Huntsville City Schools - Instructional Guide
2015 – 2016
Course: Algebra II Grade: 9-11
Math Practices
Online Resources
The Standards for Mathematical Practice describe varieties of
expertise that mathematics educators at all levels should seek to
develop in their students. These practices rest on important
“processes and proficiencies” with longstanding importance in
mathematics education. The first of these are the NCTM process
standards of problem solving, reasoning and proof, communication,
representation, and connections. The second are the strands of
mathematical proficiency specified in the National Research Council’s
report Adding It Up: adaptive reasoning, strategic competence,
conceptual understanding (comprehension of mathematical
concepts, operations and relations), procedural fluency (skill in
carrying out procedures flexibly, accurately, efficiently and
appropriately), and productive disposition (habitual inclination to see
mathematics as sensible, useful, and worthwhile, coupled with a
belief in diligence and one’s own efficacy).
Dan Meyer’s Ted Talk about teaching math:
https://youtu.be/qocAoN4jNwc
1.
2.
3.
4.
5.
6.
7.
8.
Links to his 3-act activities, sorted by standard:
https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYd
EhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0
Granite City Math Vocabulary:
http://www.graniteschools.org/mathvocabulary/
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning .
For more:
Other online resources
1
Elaboration on each practice from the Common Core website:
www.corestandards.org/Math/Practice/
www.opencurriculum.org is a website that curates activities from all
over the web, sorted by standard.
Kid-friendly language:
www.buncombe.k12.nc.us/Page/37507
http://map.mathshell.org/lessons.php has great formative
assessments and group activities, searchable by standard.
Online tools
www.desmos.com is a free online calculator. Excellent for working
with linear equations, scatterplots, and best-fit lines.
https://teacher.desmos.com/ has some great activities for introducing
and working with functions.
www.geogebra.org is a free online geometry tool. It is great for
working with transformations.
The material for this course has been arranged to roughly follow the ACT Quality Core Instructional Units. Resources also
include the Pre AP Algebra II Scope and Sequence from NMSI (formerly LTF)
LTF/NMSI lessons are used to supplement Algebra II/ Trig lessons. These materials can be found at www.apluscollegeready.org .
The Level One “I can” statements have been provided. Level Two and Three will be done by the individual schools.
Benchmarks will cover standards from the Pearson’s Algebra II Book:
1st Nine Weeks - chapters 2, 3,12
2nd Nine Weeks – Chapters 4, 10, 5.1 to 5.3
3rd Nine Weeks - Chapter 5.4 to 5.8, chapter 9, Chapter 6
4th Nine Weeks - Chapter 7, 8, 11
2
1st Nine Weeks: Chapter 2, Chapter 3, Chapter 12
Functions, Equations and Graphs: Chapter 2
Standards
21.) Create equations in two or
more variables to represent
relationships between quantities;
graph equations on coordinate
axes with labels and scales. [ACED2]
30. a. Graph square root, cube
root, and piecewise-defined
functions, including step
functions and absolute value
functions. [F-IF7b]
“I Can” Statements
1. I can write linear equations in standard form
and slope-intercept form when given two
points, a point and the slope, or the graph of
the equation
2. I can graph linear equations
3. I can graph piecewise-defines functions,
including step functions and absolute value
functions
4. I can analyze transformations of functions
5. I can graph absolute value functions
6. I can graph 2-variable inequalities
Resources
Pacing
Recommendation
/ Date(s) Taught
15 days
Mostly QC
Prerequisites
Book: Chapter 2
(suggested: 2.3, 2.4,
CB 2.4, 2.6, 2.7, 2.8)
31.) Write a function defined by
an expression in different but
equivalent forms to reveal and
explain different properties of the
function. [F-IF8]
32.) Compare properties of two
functions each represented in a
different way (algebraically,
graphically, numerically in tables,
or by verbal descriptions). [F-IF9]
34.) Identify the effect on the
graph of replacing f(x) by f(x)
+ k, k f(x), f(kx), and f(x + k) for
specific values of k (both positive
and negative); find the value
3
of kgiven the graphs. Experiment
with cases and illustrate an
explanation of the effects on the
graph using technology. Include
recognizing even and odd
functions from their graphs and
algebraic expressions for them.
[F-BF3]
Linear Systems: Chapter 3
Standard
27. Explain why the x-coordinates
of the points where the graphs of
the equations y = f(x) and y = g(x)
intersect are the solutions of the
equation f(x) = g(x); find the
solutions approximately, e.g.,
using technology to graph the
functions, make tables of values,
or find successive
approximations. Include cases
where f(x) and/or g(x) are linear,
polynomial, rational, absolute
value, exponential, and
logarithmic functions. [A-REI11]
“I Can” Statements
1) I can create equations in two or more
variables to represent relationships between
quantities.
2) I can write and use a system of inequalities to
solve a real world problem.
