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Algebra II Quarter 4 Curriculum Map
2013-2014
CCSS for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Unit
Rationals
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Enriching tasks
Unit 7: Rationals
Quarter 4
Suggested Instructional Days: 5
Timeline Standards
Learning Expectation
Vocabulary
Resources
Standards covered throughout the course. It is not
Students will recognize and use inverse
Inverse variation
Algebra 2
essential to cover 8.1 to 8.3
variation.
Combined
Common
Students will use joint and other
variation
Core
variations.
Joint variation
Sec 8.1
Students will graph reciprocal functions. Reciprocal function Algebra 2
Students will graph translations of
Branch
Common
reciprocal functions.
Core
Sec 8.2
Students will identify properties of
Rational function
Algebra 2
rational functions.
Continuous graph
Common
Students will graph rational functions.
Discontinuous
Core
graph
Sec 8.3
Point of
discontinuity
Removable
discontinuity
Non-removable
discontinuity
1 day
•
•
•
•
•
Review Standards
(M)ajor Content,
(S)upporting Content
(A)dditional Content
(+) Honors/4th Math
A.SSE.1a Interpret expressions that represent a
quantity in terms of its context. Interpret parts of an
expression, such as terms, factors, and coefficients.
(M) A.SSE.2 Use the structure of an expression to
identify ways to rewrite it. For example, see x4 – y4
as (x2)2 – (y2)2, thus recognizing it as a difference of
squares that can be factored as (x2 – y2)(x2 + y2).
Students will simplify rational
expressions.
Students will multiply and divide
rational expressions.
Rational expression
Simplest form
Algebra 2
Common
Core
Sec 8.4
(+)A.APR.7 Understand that rational expressions
form a system analogous to the rational numbers,
Students will add and subtract rational
expressions.
Complex fraction
Algebra 2
Common
Algebra II Quarter 4 p. 1
Algebra II Quarter 4 Curriculum Map
2013-2014
closed under addition, subtraction, multiplication, and
division by a nonzero rational expression; add,
subtract, multiply, and divide rational expressions.
1 day
(M) A.REI.11 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.
(S) A.CED.1 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.
(M) A.REI.2 Solve simple rational and radical
equations in one variable, and give examples
showing how extraneous solutions may arise.
Core
Sec 8.5
Students will solve rational equations.
Students will use rational equations to
solve problems.
Rational equation
Algebra 2
Common
Core
Sec 8.6
Solving Rational Equations http://marc.mtsac.edu/worksheet/math51/course/10application_problems_rational_expressions.pdf
Unit 8: Series & Sequences
Quarter 4
Suggested Instructional Days: 6
Series and
1 day
(M) A.SSE.4 Derive the formula for the sum of a
Students will identify mathematical
Sequence
Algebra 2
Sequences
finite geometric series (when the common ratio is
patterns found in a sequence.
Term of a
Common
not 1), and use the formula to solve problems.
Students will use a formula to find the
sequence
Core
nth term of a sequence.
Explicit formula
Sec 9.1
Recursive formula
½ day
(M) F.BF.2 Write arithmetic and geometric
sequences both recursively and with an explicit
formula, use them to model situations, and
translate between the two forms.
(S) F.IF.3 Recognize that sequences are functions,
sometimes defined recursively, whose domain is a
subset of the integers.
(S) F.LE.2 Construct linear and exponential
functions, including arithmetic and geometric
sequences, given a graph, a description of a
Students will define, identify and apply
arithmetic sequences.
Arithmetic
sequence
Common
difference
Arithmetic mean
Algebra 2
Common
Core
Sec 9.2
Algebra II Quarter 4 p. 2
Algebra II Quarter 4 Curriculum Map
2013-2014
relationship, or two input-output pairs (include
reading these from a table).
½ day
(M) A.SSE.4 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.
(M) F.BF.2 Write arithmetic and geometric
sequences both recursively and with an explicit
formula, use them to model situations, and
translate between the two forms.
(S) F.LE.2 Construct linear and exponential
functions, including arithmetic and geometric
sequences, given a graph, a description of a
relationship, or two input-output pairs (include
reading these from a table).
Students will define, identify and apply
geometric sequences.
Geometric
sequence
Common ratio
Geometric mean
Algebra 2
Common
Core
Sec 9.3
½ day to
1 day
(S) F.IF.3 Recognize that sequences are functions,
sometimes defined recursively, whose domain is a
subset of the integers.
