Download Algeba II Curriculum - Trenton Public Schools

TRENTON PUBLIC SCHOOLS
Department of Curriculum and Instruction
108 NORTH CLINTON AVENUE
TRENTON, NEW JERSEY 08609
Algebra II
CURRICULUM GUIDE AND INSTRUCTIONAL ALIGNMENT
August 2013-Revised June 2014
1
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
Algebra II Units at Glance
(From NJDOE Model Curriculum - each unit is designed to take approximately 30 days.)
Overview
Building on the understanding of linear, quadratic and exponential functions from Algebra I, this course will extend function concepts to include
polynomial, rational, and radical functions. The standards in this course continue the work of modeling situations and solving equations.
Unit 1 standards will focus on the similarities of arithmetic with rational numbers and the arithmetic with rational expressions. The work in unit
2 will extend student’s algebra knowledge of linear and exponential functions to include polynomial, rational, radical, and absolute value
functions.
The standards included in unit 3 builds on the students’ previous knowledge of functions, trigonometric ratios and circles in geometry to extend
trigonometry to model periodic phenomena. The work of unit 4 will explore the effects of transformations on graphs of functions and will
include identifying an appropriate model for a given situation. The standards require development of models more complex than those of
previous courses.
The standards in Unit 5 will relate the visual displays and summary statistics learned in prior courses to different types of data and to probability
distributions. Samples, surveys, experiments and simulations will be used as methods to collect data.
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M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
Unit 1: Polynomials.
Cluster
Prerequisites
Perform arithmetic
Operations with
complex
numbers.
Standard
N.RN.1, 2, 3
 Extend the properties of
exponents to rational numbers
 Use properties of rational and
irrational numbers
N.CN.1
A.REI. 2
N.CN.2
Create linear equations and
inequalities in one variable and use
them to solve problems. Justify each
step in the process and the solution
A.REI.4
Use complex
Solve quadratic equations in one
N.CN.7
numbers in
variable.
N.CN.9
polynomial identities A.APR.7
and
Perform addition, subtraction and
equations.
multiplication with polynomials and
relate it to arithmetic operations with
integers
3
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
Description
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.
Use
the relation
i2 = –1 and the commutative, associative, and
distributive
properties
to add, subtract, and multiply complex numbers.
Solve quadratic equations with real coefficients that have
complex solutions.
(+) Know the Fundamental Theorem of Algebra; show that it is
true for quadratic
polynomials.
A.C. = Additional Content
★=Modeling standards
Solve quadratic
equations in one
variable.
Interpret the
structure of
expressions.
A.SSE.3
Manipulate expressions using
A.REI.4
factoring, completing the square and
properties of exponents to produce
equivalent forms that highlight
particular properties such as the
zeros or the maximum or minimum
value of the function
b. Solve quadratic equations by inspection (e.g., for x2 = 49),
taking square roots, completing the square, the quadratic
formula and factoring, as appropriate to the initial form of the
equation. Recognize when the quadratic formula gives
A.SSE.1
A.SSE.2
Interpret parts of expressions in
terms of context including those that
represent square and cube roots; use
the structure of an expression to
identify ways to rewrite it
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).
F.LE.2 Construct linear and exponential
Write expressions in functions, including arithmetic and
A.SSE.4
geometric
sequences,
given
a
graph,
a
equivalent forms to
description of a relationship, or two
solve problems
input-output pairs (include reading these
from a table).
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M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
complex solutions and write them as a ± bi for real numbers a
and b.
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. For example, calculate mortgage
payments.★
A.C. = Additional Content
★=Modeling standards
Understand the
relationship between
zeros and factors of
polynomials
A.APR.1
. Perform addition, subtraction and A.APR.2
multiplication with polynomials and
relate it to arithmetic operations with A.APR.3
integers
Use polynomial
identities
to solve problems.
8.G.7
Apply Pythagorean theorem to
determine unknown side lengths in
right triangles.
A.APR.4
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).
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.
Prove polynomial identities and use them to describe numerical
relationships. For example, the polynomial identity (x2 + y2)2 =
(x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples.
Unit 2: Expressions and Equations (1).
Extend the
Properties of
Exponents to
rational
exponents.
5
M8.EE.1
Apply the properties of integer N.RN.1
exponents to simplify and write
equivalent numerical
expressions
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
Explain how the definition of the meaning of rational exponents
follows from extending the properties of integer exponents to
those values, allowing for a notation for radicals in terms of rational
exponents. For example, we define 51/3 to be the cube root of 5
because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
M 8.EE.2
Evaluate square roots and N.RN.2
cubic roots of small perfect
squares and cubes
respectively and use square
and cube root symbols to
represent solutions to
equations of the form x2 = p
and x3 = p where p is a
positive rational number.
Rewrite rational
expressions
6
A.SSE.1
Interpret parts of
A.APR.6
expressions in terms of
context including those that
represent square and cube
roots; use the structure of an
expression to identify ways
to rewrite it
A.SSE.3
Manipulate expressions
using factoring,
completing the square
and properties of
exponents to produce
equivalent forms that
highlight particular
properties such as the
zeros or the maximum or
minimum value of the
function
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
Rewrite expressions involving radicals and rational exponents using
the properties of exponents.
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.
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
Understand solving
equations as a
process of
reasoning and
explain the
reasoning
A.CED.4
Solve linear equations and A.REI.1
inequalities in one variable
(including literal equations).
Justify each step in the
process and solution.
A.CED.4
Understand solving
Solve linear equations and A.REI.2
equations as a
process of reasoning and inequalities in one variable
explain the reasoning. (including literal equations).
Explain each step in solving a simple equation as following from the
equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution. Construct a
viable argument to justify a solution method.
Solve simple rational and radical equations in one variable, and give examples
showing how extraneous solutions may arise.
Justify each step in the
process and solution.
Solve systems of
equations
A.REI.3
A.REI.6
Solve linear equations
and inequalities in one
variable (including literal
equations). Justify each
step in the process and
solution
A.CED.2 Create equations
in two or more variables to A.REI.7
represent relationships
between quantities; graph
equations on coordinate axes
with labels and scales
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M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
Solve systems of linear equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in two variables.
Solve a simple system consisting of a linear equation and a quadratic
equation in two variables algebraically and graphically. For example,
find the points of intersection between the line y = –3x and the circle
x2 + y2 = 3.
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
Write expressions in
equivalent forms
to solve
problems
N.RN.2 Rewrite expressions
involving radicals and
A.SSE.3
rational exponents using the
properties of exponents.
F.IF.1
