Download Alabama COS Standards

Algebra II with Trigonometry 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
Algebra II with Trig Grade Math
Pacing Guide
Textbook
Correlation
Pacing Guide
AMSTI
Big Ideas /
Essential
Question
Essential
Vocabulary
AHSGE & NAEP
Correlations / ARMT
Blueprint
Alabama COS Standards
1ST Nine Weeks
7. Solve equations, inequalities, and applied
problems involving absolute values, radicals, and
quadratics over the complex numbers, as well as
simple trigonometric, exponential, and logarithmic
functions.
Example:
solving x2- 8x > -12, 3x = 81, 2
2
sin x + sin x = 0, or logx 2 = 5
1.1-1.6
2
Weeks
Compound
inequality,
absolute value,
extraneous
solution
Solving equations using laws of
exponents, including rational and
irrational exponents
Expressing the solution of an equation,
inequality, or applied problem as a
graph on a number line or by using set
or interval notation
13. Use different forms of representation to compare
characteristics of data gathered from two
populations.
Evaluating the appropriateness of the
design of an experimental study
Describing how sample statistics reflect
values of population parameters
Experimental
probability,
simulation,
sample space,
theoretical
probability
15. Calculate probabilities of events using the laws
of probability.
Using permutations and combinations to
calculate probabilities
Calculating conditional probability
Calculating probabilities of mutually
exclusive events, independent events,
and dependent events
Page 2 of 13
NAEPA3a, b, A4a, c, N1g, j,
N5e
Technology Based Lessons / Links
13. Use different forms of representation to compare
characteristics of data gathered from two
populations.
Evaluating the appropriateness of the
design of an experimental study
Describing how sample statistics reflect
values of population parameters
2.1-2.7, 9.1,
9.2
2½
Weeks
NAEPA1h, A2a, b, d, e, f,
A3a, A4c, A1e
Relation, domain,
range, mapping
diagram,
vertical- line
test, function,
vertex,
translation,
parent function,
branch, scatter
trend line
3. Analyze families of functions, including shifts,
reflections, and dilations of y =
k
x
(inverse
variation), y = kx (direct variation/linear), y = [x]
(greatest integer), y = x2 (quadratic), y = ax
(exponential), and y = logax (logarithmic).
Example:
comparing the graphs of y =
2x, y = 2x + 1, y = 2x + 1, and
y = -2x
Identifying the domain and range of a
relation given its graph, a table of
values, or its equation, including those
with restricted domains
Example:
finding the domain of y =
1
x3
or y =
x2
Identifying real-world situations
corresponding to families of functions
Linear inequality
7.
Solve equations, inequalities, and applied
problems involving absolute values, radicals, and
quadratics over the complex numbers, as well as
simple trigonometric, exponential, and logarithmic
functions.
Example:
solving x2- 8x > -12, 3x = 81, 2
sin2x + sin x = 0, or logx 2 = 5
Solving equations using laws of
exponents, including rational and
irrational exponents
Expressing the solution of an equation,
inequality, or applied problem as a
graph on a number line or by using set
or interval notation
Page 3 of 13
8. Solve systems of linear equations or inequalities
in two or three variables using algebraic techniques,
including those involving matrices.
Example:
solving a system of linear
equations using augmented
matrices and row operations,
matrix operations of a
graphing calculator, or
substitution
Evaluating the determinant of a 2x2 or
3x3 matrix
Solving word problems involving real-life
situations
3.1-3.6
8. Solve systems of linear equations or inequalities
in two or three variables using algebraic techniques,
including those involving matrices.
Example:
solving a system of linear
equations using augmented
matrices and row operations,
matrix operations of a
graphing calculator, or
substitution
2½
Weeks
NAEPA2a, A2c, A4a, A4g
Evaluating the determinant of a 2x2 or
3x3 matrix
Solving word problems involving real-life
situations
Page 4 of 13
Algebra II with Trig Grade Math
Pacing Guide
Textbook
Correlation
Pacing Guide
13.1-13.8
1 Week
Big Ideas /
Essential
Question
AMSTI
Essential
Vocabulary
AHSGE & NAEP
Correlations / ARMT
Blueprint
Alabama COS Standards
2ND Nine Weeks
9. Graph trigonometric functions of the form y=a
sin(bx), y=a cos(bx), and y=a tan(bx).
Determining period and amplitude of
sine, cosine, and tangent functions
from graphs or basic equations
Example:
solving problems involving
harmonic motion
Problem”
Chapter 13
and some 14
Periodic
function, cycle,
period,
amplitude,
standard
position, initial
side, terminal
side, coterminal
angles, unit
circle
1 Week
ACT Review
11. Define the six trigonometric functions using
ratios of the sides of a right triangle, coordinates on
the unit circle, and the reciprocal of other functions.
