Download Algebra II/Trigonometry Continuum of Skills Algebra 2 published by

Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
This continuum is to be used as a MINIMUM guideline for compliance with local content standards and State standards; however, teachers may want to supplement this
information as long as all local and State standards from the following pages are completely met by the end of the course. The suggested teaching schedule must be followed in
order. This continuum of skills is used as a documentation source for coverage of the State required content standards. A copy of this continuum of skills must be attached to
your lesson plan book so that you can enter dates as the standards are taught.
**Pacing guide includes generous time limits to cover topics.
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CONTENT STANDARDS
Create equations that describe numbers or
relationships. (Equations using all available types
of expressions, including simple root functions.)
Rearrange formulas to highlight a quantity of interest,
using the same reasoning as in solving equations. [ACED4]
Ex: Rearrange Ohm’s law V=IR to highlight
resistance R.
Interpret functions that arise in applications in
terms of the context. (Emphasize selection of
appropriate models.)
Relate the domain of a function to its graph and,
where applicable, to the quantitative relationship it
describes.* [F-IF5]
PRACTICE
STANDARDS
TEXT
MATERIAL
2
Ch. 1:
Sec 1-3
2 wks
2 and 4
Ch 2:
Sec. 2.1
2wks for sec.
2.1, 2.4, 2.6
RESOURCES
**Pacing
Ex: If the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then
the positive integers would be an appropriate domain
for the function.
Algebra II/Trigonometry
Revised August 2014
1
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Build a function that models a relationship
between two quantities. (Include all types of
functions studied.)
Write a function that describes a relationship between
two quantities.* [F-BF1]
PRACTICE
STANDARDS
TEXT
MATERIAL
5 and 6
Ch 2:
Sec. 2.4
4 and 6
Ch 2:
Sec. 2.4
RESOURCES
**Pacing
a. Combine standard function types using
arithmetic operations. [F-BF1b]
21
Ex: 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.
Create equations that describe numbers or
relationships. (Equations using all available types of
expressions, including simple root functions.)
Create equations in two or more variables to represent
relationships between quantities; graph equations on
coordinate axes with labels and scales. [A-CED2]
Algebra II/Trigonometry
Revised August 2014
2
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Analyze functions using different representations.
(Focus on using key features to guide selection of
appropriate type of model function.)
Graph functions expressed symbolically, and show
key features of the graph, by hand in simple cases and
using technology for more complicated cases. *[F-FIF7]
a. Graph square root, cube root, and piecewise
functions, including step functions and absolute value
functions. [F-IF7b]
Create equations that describe numbers or
relationships. (Equations using all available types
of expressions
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]
PRACTICE
STANDARDS
TEXT
MATERIAL
1 and 4 and
5
Ch. 2
Sec 2.6
Ch. 3
Sec 3.13.3
RESOURCES
**Pacing
3 wks for sec.
3.1-3.3, 3.5-3.8
technology
Ex: Represent inequalities describing nutritional and
cost constraints on combinations of different foods
Algebra II/Trigonometry
Revised August 2014
3
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Perform operations on matrices and use matrices
in applications.
Use matrices to represent and manipulate data, e.g., to
represent payoffs or incidence relationships in a
network. (Use technology to approximate roots.) [NVM6]
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]
26
TEXT
MATERIAL
5 and 7
Ch. 3
Sec 3.53.8,
(3.8
RESOURCES
**Pacing
technology)
Multiply matrices by scalars to produce new matrices,
e.g. as when all the payoffs in a game are doubled.
[N-VM7]
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PRACTICE
STANDARDS
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]
Solve systems of equations.
Find the inverse of a matrix if it exists and use it to
solve systems of linear equations (using technology
for matrices of dimensions 3 x 3 or greater). [ARE19]
Algebra II/Trigonometry
Revised August 2014
4
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Interpret the structure of expressions. (Polynomial
and rational.)
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]
b. Interpret complicated expressions by viewing one
or more of their parts as a single entity. [A-SSE1b]
PRACTICE
STANDARDS
TEXT
MATERIAL
3and 4 and
2
Ch. 4
Sec 4.14.3
RESOURCES
**Pacing
4 wks for sec.
4.1-4.3, 4.4,
4.5-4.8 with
much emphasis
on sec. 4.4
factoring
Ex: Interpret P=(1 + r)n as the product of P and factor
not depending on P.
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Analyze functions using different representations.
(Focus on using key features to guide selection of
appropriate type of model function.)
Graph functions expressed symbolically, and show
key features of the graph, by hand in simple cases and
using technology for more complicated cases. *[FIF7]
b. Graph polynomial functions, identifying zeros
when suitable factorizations are available, and
showing end behavior. [F-IF7c]
Compare properties of two functions each represented
in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). [FIF9]
Ex: Given a graph of one quadratic function and an
algebraic expression for another, say which has the
larger maximum.
Algebra II/Trigonometry
Revised August 2014
5
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
1
Perform arithmetic operations with complex
numbers.