Students will define arithmetic series
and find their sums.
Series
Finite series
Infinite series
Arithmetic series
Limits
Algebra 2
Common
Core
Sec 9.4
Students will define geometric series
and find their sums.
Geometric series
Converge
Diverge
Algebra 2
Common
Core
Sec 9.5
Sequence-and-Series Project – See Department Chair for files
½ day to (M) A.SSE.4 Derive the formula for the sum of a
1 day
finite geometric series (when the common ratio is
not 1), and use the formula to solve problems.
2 days
Review and Test
Unit 9: Probability and Statistics
Probability
Covered for NMSBA Prep
and Statistics
Covered for NMSBA Prep
Quarter 4
Suggested Instructional Days: 5
Students will count permutations and
Fundamental
Algebra 2
combinations.
counting
Common
principle
Core
Permutation
Sec 11.1
N factorial
Combination
Students will find the probability of an
event using theoretical, experimental
and simulation methods.
Experimental
probability
Simulation
Sample space
Algebra 2
Common
Core
Sec 11.2
Algebra II Quarter 4 p. 3
Algebra II Quarter 4 Curriculum Map
2013-2014
Equally likely
outcomes
Theoretical
probability
HS Task A01: Charity Fair http://map.mathshell.org/materials/tasks.php?subpage=apprentice&taskid=250
HS FAL: Medical Testing http://map.mathshell.org/materials/lessons.php?taskid=438&subpage=problem
½ day
(A) S.CP.2 Understand that two events A and B are
Students will find the probability of the
independent if the probability of A and B occurring
event A and B and event A or B.
together is the product of their probabilities, and use
this characterization to determine if they are
independent.
(A) S.CP.7 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.
(A) S.CP.5 Recognize and explain the concepts of
conditional probability and independence in everyday
language and everyday situations.
Dependent events
Independent
events
Mutually exclusive
events
Algebra 2
Common
Core
Sec 11.3
(A) S.CP.3 Understand the conditional probability of
Students will find conditional
Conditional
A given B as P(A and B)/P(B), and interpret
probabilities.
probability
independence of A and B as saying that the
Students will use tables and tree
Contingency tables
conditional probability of A given B is the same as the diagrams to determine conditional
probability of A, and the conditional probability of B
probabilities.
given A is the same as the probability of B.
(A) S.CP.6 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.
(A) S.CP.4 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.
(A) S.CP.5 Recognize and explain the concepts of
conditional probability and independence in everyday
language and everyday situations.
HS FAL: Modeling Conditional Probabilities http://map.mathshell.org/materials/lessons.php?taskid=405&subpage=concept
(+)S.MD.6 Use probabilities to make fair decisions
Students will use probabilities to make
Probability model
(e.g., drawing by lots, using a random number
fair decisions and analyze decisions.
Algebra 2
Common
Core
Sec 11.4
½ day
Algebra 2
Common
Algebra II Quarter 4 p. 4
Algebra II Quarter 4 Curriculum Map
2013-2014
generator).
(+)S.MD.7 Analyze decisions and strategies using
probability concepts (e.g., product testing, medical
testing, pulling a hockey goalie at the end of a game).
(+)S.MD.6 Use probabilities to make fair decisions
(e.g., drawing by lots, using a random number
generator).
(+)S.MD.7 Analyze decisions and strategies using
probability concepts (e.g., product testing, medical
testing, pulling a hockey goalie at the end of a game).
Core
Sec 11.5
Students will calculate measures of
central tendency.
Students will draw and interpret boxand-whisker plots.
Measure of central
tendency
Mean
Median
Mode
Bimodal
Outlier
Range
Quartile
Interquartile range
Box-and-whisker
plot
Percentile
Algebra 2
Common
Core
Sec 11.6
MS Task A26: Temperatures http://map.mathshell.org/materials/tasks.php?taskid=384&subpage=apprentice
HS FAL: Modeling Conditional Probabilities 2 http://map.mathshell.org/materials/lessons.php?taskid=405&subpage=concept
HS FAL: Representing Data 1: Using Frequency Graphs http://map.mathshell.org/materials/lessons.php?taskid=404&subpage=concept
HS FAL: Representing Data Using Box Plots http://map.mathshell.org/materials/lessons.php?taskid=423&subpage=concept
1 day
(S) S.ID.6 a, b, c Represent data on two quantitative
Students will find the standard deviation Measure of
Algebra 2
variables on a scatter plot, and describe how the
and variance of a set of values.
variance
Common
variables are related. Fit a function to the data; use
Students will apply standard deviation
Variance
Core
functions fitted to data to solve problems in the
and variance.
