Download Alabama COS Standards

Pre-Calculus Pacing Guide
Suggested Book List
1st Grade
All Sorts of Numbers – counting
* Henry the Fourth – ordinal numbers
* 3 Little Firefighters – sorting
* It’s About Time!
* Bug Dance
* The Best Vacation Ever – data collecting,
problem solving skills
* Count on Clifford
2nd Grade
Amanda Bean’s Amazing Dream –
multiplication
* Clocks and More Clocks - time
* Much Bigger than Martin – size
“Slowly, Slowly, Slowly” said the Sloth
* Lemonade for Sale - money
* 100 Days of School – counting to 100
* Biggest Bed in the World – size
* Give Me Half – halves
3rd Grade
Sir Cumference and the Dragon Pi
* Grandfather’s Tang Story - changing
shape
* Chicken Soup with Rice – months
* Counting on Frank – size comparison,
math facts, counting
* Hershey’s Milk Chocolate Bar Fraction
* How Much is a Million
Mummy Math: An Adventure in Geometry
* Millions of Cats
* Three Days on a River in a Red Canoe
4th Grade
Carry On, Mr. Bowditch
Sir Cumference and the Great Knight of
Angle Land – acute, obtuse, straight
angles
Sir Cumference and the Sword in the Cone –
cubes, pyramids, prisms
Sir Cumference and the First Round Table –
measurement
* A Million Fish…More or Less
Dear Mr. Henshaw
A Higher Geometry
* The Village of Round and Square Houses
- shape
5th Grade
* How the Second Grade Got $8205.50 to
Visit the Statue of Liberty – money
Hannah, Divided
The Secret Life of Amanda K. Woods –
probability
Tuck Everlasting – calculate population
Gulliver’s Travel – geometry
Jayden’s Rescue – problem solving
The Curious Incident of the Dog in the
Night – time, probability
The Heroic of Hercules Amsterdam –
counting
6th Grade
The Da Vinci Code – Fibonacci Sequence
The Twenty-one Balloons – mathematical
reasoning
Journey to Topaz – measurement
7th Grade
The Sand-Reckoner – problem solving
The Pearl – currency calculation
Middle – High School
Imaginary Numbers
Mathematics in the Time of Pharaohs
Medieval Chinese Innovations
Math Talk: Mathematical Ideas in Poems
for Two Voices
High School
Against the Odds – number theory
Five Equations that Changed the World
The Man Who Loved Only Numbers
Math Equals: Biographies of Women
Mathematical Scandels
Archimede’s Revenge – application of math
Calculus and Pizza
* denotes AR books
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Pre-Calculus Pacing Guide
Alabama COS Standards
1
ST
Textbook
Correlation
Pacing Guide
Big Ideas /
Essential
Question
AMSTI
Essential
Vocabulary
AHSGE & NAEP
Correlations / ARMT
Blueprint
Nine Weeks
Review Algebra II
(Refer to COS)
P.1-P.6
1 Week
12. Determine the equation of a curve
of best fit from a set of data by using
exponential, quadratic, or logarithmic
functions.
1.1-1.6
3
Weeks
4. Analyze the graphs of rational,
logarithmic, exponential, trigonometric,
and piecewise-defined functions by
determining the domain and range;
identifying any vertical, horizontal, or
oblique asymptotes; and classifying the
function as increasing or decreasing,
continuous or discontinuous, and noting
the type of discontinuity if one exists.
Approximating rates of change
using the difference quotient
2.1-2.9
3
Weeks
“High Drive”
Ferris Wheel
Day 23
Quad.
Equation
(Chapter P)
“High Drive”
Ferris Wheel
Day 23
Quad.
Equation
(Chapter P)
Page 2 of 8
Range,
domain,
discontinuity,
continuous, bounded,
maximum, minimum,
relative extrema,
horizontal asymptote,
piecewise, rational
functional, asymptote,
x-intercepts, yintercepts
Technology Based Lessons / Links
Pre-Calculus Pacing Guide
Alabama COS Standards
Textbook
Correlation
Pacing Guide
Big Ideas /
Essential
Question
AMSTI
2ND Nine Weeks
5. Analyze the effects of parameter
changes on the graphs of trigonometric,
logarithmic, and exponential functions.
Example:
explaining the relationship of
the graph of y = ex -2 to the graph of
y = ex
3.1-3.6
1 Week
“High Dive”
Sine function
Day 4
Day 5
(Chapter 3)
Determining the amplitude, period,
phase shift, domain, and range
of trigonometric functions and
their inverses
1 Week
ACT Review
5. Analyze the effects of parameter
changes on the graphs of trigonometric,
logarithmic, and exponential functions.