“High Drive”
“Ferris Wheel
13.1-13.8
1 Week
“High Drive”
“Ferris Wheel
Problem”
Chapter 13
and some 14
Page 5 of 13
standard
position, initial
side, terminal
side, coterminal
angles, unit
circle , central
angle,
intercepted arc,
radian,
trigonometric
ratios for a
right triangle
NAEPM1m, G2c
Technology Based Lessons / Links
7. Solve equations, inequalities, and applied
problems involving absolute values, radicals, and
quadratics over the complex numbers, as well as
simple trigonometric, exponential, and logarithmic
functions.
Example:
solving x2- 8x > -12, 3x = 81, 2
2
sin x + sin x = 0, or logx 2 = 5
14.1-14.6
4
Weeks
NAEPA3c, A4a, A4e, M1m
Solving equations using laws of
exponents, including rational and
irrational exponents
Expressing the solution of an equation,
inequality, or applied problem as a
graph on a number line or by using set
or interval notation
Trigonometric
ratios for a
right triangle
10. Solve general triangles, mathematical problems,
and real-world applications using the Law of Sines
and the Law of Cosines.
 Deriving formulas for Law of Sines
and Law of Cosines
 Determining area of oblique triangles
11. Define the six trigonometric functions using
ratios of the sides of a right triangle, coordinates on
the unit circle, and the reciprocal of other functions.
Trigonometric
identity
12. Verify simple trigonometric identities using
Pythagorean and/or reciprocal identities.
Example: verifying cos2  + tan2  cos2  = 1
Page 6 of 13
Algebra II with Trig Grade Math
Pacing Guide
Textbook
Correlation
Pacing Guide
AMSTI
Big Ideas /
Essential
Question
Essential
Vocabulary
AHSGE & NAEP
Correlations / ARMT
Blueprint
Alabama COS Standards
3RD Nine Weeks
8. Solve systems of linear equations or inequalities
in two or three variables using algebraic techniques,
including those involving matrices.
Example:
solving a system of linear
equations using augmented
matrices and row operations,
matrix operations of a
graphing calculator, or
substitution
4.1-4.8
3 Weeks
Evaluating the determinant of a 2x2 or
3x3 matrix
Solving word problems involving real-life
situations
1. Determine the relationships of subsets of complex
numbers.
Example:
using Venn diagrams or tree
diagrams to show how
subsets of complex numbers
are related
5.1-5.8
5
Weeks
“Fireworks”
“High Dive”
Day 23
(Chapter 5)
2. Simplify expressions involving complex numbers,
using order of operations and including conjugate
and absolute value.
Examples:
simplifying
3i
and
3i
 8 , (4-2i)2,
Page 7 of 13
Matrix, matrix
element, zero
matrix, scalar,
square matrix,
coefficient
matrix, variable
matrix, constant
matrix,
augmented
matrix
NAEPA4a, A4g, N3a, A4d,
G2c
Imaginary#, i,
complex #,
Complex # plane
NAEPA1e, A2a, A2c, A2g,
A4a, A3b, A3c, A4c,
G2c
Technology Based Lessons / Links
Quadratic
function,
vertex, axis
zero, of
symmetry,
parabola, zero
of a function,
discriminant
3. Analyze families of functions, including shifts,
reflections, and dilations of y = k (inverse
x
variation), y = kx (direct variation/linear), y = [x]
(greatest integer), y = x2 (quadratic), y = ax
(exponential), and y = logax (logarithmic).
Example:
comparing the graphs of y =
2x, y = 2x + 1, y = 2x + 1, and
y = -2x
Identifying the domain and range of a
relation given its graph, a table of
values, or its equation, including those
with restricted domains
Example:
finding the domain of y =
1
x3
or y =
x2
Identifying real-world situations
corresponding to families of functions
Factoring, GCF,
perfect square
trinomial,
difference of
two squares,
completing the
square
Parabola, axis of
symmetry,
vertex
4. Determine approximate real zeros of functions
graphically and numerically and exact real zeros of
polynomial functions.
Using the zero product property,
completing the square, and the
quadratic formula
Deriving the quadratic formula
5. Identify the characteristics of quadratic functions
from their roots, graphs, or equations.
Generating an equation when given its
roots or graph
Graphing a function when given its
equation
Examples: graphing equations of the
form y = a(x-h)2 + k;
graphing equations of the
form y = ax2 + bx + c
Determining the maximum or minimum
values of quadratic functions both
graphically and algebraically
Applying functions to real-world
problems
Page 8 of 13
6. Perform operations on functions, including
addition, subtraction, multiplication, division, and
composition.
Determining the inverse of a function or a
relation
Performing operations on polynomial and
rational expressions containing
variables
Example:
simplifying
3
x5
+
5
2
x  6x  5
Constructing graphs by analyzing their
functions as sums, differences, or
products
14. Determine an equation of linear regression from
a set of data.
Examining data to determine if a linear,
quadratic, or exponential relationship
exists and to predict outcomes
Page 9 of 13
Algebra II with Trig Grade Math
Pacing Guide
Textbook
Correlation
Pacing Guide
AMSTI
Big Ideas /
Essential
Question
Essential
Vocabulary
AHSGE & NAEP
Correlations / ARMT
Blueprint
Alabama COS Standards
4TH Nine Weeks
4. Determine approximate real zeros of functions
graphically and numerically and exact real zeros of
polynomial functions.