Interpret functions that F.IF.2
arise in applications in
Explain
terms of a context.
F.IF.4
and interpret the
definition of functions
including domain and
range and how they are
related; correctly use
function notation in a
context and evaluate
functions for inputs and
their corresponding
outputs.
F.IF.2 Use function
Analyze functions using
notation, evaluates functions F.IF.8
different
for inputs in their domains,
representations.
and interprets statements
that use function notation in
terms of a context.
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M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
c. Use the properties of exponents to transform expressions for exponential
functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈
1.01212t to reveal the approximate equivalent monthly interest rate if the
annual rate is 15%.
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.★
Write a function defined by an expression in different but equivalent forms to
reveal and explain different properties of the function.
b. Use the properties of exponents to interpret expressions for exponential
functions. For example, identify percent rate of change in functions such as y =
(1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as
representing exponential growth or decay.
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
Translate between the
geometric
description and
the equation for
a
conic section
F.IF.7
Graph functions by hand (in G.PE.2
simple cases) and with
technology (in complex
cases) to describe linear
relationships between two
quantities and identify,
describe, and compare
domain and other key
features in one or multiple
representations
Derive the equation of a parabola given a focus and directrix.
Unit 3: Expressions and Equations (2).
A.REI.5
Represent and solve
equations and
A.REI.6
inequalities graphically. A.REI.7
Build a function that
models a relationship
between two quantities
F.BF.1
Interpret
Expressions for
functions in terms of
the situation they
model
8.F.1
Build new functions from F.IF.1
F.IF.2
existing functions.
F.IF.7
9
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.★
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.★
F.LE.5
Interpret the parameters in a linear or exponential function in terms of a context.
F.BF.4
Find inverse functions.
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. For example, f(x) = 2 x3 or f(x) = (x+1)/(x-1) for x ≠1.
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
Extend the domain of
trigonometric
functions using the
unit circle.
F.TF.1
Understand radian measure of an angle as the length of the arc on the unit circle
subtended by the angle.
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.
F.TF.5
Choose trigonometric functions to model periodic phenomena
with specified amplitude, frequency, and midline.★
F.TF.8
Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin (θ), cos (θ),
or tan (θ), given sin (θ), cos (θ), or tan (θ), and the quadrant of the angle.
F.TF.1
Model periodic
phenomena with
trigonometric functions.
8.G.6
Prove and apply
8.G.7
trigonometric identities.
Interpret functions
that arise in
applications in terms
of a context.
nalyze functions using
different
representations.
S.ID.7
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.★
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.★
e. Graph trigonometric functions, showing period, midline, and amplitude
N.Q.2
Define appropriate quantities for the purpose of descriptive modeling.
A.REI.4
Reason quantitatively
and use units to solve
problems
10
F.IF.
4
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
Unit 4: Modeling with Functions
F.IF.4
F.IF.6
Calculate and interpret the average rate of change of a function (presented
symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★
F.IF.9
Compare properties of two functions each represented in a
different way (algebraically, graphically, numerically in tables, or by verbal
descriptions). For example, given a graph of one quadratic function and an algebraic
expression for another, say which has the
larger maximum.
F.BF.1
Write a function that describes a relationship between two quantities.*
b. Combine standard function types using arithmetic operations. For example, 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.
Build new functions from
existing functions.
F.BF.3
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.
Construct and compare
linear, quadratic, and
exponential models
and solve problems.
F.LE.4
Understand and evaluate
random processes
underlying statistical
experiments.
S.IC.1
Interpret functions that
arise in applications in
terms of a context.
Analyze functions using
different representations.
F.IF.7
A.REI.4
F.IF.3
Build a function that
models a relationship
between two
quantities.
F.IF.7
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M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
For exponential models, express as a logarithm the solution to a bct = d where a, c,
and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
Understand statistics as a process for making inferences about population parameters based on a
random sample from that population.
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
S.ic.1
S.IC.2
Decide if a specified model is consistent with results from a given data-generating process, e.g.,
using simulation. For example, a model says a spinning coin falls heads up with
probability 0.5. Would a result of 5 tails in a row cause you to question the model?
S.IC.3
Make inferences and justify
conclusions from sample
surveys, experiments, and
observational studies.
S.ic.3
Recognize the purposes of and differences among sample surveys, experiments, and observational
studies; explain how randomization relates to each
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.
s.ic.3
s.ic.3
S.IC.5
Use data from a randomized experiment to compare two treatments; use simulations to
decide if differences between parameters are significant
S.IC.6
Evaluate reports based on data
S.CP.1
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”).
Unit 5: Probability and Statistics
Understand independence
and nditional
probability and use
them
to interpret
data.
12
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
s.cp.1
S.CP.2
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.cp.1
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.CP.3
s.cp.1
s.cp.1
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. For example, collect data from a random sample of students in your
school on their favorite subject among math, 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.
S.CP.4
S.CP.5
.
Use the rules of
probability to compute
probabilities of
compound events in a
uniform probability
model
13
S.CP.6
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.
Apply the
S.CP.7
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
Recognize and explain the concepts of conditional probability and independence in
everyday language and everyday situations. For 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.
Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
Grade level: HS
Unit #1
UNIT NAME: Polynomials
District-Approved Text: Pearson
Stage 1 – Desired Results
Enduring Understandings/Goals:
 Operations and properties of the real number system can be extended to situations involving
complex numbers
 Expressions can be written in multiple ways using the rules of algebra.
Essential Questions:
 How does knowledge of real numbers help when working with complex numbers?
 Why structure expressions in different ways?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
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.
Standard:
Student Learning
Suggested
Suggested
Objectives
Instructional
Resources
Strategies
N.CN.1 Know there is a
1) Use properties of
Pearson 4-8
 Use
complex number i such that i2
operations to add, subtract,
Algebra
pp. 248-255
= −1, and every complex
and multiply complex
tiles to
number has the form a + bi
numbers.
create
with a and b real. A.C.*
examples
of
14
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
N.CN.2 Use the relation i2 = –
1 and the commutative,
associative, and distributive
properties to add, subtract,
and multiply complex
numbers. A.C