Standard deviation
Sec 11.7
context of the data. Use given functions or choose a
function suggested by the context. Emphasize linear,
quadratic, and exponential models. Informally assess
the fit of a function by plotting and analyzing
residuals. Fit a linear function for a scatter plot that
suggests a linear association.
(A) S.ID.4 Use the mean and standard deviation of a
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.
HS FAL: Devising a Measure of Correlation http://map.mathshell.org/materials/lessons.php?taskid=420#task420
1 day
(M) S.IC.3 Recognize the purposes of and
Students will identify sampling methods. Population
Algebra 2
differences among sample surveys, experiments,
Students will recognize bias in samples
Sample
Common
Algebra II Quarter 4 p. 5
Algebra II Quarter 4 Curriculum Map
2013-2014
Convenience
Core
sample
Sec 11.8
Self-selected
sample
Systematic sample
Random sample
Bias
Observational
study
Controlled
experiment
Survey
HS FAL: Interpreting Statistics: A Case of Muddying the Waters http://map.mathshell.org/materials/lessons.php?taskid=217&subpage=problem
+
Students will find binomial probabilities Binomial
Algebra 2
and use binomial distributions.
experiment
Common
Binomial
Core
probability
Sec 11.9
Binomial theorem
1 day
Trigonometry
and observational studies; explain how
randomization relates to each.
(M) S.IC.4 Use data from a sample survey to
estimate a population mean or proportion; develop
a margin of error through the use of simulation
models for random sampling.
(M) S.IC.6 Evaluate reports based on data.
(S) S.IC.1 Understand statistics as a process for
making inferences about population parameters based
on a random sample from that population.
and surveys.
(A) S.ID.4 Use the mean and standard deviation of a
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.
(M) S.IC.5 Use data from a randomized
experiment to compare two treatments; use
simulations to decide if differences between
parameters are significant.
Students will use a normal distribution.
Discrete probability
distribution
Continuous
probability
distribution
Normal
distribution
Algebra 2
Common
Core
Sec 11.10
Concept
Byte b
Unit 10: Trigonometry
Quarter 4
Suggested Instructional Days: 9
1 day
(M) F.IF.4 For a function that models a
Students will identify cycles and periods Periodic function
Algebra 2
relationship between two quantities, interpret key
of periodic functions.
Cycle
Common
features of graphs and tables in terms of the
Students will find the amplitude of
Period
Core
quantities, and sketch graphs showing key features periodic functions.
Amplitude
Sec 13.1
given a verbal description of the relationship. Key
features include: intercepts; intervals where the
function is increasing, decreasing, positive, or
negative; relative maximums and minimums;
symmetries; end behavior; and periodicity.
Algebra II Quarter 4 p. 6
Algebra II Quarter 4 Curriculum Map
2013-2014
(A) F.TF.5 Choose trigonometric functions to model
periodic phenomena with specified amplitude,
frequency, and midline.
HS FAL: Ferris Wheel http://map.mathshell.org/materials/lessons.php?taskid=427&subpage=concept
1 day
(A) F.TF.2 Explain how the unit circle in the
Students will work with angles in
coordinate plane enables the extension of
standard position.
trigonometric functions to all real numbers,
Students will find coordinates of points
interpreted as radian measures of angles traversed
on the unit circle.
counterclockwise around the unit circle.
Standard position
Initial side
Terminal side
Coterminal angles
Unit circle
Cosine of θ
Sine of θ
Algebra 2
Common
Core
Sec 13.2
1 day
(A) F.TF.1 Understand radian measure of an angle as
the length of the arc on the unit circle subtended by
the angle.
Students will use radian measure for
angles.
Students will find the length of an arc of
a circle.
Central angle
Intercepted arc
Radian
Algebra 2
Common
Core
Sec 13.3
1 day
(A) F.TF.2 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.