3) I can recognize that the equations or
inequalities represent the constraints of the
problem.
4) I can solve a system of equations by using
substitution or elimination
5) I can solve a system of inequalities by
graphing.
6) I can create simple rational inequalities in one
variable and use them to solve problems.
7) I can explain why the intersection of y = f(x)
and y = g(x) is the solution of f(x) = g(x).
Resources
QC Unit 2
Pacing
Recommendation
/ Date(s) Taught
17 Days
Book 3.1 - 3.5
NMSI Unit 1
NMSI Lessons:
Literal
Equations
Introducing
Interval
Notation
4
21. Create equations in two or
more variables to represent
relationships between quantities;
graph equations on coordinate
axes with labels and scales.
[A-CED2]
22. Represent constraints by
equations or inequalities, and by
systems of equations and/or
inequalities, and interpret
solutions as viable or nonviable
options in a modeling context.
[A-CED3]
ACT D.1.a: Solve inequalities
containing absolute value.
ACT D.1.b: Solve compound
inequalities containing “and” and
“or” and graph the solution set.
ACT D.1.c: Solve algebraically a
system containing three variables
ACT D.2.a: Graph a system of
linear inequalities in two
variables with and without
technology to find the solution
set to the system
ACT D.2.b: Solve linear
programming problems by finding
maximum and minimum values
of a function over a region
defined by linear inequalities
8) I can approximate solutions to linear
equations by using technology to graph the
equation, creating a table of values, or finding
successive approximations.
9) I can use Linear Programming to find the
maximum and/or minimum to a real world
problem.
10) I can solve systems of equations which have 3
variables, and can determine whether there
are zero, one, or infinitely many solutions.
Transformations
of Functions
Exploration
Even/Odd
Functions
Transforming
Domain and
Range
Applying
Piecewise
Functions
Exploring
Inequalities
Systems of
Linear
Inequalities
Matrices: Chapter 12
5
Standards
7. Use matrices to represent and
manipulate data, e.g., to represent
payoffs or incidence relationships in
a network. (Use technology to
approximate roots.) [N-VM6]
8. Multiply matrices by scalars to
produce new matrices, e.g., as
when all of the payoffs in a game
are doubled. [N-VM7]
9. Add, subtract, and multiply
matrices of appropriate dimensions.
[N-VM8]
10. Understand that, unlike
multiplication of numbers, matrix
multiplication for square matrices
is not a commutative operation,
but still satisfies the associative
and distributive properties.
[N-VM9]
“I Can” Statements
I can:
1. I can use matrices to represent data in
context.
2. I can multiply a matrix by a scalar.
3. I can add subtract and multiply matrices
when possible.
4. I can understand matrix multiplication is not
commutative.
5. I can understand that the associative and
distributive properties do apply.
6. I can calculate the determinant of 2x2 and
3x3 matrices.
Resources
QC Unit 3
Pacing
Recommendation
/ Date(s) Taught
8 days
Book Ch 12.1 – 12.4,
(3.6)
NMSI –Unit 2
Note:
ACT D.1.c Solve
algebraically a system
of equations
containing three
variables. Can be
done using technology
and matrices.
11. Understand that the zero and
identity matrices play a role in
matrix addition and multiplication
similar to the role of 0 and 1 in the
real numbers. The determinant of
a square matrix is nonzero if and
only if the matrix has a
multiplicative inverse. [N-VM10]
26. Find the inverse of a matrix if
it exists and use it to solve
systems of linear equations (using
technology for matrices of
6
dimension 3 × 3 or greater). [AREI9]
ACT I.1.a Add, subtract, and
multiply matrices.
ACT I.1.b Use addition, subtraction,
and multiplication of matrices to
solve real world problems.
ACT I.1.c Calculate the determinant
of 2x2 and 3x3 matrices.
ACT I.1.d Find the inverse of a 2x2
matrix
ACT I.1.e Solve systems of
equations using inverses of
matrices and determinants.
ACT I.1.f Use technology to perform
operations on matrices, find
determinants, and find inverses.
7
SECOND NINE WEEKS
Quadratic Function Equations: Chapter 4 (4.1-4.3, 4.6)
Standards
3. Find the conjugate of a
complex number; use conjugates
to find moduli and quotients of
complex numbers. [N-CN3]
20. Create equations and
inequalities in one variable and
use them to solve problems.
Include equations arising from
linear and quadratic functions,
and simple rational and
exponential functions. [A-CED1]
21. Create equations in two or
more variables to represent
relationships between quantities;
graph equations on coordinate
axes with labels and scales. [ACED2]
29. Relate the domain of a
function to its graph and, where
applicable, to the quantitative
relationship it describes. [F-IF5]
30. Graph functions expressed
symbolically and show key
features of the graph, by hand in
simple cases and using
technology for more complicated
cases. [F-IF7]
“I Can” Statements
1. I can create quadratic equations in one
variable and use them to solve problems.