Example:
explaining the relationship of
the graph of y = ex -2 to the graph of
y = ex
3.1-3.6
2
Weeks
Determining the amplitude, period,
Page 3 of 8
Essential
Vocabulary
AHSGE & NAEP
Correlations / ARMT
Blueprint
Technology Based Lessons / Links
phase shift, domain, and range
of trigonometric functions and
their inverses
6. Apply the laws of logarithms to
simplify expressions and to solve
equations using common logarithms,
natural logarithms, and logarithms with
other bases.
4.1-4.8
4
Weeks
Exponential
function, base,
growth factor,
decay factor,
limit to growth,
logarithmic
function,
common
logarithmic ,
natural
logarithmic ,
sinusoid,
amplitude,
frequency,
phase shift
Page 4 of 8
Pre-Calculus Pacing Guide
Alabama COS Standards
Textbook
Correlation
Pacing Guide
AMSTI
Big Ideas /
Essential
Question
Essential
Vocabulary
3RD Nine Weeks
7. Solve trigonometric equations and
inequalities using sum, difference, and
half- and double-angle identities.
Verifying trigonometric identities
5.1 – 5.4
2 weeks
1. Perform the vector operations of
addition, scalar multiplication, and
absolute value.
Determining coincidence,
parallelism, collinearity, or
perpendicularity of vectors
Using vectors to model real life
and mathematical situations
6.1, 6.2
3 weeks
for
6.1–6.5
8. Use parametric equations to
represent real-life and mathematical
situations.
6.3
Reduction
formula
High Dive –
day 9 and 17
Scalar, initial
point, terminal
point, vector,
magnitude,
standard
position,
component
form, velocity,
dot product,
orthogonal,
vector
projection
Parametric
curve,
parametric
equations,
parameter,
parameter
interval
Page 5 of 8
AHSGE & NAEP
Correlations / ARMT
Blueprint
Technology Based Lessons / Links
Pre-Calculus Pacing Guide
Textbook
Correlation
Pacing Guide
Alabama COS Standards
11. Convert coordinates, equations,
6.4, 6.5
and complex numbers in Cartesian form 6.5 (graph
to polar form and from polar form to
only)
Cartesian form.
Graphing simple polar equations in
the polar coordinate plane
AMSTI
Big Ideas /
Essential
Question
Polar coordinate
system, polar
axis, polar
coordinates,
directed
distance,
directed angle,
maximum r value
Example: graphing r = 2 + 2 cosф or r =
2 + sin 3ф
Graphing polar coordinates and
complex numbers
3. Graph conic sections, including
parabolas, hyperbolas, ellipses, circles,
and degenerate conics, from seconddegree equations.
8.1-8.4
Essential
Vocabulary
3 weeks
Conic section,
vertex,
degenerate
conic sections,
parabola, focus
(foci), directrix,
axis, chord,
ellipse, minor
axis, major axis,
hyperbola,
transverse axis,
conjugate axis
Example: graphing x2 – 6x + y2 – 12y +
41 = 0 or y2 – 4x + 2y + 5=0
Formulating equations of conic
sections from their determining
characteristics
Example: writing the equation of an
ellipse with center (5, -3),
horizontal major axis of
length 10, and minor axis of
length 4.
Page 6 of 8
AHSGE & NAEP
Correlations / ARMT
Blueprint
Technology Based Lessons / Links
Pre-Calculus Pacing Guide
Alabama COS Standards
Textbook
Correlation
Pacing Guide
AMSTI
Big Ideas /
Essential
Question
Essential
Vocabulary
4th Nine Weeks
12. Determine the equation of curve of
best fit form from a set of data by using
exponential, quadratic, or logarithmic
functions.
9.1, 9.2
9. Solve applied problems involving
sequences with recurrence relations.
Determining characteristics of
arithmetic and geometric
sequences and series, including
those defined with recurrence
relations, first terms, common
differences or ratios, nth terms,
limits, or statements of
convergence or divergence.
Expanding binomials raised to a
whole number power using the
Binomial Theorem.
9.4, 9.5
3 weeks
for
9.1, 9.2,
9.4, 9.5
Sequence, finite
sequence,
infinite
sequence,
recursively,
arithmetic
sequence,
geometric
sequence,
common
difference,
common ratio,
summation
notation, index
of summation,
infinite series,
partial sums,
converges,
diverges
Page 7 of 8
AHSGE & NAEP
Correlations / ARMT
Blueprint
Technology Based Lessons / Links
Pre-Calculus Pacing Guide
Alabama COS Standards
2. Define e using the limit forms of
sigma notation lim(1 + 1/n)n, and
lim(1 + n)1/n.
10. Find limits of functions at specific
values and at infinity numerically,
algebraically, and graphically.
Applying limits in problems
involving convergence and
divergence.
Textbook
Correlation
Pacing Guide
10.1–10.3
3 weeks
10.1-10.3
5 weeks
AMSTI
Big Ideas /
Essential
Question
Essential
Vocabulary
Left hand limit,
right hand limit,
two sided limit
Page 8 of 8
AHSGE & NAEP
Correlations / ARMT
Blueprint
Technology Based Lessons / Links