(A) F.TF.5 Choose trigonometric functions to model
periodic phenomena with specified amplitude,
frequency, and midline.
(S) F.IF.7 Graph functions expressed symbolically
and show key features of the graph, by hand in simple
cases and using technology for more complicated
cases. Graph exponential and logarithmic functions,
showing intercepts and end behavior, and
trigonometric functions, showing period, midline, and
amplitude.
(S) F.IF.7b Graph functions expressed symbolically
and show key features of the graph, by hand in simple
cases and using technology for more complicated
cases. Graph square root, cube root, and piecewisedefined functions, including step functions and
absolute value functions.
Students will identify properties of the
sine function.
Students will graph sine functions.
Sine function
Sine curve
Algebra 2
Common
Core
Sec 13.4
1 day
(A) F.TF.2 Explain how the unit circle in the
Students will graph and write cosine
Cosine function
Algebra 2
Algebra II Quarter 4 p. 7
Algebra II Quarter 4 Curriculum Map
2013-2014
1 day
coordinate plane enables the extension of
trigonometric functions to all real numbers,
interpreted as radian measures of angles traversed
counterclockwise around the unit circle.
(A) F.TF.5 Choose trigonometric functions to model
periodic phenomena with specified amplitude,
frequency, and midline.
(S) F.IF.7 Graph functions expressed symbolically
and show key features of the graph, by hand in simple
cases and using technology for more complicated
cases. Graph exponential and logarithmic functions,
showing intercepts and end behavior, and
trigonometric functions, showing period, midline, and
amplitude.
(M) F.IF.4 For a function that models a
relationship between two quantities, interpret key
features of graphs and tables in terms of the
quantities, and sketch graphs showing key features
given a verbal description of the relationship. Key
features include: intercepts; intervals where the
function is increasing, decreasing, positive, or
negative; relative maximums and minimums;
symmetries; end behavior; and periodicity.
(S) F.IF.7 c Graph functions expressed symbolically
and show key features of the graph, by hand in simple
cases and using technology for more complicated
cases. Graph polynomial functions, identifying zeros
when suitable factorizations are available, and
showing end behavior
functions.
Students will solve trigonometric
equations.
(A) F.TF.2 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.
(A) F.TF.5 Choose trigonometric functions to model
periodic phenomena with specified amplitude,
frequency, and midline.
(S) F.IF.7 Graph functions expressed symbolically
and show key features of the graph, by hand in simple
Students will graph the tangent function.
Common
Core
Sec 13.5
Tangent of θ
Tangent function
Algebra 2
Common
Core
Sec 13.6
Algebra II Quarter 4 p. 8
Algebra II Quarter 4 Curriculum Map
2013-2014
cases and using technology for more complicated
cases. Graph exponential and logarithmic functions,
showing intercepts and end behavior, and
trigonometric functions, showing period, midline, and
amplitude.
With 4-7
(A) F.TF.5 Choose trigonometric functions to model
Students will graph translations of
Phase shift
Algebra 2
periodic phenomena with specified amplitude,
trigonometric functions.
Common
frequency, and midline.
Students will write equations of
Core
(S) F.IF.7 Graph functions expressed symbolically
translations.
Sec 13.7
and show key features of the graph, by hand in simple
cases and using technology for more complicated
cases. Graph exponential and logarithmic functions,
showing intercepts and end behavior, and
trigonometric functions, showing period, midline, and
amplitude.
Roller Coaster http://www.uni.illinois.edu/~hcrussel/ICTM2007/coasters.pdf
1 day
(A) F.TF.8 Prove the Pythagorean identity sin2(θ) +
Students will verify trigonometric
Trigonometric
Algebra 2
cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ)
identities.
identity
Common
given sin(θ), cos(θ), or tan(θ) and the quadrant of the
Core
angle.
Sec 14.1
HS Task N09: Trigonometric Functions http://map.mathshell.org/materials/tasks.php?taskid=297&subpage=novice
2 days
Review and Quarter 4 Test
EOC
HS Task N10: Expressing Geometric Properties with Equations http://map.mathshell.org/materials/tasks.php?taskid=298&subpage=novice
HS Task N11: Interpreting Categorical and Quantitative Data http://map.mathshell.org/materials/tasks.php?taskid=299&subpage=novice
NOTES/REFLECTIONS:
Algebra II Quarter 4 p. 9