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]
2
Use the relation i2= -1 and the commutative,
associative, and distributive properties to add,
subtract, and mulitply complex numbers. [N-CN2]
3
PRACTICE
STANDARDS
TEXT
MATERIAL
5 and 1
Ch. 4
Sec 4.4
RESOURCES
**Pacing
Find the conjugate of a complex number; use
conjugates to find moduli and quotients of complex
numbers. [N-CN3]
Algebra II/Trigonometry
Revised August 2014
6
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Use complex numbers in polynomial identities and
equations. (Polynomial with real coefficients.)
Solve quadratic equations with real coefficients that
have complex solutions. [N-CN7]
PRACTICE
STANDARDS
TEXT
MATERIAL
5,6,3
Ch. 4
Sec 4.54.8
RESOURCES
**Pacing
Extend polynomial identities to the complex numbers.
[N-CN8]
Ex: Rewrite x2+4 as (x+2i)(x-2i).
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Solve equations and inequalities in one variable.
Recognize when the quadratic formula gives complex
solutions, and write them as a ± bi for real numbers a
and b. [A-RE14b]
Write a function defined by an expression in different
by equivalent forms to reveal and explain different
properties of the function. [F-IF8]
Create equations that describe numbers or
relationships. (Equations using all available types
of expressions
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]
Algebra II/Trigonometry
Revised August 2014
7
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Perform arithmetic operations on polynomials.
(Beyond quadratic.)
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]
Understand the relationship between zeros and
factors of polynomials.
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]
PRACTICE
STANDARDS
TEXT
MATERIAL
5,6,1
Ch. 5
Sec 5.15.7
RESOURCES
**Pacing
3 wks for sec.
5.1-5.7, 5.5
technology
(Use 5-5
Graphing
Technology
Lab for
Polynomial
Identities)
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]
Use complex numbers in polynomial identities and
equations. (Polynomials with real coefficients.)
Know the Fundamental Theorem of Algebra; show
that it is true for quadratic polynomials. [N-CN9]
Algebra II/Trigonometry
Revised August 2014
8
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Rewrite rational expressions. (Linear and quadratic
denominators.)
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]
Interpret the stucture of expressions. (Polynomial and
rational.)
Use the structure of an expression to identify ways to
rewrite it. [A-SSE2]
Ex. See x4 - y4 as (x2)2 – (y2)2, thus recognizing it as a
difference of squares that can be factored(x2–y2) (x2+y2).
Use polynomial identities to solve problems
Prove polynomial identities and use them to describe
numerical relationships. [A-APR4]
Ex. The polynomial identity (x2 + y2) = (x2 – y2)2 + (2xy)2
can be used to generate Pythagorean triples.
PRACTICE
STANDARDS
TEXT
MATERIAL
8,2,5,6
(Use 5-5
Graphing
Technology
Lab for
Polynomial
Identities)
RESOURCES
**Pacing
Supplement
(Use 5-5
Graphing
Technology
Lab for
Solving
Polynomial
Equations
by
Graphing)
Represent and solve equations and inequalities
graphically. (Combine polynomial, rational, radical,
absolute value, and exponential functions.)
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]
Algebra II/Trigonometry
Revised August 2014
9
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Build new functions from existing functions. (Include
simple radical, rational, and exponential functions;
emphasize common effect on each transformation
across function types.)
Write a function that describes a relationship between two
quantities.* [F-BF1]
a. Combine standard function types using arithmetic
operations. [F-BF1b]
Ex: 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.
PRACTICE
STANDARDS
TEXT
MATERIAL
6,3,1
Ch. 6
Sec 6.16.3
RESOURCES
**Pacing
2wks for sec.
6.1-6.3, 6.7
Find inverse functions.
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]
x 1
Example: f ( x)  2 x 3 or f ( x) 
for x  1 .
x 1
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]
Ch. 6
6.7
Understand solving equations as a process of reasoning,
and explain the reasoning. (Simple rational and radical.)
Solve simple rational and radical equations in one variable,
and give examples showing how extraneous solutions may
arise. [A-RE12]
Algebra II/Trigonometry
Revised August 2014
10
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Analyze functions using different representations.
(Focus on using key features to guide selection of
appropriate type of model function.)
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]
PRACTICE
STANDARDS
TEXT
MATERIAL
4 and 5 and
6
Ch. 7
Sec 7.17.8
RESOURCES
**Pacing
4 wks for sec.
7.1-7.8
Interpret the structure of expressions. (Polynomial and
rational.)
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]
b. Interpret complicated expressions by viewing one or
more of their parts as a single entity. [A-SSE1b]
Ex: Interpret P=(1 + r)n as the product of P and factor not
depending on P.
Represent and solve equations and inequalities
graphically. (Combine polynomial, rational, radical,
absolute value, and exponential functions.)
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]
Algebra II/Trigonometry
Revised August 2014
11
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
PRACTICE
STANDARDS
Construct and compare linear, quadratic, and
exponential models and solve problems.
(Logarithms as solutions for exponentials.)
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]
1 and 3 and
4
Rewrite rational expressions. (Linear and
quadratic denominators.)