2. I can graph equations in two variables on a
coordinate plane and label the axes and
scales.
3. Given a function, I can identify intercepts in
graphs and tables.
4. I can sketch a graph of a function given key
features of a function.
5. I can relate the domain of a function to its
graph and to the relationship it describes.
6. I can determine intercepts for a function
given its equation.
7. I can determine intervals where a function is
increasing and decreasing given its equation.
8. I can determine intervals where a function is
positive or negative given its equation.
9. I can identify relative maximums and
minimums given the equation of a function.
10. I can graph by hand functions given the
equation
11. I can translate a given expression into
equivalent forms designed to highlight
different properties of the function.
12. I can write a function to describe a
relationship between two quantities.
13. I can identify the different parts of an
expression and explain their meaning within
the context of a problem.
14. I can determine the domain and range of a
quadratic function
Resources
QC Unit 4
Pacing
Recommendation
/ Date(s) Taught
9 days
Book 4.1 – 4.3,
4.6 Completing the
Square to put in
vertex form
NMSI
Analyzing Function
Behavior Using
Graphical Displays
Quadratic Functions:
Adaption of AP
Calculus 1997 AB2
Part I only
8
31. Write a function defined by
an expression in different but
equivalent forms to reveal and
explain different properties of the
function. [F-IF8]
32. Compare properties of two
functions each represented in a
different way (algebraically,
graphically, numerically in tables,
or by verbal descriptions). [F-IF9]
15. I can Identify the effect on the graph of
replacing f(x) by f(x) + k, k f(x), f(kx), and f(x +
k) for specific values of k (both positive and
negative); find the value of k given the
graphs.
16. I can convert from standard form of a
quadratic to vertex form by completing the
square.
33. Write a function that
describes a relationship between
two quantities. [F-BF1]
34. Identify the effect on the
graph of replacing f(x) by f(x) + k,
k f(x), f(kx), and f(x + k) for
specific values of k (both positive
and negative); find the value of k
given the graphs. Experiment
with cases and illustrate an
explanation of the effects on the
graph using technology. Include
recognizing even and odd
functions from their graphs and
algebraic expressions for them.
[F-BF3]
ACT E.2.a Determine the domain
and range of a quadratic function,
graph the function with and
without technology
ACT E.2.b Use transformations
(e.g. translation, reflection) to
draw the graph of a relation and
9
determine a relation that fits a
graph.
ACT E.3.a Identify conic sections
(e.g. parabola, circle, ellipse, and
hyperbola) from their equations
in standard form.
ACT E.3.b Graph circles and
parabolas and their translations
from given equations or
characteristics with and without
technology
ACT E.3.c Determine
characteristics of circles and
parabolas from their equations
and graphs
ACT E.3.d Identify and write
equations for circles and
parabolas from given
characteristics and graphs
Quadratic Function Equations: Chapter 4.4-4.9
Standards
20. Create equations and
inequalities in one variable and
use them to solve problems.
Include equations arising from
linear and quadratic functions,
and simple rational and
exponential functions. [A-CED1]
“I Can” Statements
1.
2.
3.
4.
21. Create equations in two or
more variables to represent
I can create quadratic equations in one
variable and use them to solve problems.
I can determine when the solutions to a
quadratic equation will be complex and can
write the solutions in the form a±bi.
I can create quadratic inequalities in one
variable and use them to solve problems.
I can graph equations in two variables on a
coordinate plane and label the axes and
scales.
Resources
QC Unit 5
Pacing
Recommendation
/ Date(s) Taught
20 days
Book 4.4 – 4.9
(4.6 Completing the
Square to solve)
NMSI
Another Way to Look
at Factoring
10
relationships between quantities;
graph equations on coordinate
axes with labels and scales.
[A-CED2]
5.
6.
7.
22. Represent constraints by
equations or inequalities, and by
systems of equations and/or
inequalities, and interpret
solutions as viable or nonviable
options in a modeling context.
[A-CED3]
8.
9.
10.
11.
25. Recognize when the quadratic
formula gives complex solutions,
and write them as a ± bi for real
numbers a and b. [A-REI4b] (17 b
from Algebra I
31. Write a function defined by
an expression in different but
equivalent forms to reveal and
explain different properties of the
function. [F-IF8]
12.
13.
14.
15.
16.
34. Identify the effect on the
graph of replacing f(x) by f(x) + k,
k f(x), f(kx), and f(x + k) for
specific values of k (both positive
and negative); find the value of k
given the graphs. Experiment
with cases and illustrate an
explanation of the effects on the
graph using technology. Include
recognizing even and odd
functions from their graphs and
algebraic expressions for them.
[F-BF3]
17.
18.
19.
20.
21.
Given a function, I can identify intercepts in
graphs and tables.
I can sketch a graph of a function given key
features of a function.
I can determine intercepts for a function
given its equation.
I can determine intervals where a function is
increasing and decreasing given its equation.