Using the zero product property,
completing the square, and the
quadratic formula
Deriving the quadratic formula
6.1-6.6
2
Weeks
Relative
maximum,
relative
minimum,
multiple zero,
multiplicity, sum
of cubes,
difference of
cubes,
conjugates
Synthetic
division,
remainder
theorem
6. Perform operations on functions, including
addition, subtraction, multiplication, division, and
composition.
Determining the inverse of a function or a
relation
Performing operations on polynomial and
rational expressions containing
variables
Example:
simplifying
3
x5
+
5
x2  6x  5
Constructing graphs by analyzing their
functions as sums, differences, or
products
Page 10 of 13
NAEPA2g, A3b, A3c, A4a
Technology Based Lessons / Links
3. Analyze families of functions, including shifts,
reflections, and dilations of y =
k
x
(inverse
variation), y = kx (direct variation/linear), y = [x]
(greatest integer), y = x2 (quadratic), y = ax
(exponential), and y = logax (logarithmic).
Example:
comparing the graphs of y =
2x, y = 2x + 1, y = 2x + 1, and
y = -2x
7.1-7.8
3
Weeks
Radical function
Identifying the domain and range of a
relation given its graph, a table of
values, or its equation, including those
with restricted domains
Example:
finding the domain of y =
1
x3
or y =
x2
Identifying real-world situations
corresponding to families of functions
Composite
function,
inverse relation,
inverse function
6. Perform operations on functions, including
addition, subtraction, multiplication, division, and
composition.
Determining the inverse of a function or a
relation
Performing operations on polynomial and
rational expressions containing
variables
Example:
simplifying
3
x5
+
5
2
x  6x  5
Constructing graphs by analyzing their
functions as sums, differences, or
products
Radical equation
7. Solve equations, inequalities, and applied
problems involving absolute values, radicals, and
quadratics over the complex numbers, as well as
simple trigonometric, exponential, and logarithmic
functions.
Example:
solving x2- 8x > -12, 3x = 81, 2
2
sin x + sin x = 0, or logx 2 = 5
Page 11 of 13
NAEPA1e, A1g, A2a, A3b,
A4a, N1d, N5f
Solving equations using laws of
exponents, including rational and
irrational exponents
Expressing the solution of an equation,
inequality, or applied problem as a
graph on a number line or by using set
or interval notation
3. Analyze families of functions, including shifts,
reflections, and dilations of y = k (inverse
x
variation), y = kx (direct variation/linear), y = [x]
(greatest integer), y = x2 (quadratic), y = ax
(exponential), and y = logax (logarithmic).
Example:
comparing the graphs of y =
2x, y = 2x + 1, y = 2x + 1, and
y = -2x
8.1-8.6
3
Weeks
Exponential
function, growth
factor, decay
factor,
asymptote,
logarithm,
common
logarithm,
logarithmic
function
Identifying the domain and range of a
relation given its graph, a table of
values, or its equation, including those
with restricted domains
Example:
=
finding the domain of y =
1
x3
or y
x2
Identifying real-world situations
corresponding to families of functions
6. Perform operations on functions, including
addition, subtraction, multiplication, division, and
composition.
Determining the inverse of a function or a
relation
Performing operations on polynomial and
rational expressions containing
variables
Example:
simplifying
3
x5
+
5
x2  6x  5
Constructing graphs by analyzing their
functions as sums, differences, or
products
Page 12 of 13
NAEPA13, A1h, A2a, A2b,
A2e, A2h, A3a, A3b
Exponential
equation, change
of base formula,
logarithmic
equation,
natural
logarithmic
function
7. Solve equations, inequalities, and applied
problems involving absolute values, radicals, and
quadratics over the complex numbers, as well as
simple trigonometric, exponential, and logarithmic
functions.
Example:
solving x2- 8x > -12, 3x = 81, 2
2
sin x + sin x = 0, or logx 2 = 5
Solving equations using laws of
exponents, including rational and
irrational exponents
Expressing the solution of an equation,
inequality, or applied problem as a
graph on a number line or by using set
or interval notation
13. Use different forms of representation to compare
characteristics of data gathered from two
populations.
Evaluating the appropriateness of the
design of an experimental study
Describing how sample statistics reflect
values of population parameters
6.7, 9.7
12.1-12.5
1 Week
Sample, sample
proportion,
random sample,
margin of error
14. Determine an equation of linear regression from
a set of data.
Examining data to determine if a linear,
quadratic, or exponential relationship
exists and to predict outcomes
15. Calculate probabilities of events using the laws
of probability.
Using permutations and combinations to
calculate probabilities
Calculating conditional probability
Calculating probabilities of mutually
exclusive events, independent events,
and dependent events
Page 13 of 13
NAEPD1b, D1d, D2a, D2d,
D4c, D4e, D4i