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]
7,8 and 5,6
TEXT
MATERIAL
Ch 8
Sec 8.18.2, 8.4,
8.6
RESOURCES
**Pacing
3 wks for sec.
8.1-8.2, 8.4, 8.6
Understand solving equations as a process of
reasoning and explain the reasoning. (Simple
rational and radical.)
Solve simple rational and radical equations in one
variable, and give examples showing how extraneous
solutions may arise. [A-REI2]
Algebra II/Trigonometry
Revised August 2014
12
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Understand the graphs and equations of conic
sections. (Emphasize understanding graphs and
equations of circles and parabolas.)
Create graphs of conic sections, including parabolas,
hyperbolas, ellipses, circles, and degenerate conics,
from second-degree equations.
Ex: Graph x2 – 6x + y2 - 12y + 41=0 or y2 – 4x + 2y
+5= 0.
PRACTICE
STANDARDS
TEXT
MATERIAL
1,4,8
Cha 9
Sec 9.29.5
RESOURCES
**Pacing
3 wks for sec.
9.2-9.5
a. Formulate equations of conic sections from their
determining characteristics.
Ex: Write the equation of an ellipse with the center
(5, -3), a horizontal major axis of length 10, and a
minor axis length 4.
Algebra II/Trigonometry
Revised August 2014
13
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
39
Extend the domain of trigonometric functions
using the unit circle.
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
37
Understand radian measure of an angle as the length
of the arc on the unit circle subtended by the angle.[F-
PRACTICE
STANDARDS
TEXT
MATERIAL
2,3,4
Ch. 12
Sec 12.112.3, 12.6
RESOURCES
**Pacing
2 wks for sec.
12.1-12.3, 12.6
TF1]
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40
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. [FTF2]
Model periodic phenomena with trigonometric
functions.
Choose trigonometric functions to model periodic
phenomena with specified amplitude, frequency, and
midline.* [F-TF5]
Algebra II/Trigonometry
Revised August 2014
14
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Analyze functions using different representations.
(Focus on using key features to guide selection of
appropriate type of model function.)
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]
PRACTICE
STANDARDS
TEXT
MATERIAL
5 and 6
Ch 10:
Sect 10.1,
10.3
RESOURCES
**Pacing
1 wk for sec.
10.1, 10.3
Write expressions in equivalent forms to solve
problems.
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]
Ex: Calculate mortgage payments.
Algebra II/Trigonometry
Revised August 2014
15
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Use probability to evaluate outcomes of decisions.
(Include more complex situations.)
Use probablities to make fair decisions (e.g., drawing
by lots, using random number generator).
[SMD6]
Analyze decisions and strategies using probabilties
concepts (e.g., product testing, medical testing,
pulling a hockey goalie at the end of a game). [SMD7]
PRACTICE
STANDARDS
TEXT
MATERIAL
5 and 3
Ch 11
Sec 11.111.4
RESOURCES
**Pacing
2 wks for the P
pages and sec.
11.1-11.4
P pages
in the
front of
the book
P.9-P19
Understand independence and conditional
probability and use them to interpret data (Link to
data from simulations or experiments.)
Describe events such as subsets of a sample space (the
set of outcomes), using charateristics (or categories)
of the outcomes, or as unions, intersections, or
complements of other events (“or”, “and”, “not”).
[S-CP1]
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]
Algebra II/Trigonometry
Revised August 2014
16
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
Construct and interpret two-way 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 events are independent and
to approximate conditional probabilities. [S-CP4]
Ex. 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
the tenth grade. Do the same for other subjects and
compare the results.
46
PRACTICE
STANDARDS
TEXT
MATERIAL
7
Ch 11
Sec 11.111.4
RESOURCES
**Pacing
P pages
in the
front of
the book
P.9-P19
Recognize and explain the concepts of conditional
probability and independence in everyday language
and everyday situtations.
[S-CP5]
Ex. Compare the chance of having lung cancer if you
are a smoker with the chance of being a smoker if you
have lung cancer.
47
Use the rules of probabilty to compute
probabilities of compound events in a uniform
probability model.
Find the conditional probability of A given B as the
fraction of B’s outcomes that also belond to A, and
interpret the answer in terms of the model. [S-CP6]
Algebra II/Trigonometry
Revised August 2014
17
DOCUMENTATION
DATES
Algebra II/Trigonometry Continuum of Skills
Algebra 2 published by Glencoe
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CONTENT STANDARDS
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 Mulitplication Rule in a uniform
probability model, P(A and B)= P(A)P(B/A)=
P(B)P(A/B), and interpret the answer in terms of the
model. [S-CP8]
50
Use permutations and combinations to compute
probabilities of compound events and solve problems.
[S-CP9]
PRACTICE
STANDARDS
TEXT
MATERIAL
1,2,5
Ch 11
Sec 11.111.4
RESOURCES
**Pacing
pages in
the front
of the
book
P9-P19
Algebra II/Trigonometry
Revised August 2014
18
DOCUMENTATION
DATES