I can determine intervals where a function is
positive or negative given its equation.
I can identify relative maximums and
minimums given the equation of a function.
I can graph by hand functions given the
equation
I can translate a given expression into
equivalent forms designed to highlight
different properties of the function.
I can identify the different parts of an
expression and explain their meaning within
the context of a problem.
I can identify the zeros of polynomials when
the polynomial is factored.
I know that there is a complex number i such
that i2= -1.
I know that every number is a complex
number which can be written as a+bi , where
a and b are real numbers.
I can apply the fact that i2 = -1.
I can use the commutative, associative, and
distributive properties to add, subtract, and
multiply complex numbers.
I can use conjugates to divide complex
numbers.
I can solve quadratic equations with real
coefficients that have complex solutions a +
bi and a - bi.
I can use polynomial identities to write
equivalent expressions for complex numbers.
Investigation
Graphing Quadratic
Functions
Taking Care of
Business
Literal Equations and
Quadratic
Optimization
Accumulation with
quadratics
Quadratic
Optimization
11
12. Interpret expressions that
represent a quantity in terms of
its context. [A-SSE1]
a. Interpret parts of an
expression such as terms, factors,
and coefficients. [A-SSE1a]
17. Identify zeros of polynomials
when suitable factorizations are
available, and use the zeros to
construct a rough graph of the
function defined by the
polynomial. [A-APR3]
1. Know there is a complex
number i such that i2 = –1, and
every complex number has the
form a + bi with a and b real.
[N-CN1]
22. I can solve quadratic systems graphically with
and without technology
23. I can solve quadratic systems algebraically
with and without technology
24. I can solve quadratic equations by completing
the square
25. I can solve quadratic equations by using the
Quadratic Formula
26. I can find the discriminant and use it to
determine the number of solutions for a
quadratic equation
27. I can graph a system of quadratic inequalities
with or without technology
28. I can Identify the effect on the graph of
replacing f(x) by f(x) + k, k f(x), f(kx), and f(x +
k) for specific values of k (both positive and
negative); find the value of k given the
graphs.
2. Use the relation i2 = –1 and the
commutative, associative, and
distributive properties to add,
subtract, and multiply complex
numbers. [N-CN2]
3. Find the conjugate of a
complex number; use conjugates
to find moduli and quotients of
complex numbers. [N-CN3]
4. Solve quadratic equations with
real coefficients that have
complex solutions. [N-CN7]
ACT E.1.a Solve quadratic
equations and inequalities using
12
various techniques, including
completing the square and using
the Quadratic Formula
ACT E.1.b Use the discriminant to
determine the number and type
of roots for a given quadratic
equation
ACT E.1.c Solve quadratic
equations with complex number
solutions
ACT E.1.d Solve quadratic systems
graphically and algebraically with
and without technology
ACT E.2.b Use transformations
(e.g. translation, reflection) to
draw the graph of a relation and
determine a relation that fits a
graph.
ACT E.2.c Graph a system of
quadratic inequalities with and
without technology to find the
solution set to the system
Conic Sections: Chapter 10
**Note: It is not recommended to use the textbook for conics. QC does not require the same depth that the book does. Please
see QC standards for conics before teaching conic sections.
Standards
“I Can” Statements
Resources
QC Unit 4
28.) Create graphs of conic
sections, including parabolas,
hyperbolas, ellipses, circles,
1. I can identify conic sections (e.g., parabola,
circle, ellipse, hyperbola) from their
equations in standard form
Pacing
Recommendation
/ Date(s) Taught
6 days
Book 10.1-10.3
(10.4 and 10-5
Are for
Alabama
13
and degenerate conics, from
second-degree equations.
(Alabama) not in quality core.
a. Formulate equations of conic
sections from their determining
characteristics. (Alabama)
Example: Write the equation of
an ellipse with center (5, -3), a
horizontal major axis of length
10, and a minor axis of length 4.
29. Relate the domain of a
function to its graph and, where
applicable, to the quantitative
relationship it describes. [F-IF5]
34. Identify the effect on the
graph of replacing f(x) by f(x) + k,
k f(x), f(kx), and f(x + k) for
specific values of k (both positive
and negative); find the value of k
given the graphs. Experiment
with cases and illustrate an
explanation of the effects on the
graph using technology. Include
recognizing even and odd
functions from their graphs and
algebraic expressions for them.
[F-BF3]
2. I can graph circles and parabolas and their
translations from given equations
3. I can graph circles and parabolas and their
translations from given properties
4. I can identify and write equations for circles
and parabolas from given characteristics and
equations
5. I can sketch a graph of a function given key
features of a function.
6. I can relate the domain of a function to its
graph and to the relationship it describes.
7. I can determine intercepts for a function
given its equation.
8. I can graph by hand functions given the
equation
9. I can Identify the effect on the graph of
replacing f(x) by f(x) + k, k f(x), f(kx), and f(x +
k) for specific values of k (both positive and
negative); find the value of k given the
graphs.
