2.2,
10.2.3
Adding and Subtracting Vectors; Magnitude,
Direction, and Unit Vectors; Using Vectors to
Solve Word Problems; Finding the Angle
Between Two Vectors (Dot Product); Work;
Vector Equations of Lines; Graphing
Parametric Equations by Hand; Graphing
Parametric Equations with a Calculator;
Modeling Motion With Parametric Equations;
and Inverses Using Parametric Equations.
Assessments
Participation quiz 10.2.2
Half from previous
chapters
From assessment bank
10.1.1 1-2
10.1.2 1, 4
10.1.3 1-3
10.1.4 1, 3, 4
10.2.1 1
10.2.2 2
10.2.3 1,3,4
11.1.1, 11.1.2, 11.1.3, 11.1.4, 11.2.1, 11.2.2 Participation quiz 11.1.3.
half from previous
Plotting Polar Coordinates by Hand; Graphs of
chapters
from assessment
Polar Equations with a Calculator; Rotating
11.1.1 2, 3
Polar Graphs; Converting Between
Rectangular and Polar Coordinates;
11.1.2 2
Rectangular and Polar Forms of Complex
11.1.3 1, 5
Numbers; Graphing Complex Numbers;
11.2.1 1, 3
Products and Quotients of Complex Numbers;
11.2.2 1, 2, 3, 4
DeMoivre’s Theorem and Roots of Complex
Numbers
Academic
Vocabulaty
Vector addition,
magnitude and
standard angle of a
vector, component
form of a vector, unit
vectors, dot product,
parametric
equations, vector
equations, inverses
and parametric
equations
Polar coordinates,
polar graphs,
rotations, polar
forms of complex
numbers Demoivre’s
theorem
Standards
4C
Block
Topic(s)/
Essential
Question(s)
Content/Materials
Assessments
Participation quiz 12.2.2
Half from previous
12.1.1, 12.1.2, 12.1.3, 12.2.1, 12.2.2,
What are matrices
chapters
12.2.3
Basic
Matrix
Operations;
Solving
and why are they
From assessment
Systems Using Matrices; Applications of
useful? How can you
12.1.1 1
Matrices;
Using
Matrices
to
Complete
Linear
use a calculator to
12.1.2 1
Transformations; Composition of
complete matrix
12.1.3 1,3,5
Transformations and Properties of
operations? How do
12.2.1 2
Transformations.
you use matrices to
12.2.2 2
13.1.1, 13.1.2, 13.1.3, 13.1.4, 13.2.1
complete linear
12.2.3 1-3, 6
Circles, Ellipses, Hyperbolas, Parabolas and
transformations?
13.1.1 1 – 3
Eccentricity.
How does this apply
13.1.2 1, 4, 5
to the real world?
13.1.3 2,3,4
13.1.4 1, 4
word problems 1, 2, 5
Academic
Vocabulaty
Matrices, Matrix
operations, identity
matrix, inverse
matrix, linear
transformation,
rotation matrix,
vectors, eigenvalues
Ellipses, hyperbolas,
parabolas, second
degree equations.