Standard # 28)
Note: QC emphasizes
circles and parabolas
NMSI
Transformations of
Conic Sections
ACT E.3.a Identify conic sections
(e.g. parabola, circle, ellipse, and
hyperbola) from their equations
in standard form.
ACT E.3.b Graph circles and
parabolas and their translations
14
from given equations or
characteristics with and without
technology
ACT E.3.c Determine
characteristics of circles and
parabolas from their equations
and graphs
ACT E.3.d Identify and write
equations for circles and
parabolas from given
characteristics and graphs
15
THIRD NINE WEEKS – Begins within Chapter 5. You should be able to complete through Section 5.3 in the
second nine weeks
Polynomials and Polynomial Functions: Chapter 5
Standard
6. Know the Fundamental
Theorem of Algebra; show that it
is true for quadratic polynomials.
[N-CN9]
13. Use the structure of an
expression to identify ways to
rewrite it. [A-SSE2]
15.) Understand that polynomials
form a system analogous to the
integers; namely, they are closed
under the operations of addition,
subtraction, and multiplication;
add, subtract, and multiply
polynomials. [A-APR1]
16. Know and apply the
Remainder Theorem: For a
polynomial p(x) and a number a,
the remainder on division by x - a
is p(a), so p(a) = 0 if and only if (x
- a) is a factor of p(x). [A-APR2]
17. Identify zeros of
polynomials when suitable
factorizations are available,
and use the zeros to construct
“I Can” Statements
1) I can break down expressions and make sense
of the multiple factors and terms by
explaining the meaning of the individual
parts.
2) I can rewrite algebraic expressions in a
variety of equivalent forms using factoring,
combining like terms, applying properties, or
using other operations.
3) I can use factoring techniques such as
common factors, grouping, the difference of
two squares, the sum or difference of two
cubes, or a combination of methods to factor
completely.
4) I understand that polynomial identities
include, but are not limited to, the product of
the sum and difference of two terms, the
difference of two squares, the sum and
difference of two cubes, the square of a
binomial, etc….
5) I can add, subtract and multiply polynomials.
6) I understand that a is a root of a polynomial
function if and only if x-a is a factor of the
function.
7) I understand how the Remainder Theorem
relates to the factoring of a quadratic
function.
8) I understand the Remainder Theorem.
9) I understand the Fundamental Theorem of
Algebra which states that the number of
Resources
Book:
Pacing
Recommendation
/ Date(s) Taught
20 days
5.1 – 5.6
Concept Byte 5-5
NMSI:
Graphical
Transformations
Investigating
Functions
Adaptation of AP
Calculus 1997 AB1
16
a rough graph of the function
defined by the polynomial. [AAPR3]
18. Prove polynomial
identities and use them to
describe numerical
relationships. [A-APR4]
Example: The polynomial
identity (x2 + y2)2 = (x2 - y2)2 +
(2xy)2 can be used to generate
Pythagorean triples
19.) 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.
[A-APR6]
ACT.F.1.a Evaluate and simplify
polynomial expressions and
equations
ACT.F.1.b: Factor polynomials
using a variety of methods(e.g.,
factor theorem, synthetic
division, long division, sums and
differences of cubes, grouping)
ACT. F.2.a Determine the number
and type of rational zeros for a
polynomial function
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
complex solutions to a polynomial equation is
the same as the degree of the polynomial.
I can use the zeros of polynomials to sketch a
graph of the function defined by the
polynomial.
Given a function, I can identify intercepts in
graphs and tables.
Given a function, I can identify intervals
where a graph is increasing, decreasing,
positive, or negative.
Given a function, I can identify symmetry
given equations, graphs and tables.
Given a function, I can identify end behavior
given equations, graphs and tables.
I can sketch a graph of a function given key
features of a function.
I can relate the domain of a function to its
graph and to the relationship it describes.
I can determine intercepts for a function
given its equation.
I can use technology to graph more
complicated functions.
I can graph polynomial functions by hand,
identifying zeros when factorable and
showing end behavior.
I can recognize even and odd functions from
graphs and equations.
I can use technology and experimentation to
illustrate the effect on the graph of f(x) for
f(x) + k, k f(x), f(kx), and f(x + k).
I can approximate solutions to polynomial
equations by using technology to graph the
equation, creating a table of values, or finding
I can evaluate and simplify polynomial
expressions
I can solve polynomial equations
I can solve quadratic equations with real
coefficients that have complex solutions
17
ACT.F.2.b Find all rational zeros of
a polynomial function
ACT.F.2.c: Recognize the
connection among zeros of
polynomial function, x-intercepts,
factors of polynomials solutions
and solutions of polynomial
equations
ACT.F.2.d: Use technology to
graph a polynomial function and
approximate the zeros, minimum,
and maximum; determine
domain and range of the
polynomial function
26) I can determine the number of rational zeros
of a polynomial function
27) I use technology to find the minimum and
maximum values of a polynomial function
Sequences and Series: Chapter 9
Standards
“I Can” Statements
14. Derive the formula for the
sum of a finite geometric series
(when the common ratio is not 1),
and use the formula to solve
problems. [A-SSE4]
ACT H.2.a Find the nth term of an
arithmetic or geometric
sequence.
ACT H.2.b Find the position of a
given term of an arithmetic or
geometric sequence.
ACT H.2.c Find sums of a finite
arithmetic or geometric series
ACT H.2.d Use sequences and
series to solve real-world
problems
1. I can derive the formula for the sum of a
finite geometric series when the common
ratio is not 1.
2. I can use the formula for a finite geometric
series to solve real world problems.
3. I can calculate mortgage payments.
4. I can derive the formula for the sum of a
finite arithmetic series
5. I can use the formula for a finite arithmetic
series to solve real world problems.
6. I can find the nth term of an arithmetic or
geometric sequence.
7. I can find the position of a given term of an
arithmetic or geometric sequence.
8. I can find the sum of a finite arithmetic or
geometric series.
Resources
QC Unit 1
Pacing
Recommendation
/ Date(s) Taught
12 days
Book 9.1 – 9.5
NMSI Unit 2 first
part - arithmetic
sequences and series
(important to make
connections between
arithmetic sequences
and linear functions)
NMSI Unit 5 last part
on geometric
sequences and series
18
ACT H.2.e Use sigma notation to
express sums.
9. I can use sequences and series to solve real
world problems.
10. I can use sigma notation to express sums.
Note: arithmetic and
geometric sequences
covered in Algebra I
ALCOS #34, 35, 38
Third and Fourth Nine Weeks—Chapter 6 Chapter 8, Chapter 7, Chapter 11
4th 9 weeks should cover chapter 7 , 8 and 11.
Standards
21. Create equations in two or
more variables to represent
relationships between quantities;
graph equations on coordinate
axes with labels and scales.
[A-CED2]
23. Rearrange formulas to
highlight a quantity of interest,
using the same reasoning as in
solving equations. [A-CED4]
30. Graph functions expressed
symbolically and show key
features of the graph, by hand in
simple cases and using
technology for more complicated
cases. [F-IF7]
30a. Graph square root, cube
root, and piecewise-defined
functions, including step
“I Can” Statements
1. I can graph equations in two variables on a
coordinate plane and label the axes and
scales.
2. I can solve multi-variable formulas or literal
equations for a specific variable.
3. I can use technology to graph more
complicated functions.
4. I can write a function to describe a
relationship between two quantities.
5. I can explain the difference between the
graph of f(x) and the graph of f(x) + k for both
positive and negative k values.
6. I can explain the difference between the
graph of f(x) and the graph of k f(x) for both
positive and negative k values.
7. I can explain the difference between the
graph of f(x) and the graph of f(x +k), for both
positive and negative k values.
8. I can interpret expressions that represent a
quantity in terms of its context.
9. I can identify the different parts of an
expression and explain their meaning within
the context of a problem
Resources
QC Unit 7
Pacing
Recommendation
/ Date(s) Taught
33 days
Book Ch 6 Ch 8
NMSI
Lots of Rational info
RF stands for
Rational function
RF Exploration
RF Long Run
RF Short Run
RF with removeable
discontinuities
Transformation of RF
Not much at NMSI
for Radical Functions
Solving equations
graphically (includes
a little)
19
functions and absolute value
functions
33. Write a function that
describes a relationship between
two quantities. [F-BF1]
34. Identify the effect on the
graph of replacing f(x) by f(x) + k,
k f(x), f(kx), and f(x + k) for
specific values of k (both positive
and negative); find the value of k
given the graphs. Experiment
with cases and illustrate an
explanation of the effects on the
graph using technology. Include
recognizing even and odd
functions from their graphs and
algebraic expressions for them.
[F-BF3]
12. Interpret expressions that
represent a quantity in terms of
its context. [A-SSE1]
a. Interpret parts of an
expression such as terms,
factors, and coefficients. [ASSE1a]
b. Interpret complicated
expressions by viewing one or
more of their parts as a single
entity. [A-SSE1b]
13. Use the structure of an
expression to identify ways to
rewrite it. [A-SSE2]
10. I can break down expressions and make sense
of the multiple factors and terms by
explaining the meaning of the individual parts
11. I can rewrite simple rational expressions,
12. I can use a computer algebra system to
rewrite more complicated rational
expressions and assist with building a broader
conceptual understanding.
13. I can add, subtract, multiply and divide
rational expressions.
14. I can provide examples to illustrate how
extraneous solutions may arise for a rational
or radical equation.
15. Given a function, I can identify intercepts in
graphs and tables.
16. I can create simple rational inequalities in one
variable and use them to solve problems.
17. I can solve multi-variable formulas or literal
equations for a specific variable
18. I can solve simple radical equations , and
recognize extraneous solutions.
19. I can write a function to describe a
relationship between two quantities.
20. I can write an expression for the inverse of
f(x) = c by interchanging the values of the
dependent and independent variables and
solving for the dependent variable.
21. I can graph square and cube root functions by
hand.
22. I can translate a given expression into
multiple functions designed to highlight
different properties of the function.
23. I can find the inverse of a function
algebraically.
20
24. Solve simple rational and
radical equations in one variable,
and give examples showing how
extraneous solutions may arise.
[A-REI2]
27. Explain why the x-coordinates
of the points where the graphs of
the equations y = f(x) and y = g(x)
intersect are the solutions of the
equation f(x) = g(x); find the
solutions approximately, e.g.,
using technology to graph the
functions, make tables of values,
or find successive
approximations. Include cases
where f(x) and/or g(x) are linear,
polynomial, rational, absolute
value, exponential, and
logarithmic functions. [A-REI11]
35. Find inverse functions. [F-BF4]
a. 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.
[F-BF4a]
Example: f(x) =2x3 or
f(x) = (x+1)/(x-1) for x ≠ 1.
ACT C.1.d Perform operations on
functions and determine domain
and range.
ACT G.1.a. Solve mathematical
and real-world rational equation
problems ( e.g., work or rate
problems)
ACT G.1.b Simplify Radicals with
various indices.
21
ACT G.1.c Use properties of roots
and rational exponents to
evaluate and simplify
expressions.
ACT G.1.d Add, subtract, multiply,
and divide expressions containing
radicals.
ACT G.1.e Rationalize
denominators containing radicals
and find the simplest common
denominator
ACT G.1.f Evaluate expressions
and solve equations containing
nth roots or rational exponents
ACT G.1.g Evaluate and solve
radical equations given a formula
for a real world situation
Exponential and Logarithmic Functions: Chapter 7
Standard
30c. Graph exponential and
logarithmic functions showing
intercepts and end behavior; and
trigonometric functions, showing
period, midline, and amplitude.
[F-IF7c]
33. Write a function that
describes a relationship between
two quantities. [F-BF1]
“I Can” Statements
1. I can break down expressions and make
sense of the multiple factors and terms by
explaining the meaning of the individual
parts.
2. I can create equations in two or more
variables to represent relationships between
quantities.
3. I can graph exponential functions by hand
showing intercepts and end behavior.
4. I can graph logarithmic functions by hand
showing intercepts and end behavior.
Resources
Book:
Chapter 7.1 – 7.6
If not already
done Chapter 6.6
Pacing
Recommendation
/ Date(s) Taught
16 days
NMSI:
And So They Grow
Graphing
Exponential and
Logarithmic
Functions
22
33a. Combine standard
function types using
arithmetic operations.
[F-BF1b]
Example for 33a: 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
mode
30.) Graph functions expressed
symbolically, and show key
features of the graph, by hand in
simple cases and using
technology for more complicated
cases. [F-IF7]
c. Graph exponential and
logarithmic functions, showing
intercepts and end behavior, and
trigonometric functions, showing
period, midline, and amplitude.
[F-IF7e]
5. I can translate a given expression into
multiple functions designed to highlight
different properties of the function.
6. I can combine standard function types, such
as linear and exponential, using arithmetic
operations.
7. I can compare the key features of two
functions presented algebraically, graphically,
in tables, or using verbal descriptions.
8. I can use technology to evaluate the
logarithm that is the solution to abct = d
where a, c, and d are numbers, and the base
b is 2, 10, or e.
9. I can approximate solutions to exponential
equations by using technology to graph the
equation, creating a table of values, or finding
successive approximations.
10. I can approximate solutions to logarithmic
equations by using technology to graph the
equation, creating a table of values, or finding
successive approximations.
Exponential and Log
Laws
Solving Systems of
Exponential,
Logarithmic,
and Linear Equations
Exponential and
Natural Log
Functions
Linearization of
Exponential,
Logarithmic, and
Linear Equations
Motion Problems
Using Exponential
and
Natural Logarithmic
Functions
Curing the Sniffles
36.) For exponential models,
express as a logarithm the
solution to abct = d where a, c,
and d are numbers, and the base
b is 2, 10, or e; evaluate the
logarithm using technology.
[F-LE4]
C.1.d: Perform operations on
functions, including function
composition, and determine
23
domain and range for each of
the given functions
G.2.a: Graph exponential
and logarithmic functions
with and without technology
G.2.b: Convert exponential
equations to logarithmic form
and logarithmic equations to
exponential form
Probability and Data Analysis: Chapter 11
Standard
“I Can” Statements
37. Use the mean and standard
deviation of data set to fit it to a
normal distribution and to
estimate population percentages.
Recognize that there are data sets
for which such a procedure is not
appropriate. Use calculators,
spreadsheets and tables to
estimate areas under the normal
curve [S-ID4]
1.
38. (+) Analyze decisions and
strategies using probability
concepts (e.g., product testing,
medical testing, pulling a
hockey goalie at the end of a
game). [S-MD7]
5.
2.
3.
4.
6.
Construct two-way frequency tables of
data for two categorical variables.
Interpret two-way frequency tables of
data for two categorical variables.
Use the probabilities from the table to
evaluate independence of two variables.
The student will be able to recognize and
explain the concepts of independence
and conditional probability in everyday
situations.
Identify situations as appropriate for the
use of permutation or combination to
calculate probabilities
Use permutations and combinations in
conjunction with other probability
Resources
Book Chapter
5.7
11.1 to 11.8 and
11.10
Pacing
Recommendation
/ Date(s) Taught
15 days
11.9 is not in the
course of study
or the Quality
Core for Algebra
II/Trig
NMSI:
Calculate Probabilities
with Tree Diagrams
Independence
24
40. Understand the conditional
probability of A given B as P(A
and B)/P(B), and interpret
independence of A and B as
saying that the conditional
probability of A given B is the
same as the probability of A,
and the conditional probability
of B given A is the same as the
probability of B. [S-CP3]
41. Construct and interpret
two-way frequency tables of
data when two categories are
associated with each object
being classified. Use the twoway table as a sample space to
decide if events are
independent and to
approximate conditional
probabilities. [S-CP4]
43. Describe events as subsets of
a sample space (the set of
outcomes), using characteristics
(or categories) of the outcomes,
or as unions, intersections, or
complements of other events
(―or,‖ ―and,‖ ―not‖). [S-CP1]
method to calculate probabilities of
compound events and solve problems
7. Identify two events as disjoint (mutually
exclusive).
8. Calculate probabilities using the Addition
Rule.
9. Interpret the probability in context.
10. Calculate the probabilities using the
General Multiplication Rule.
11. Interpret the results in context.
12. Define and calculate conditional
probabilities
13. Use the Multiplication Principal to decide
if two events are independent
14. Use the Multiplication Principal to
calculate conditional probabilities.
15. Calculate the conditional probabilities
using the definition “the conditional
probability of A given B as the fractions of
B’s outcomes that also belong to A”.
16. Interpret the probability in context.
17. The student will be able to make
decisions based on expected values.
Probability Using
Sample Spaces,
Permutations,
and Combinations
18. The student will be able to explain in context
the decisions made based on expected
values.
19. I can use the counting principle to find the
number of ways an event can happen.
45. Construct and interpret twoway frequency tables of data
when two categories are
associated with each object being
classified. Use the two-way table
as a sample space to decide if
25
events are independent and to
approximate conditional
probabilities. [S-CP4]
Example: Collect data from a
random sample of students in
your school on their favorite
subject among mathematics,
science, and English. Estimate the
probability that a randomly
selected student from your
school will favor science given
that the student is in tenth grade.
Do the same for other subjects
and compare the results.
46. Recognize and explain the
concepts of conditional
probability and independence in
everyday language and everyday
situations. [S-CP5]
Example: Compare the chance of
having lung cancer if you are a
smoker with the chance of being
a smoker if you have lung cancer.
50. Use permutations and
combinations to compute
probabilities of compound events
and solve problems. [S-CP9]
48. Apply the Addition Rule, P(A
or B) = P(A) + P(B) - P(A and B),
and interpret the answer in terms
of the model. [S-CP7]
49. Apply the general
Multiplication Rule in a uniform
probability model, P(A and B) =
26
P(A)P(B|A) = P(B)P(A|B), and
interpret the answer in terms of
the model. [S-CP8]
Understand that two events A
and B are independent if the
probability of A and B occurring
together is the product of their
probabilities, and use this
characterization to determine if
they are independent. [S-CP2]
44. Understand the conditional
probability of A given B as P(A
and B)/P(B), and interpret
independence of A and B as
saying that the conditional
probability of A given B is the
same as the probability of A, and
the conditional probability of B
given A is the same as the
probability of B. [S-CP3]
47. Find the conditional
probability of A given B as the
fraction of B’s outcomes that also
belong to A, and interpret the
answer in terms of the model. [SCP6]
H1a. Use the fundamental
counting principle to count the
number of ways an event can
happen
(Ex. If George has 5 pairs
of jeans, 2 shirts and, 3 hats, how
many ways
27
can he create an outfit
with a pair of jeans, a shirt, and a
hat)
H1b- Use counting techniques,
like combinations and
permutations, to solve problems
(e.g., to calculate probabilities)
H
H.1.c: Find the probability of
mutually exclusive and
nonmutually exclusive events
H.1.d: find the probability of
independent and dependent
events
H.1.e: Use unions, intersections,
and complements to find
probabilities
H.1.f: Solve problems involving
conditional probability
28