15
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
polynomial
s.
Use
different
colored
chalk/mark
ers for
each of the
terms.
Create a
column for
the 4 parts
of FOIL.
Use FOIL
method
(First,
Outers,
Inners,
Last) to
reinforce
the
commutati
ve,
associative
, and
distributive
properties.
Algebra
tiles to
solve
multi-step
equations.
A.C. = Additional Content
★=Modeling standards
N.CN.7 Solve quadratic
equations with real coefficients
that have complex solutions.
A.C*
2) Solve quadratic equations
with real coefficients that
have complex solutions.

A.REI.4.b Solve quadratic
equations in one variable.
b. Solve quadratic equations
by inspection (e.g., for x2 =
49), taking square roots,
completing the square, the
quadratic formula and
factoring, as appropriate to the
initial form of the equation.
Recognize when the quadratic
formula gives complex
solutions and write them as a
± bi for real numbers a and b.
S.C.

N.CN.9 (+) Know the
Fundamental Theorem of
Algebra; show that it is true
for quadratic polynomials.
Product of P and a factor not
16
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
3) Show that the
Fundamental Theorem of
Algebra is true for quadratic
polynomials. +
S.C. = Supporting Content

Provide
students
with a
variety of
parabolas
and then
sort into 3
piles.
(Those
that model
a real
solution;
those that
model with
2 real
solutions,
and those
that model
no real
solution.
Scatterplot
to gain
insight into
possible
relationship
s between
two
variables.
Have
students
work in
pairs or
groups to
Pearson 5-5,56
pp.
312-324
Pearson 5-6
pp. 319-324
A.C. = Additional Content
★=Modeling standards
depending on P.

17
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
create a
jingle,
poem, or
rap that
describes
the
patterns
found.
Construct
videos
about
expanding
powers of
binomials
and
polynomial
s.
A.C. = Additional Content
★=Modeling standards
A.APR.2 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). M.C.
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. For example,
calculate mortgage payments.
M.C.
A.SSE.2 Use the structure of
18
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
4) Restructure by performing
arithmetic operations on
polynomial and rational
expressions.
5) 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.
For example, calculate
mortgage payments.★
6) Use an appropriate
S.C. = Supporting Content

Make
connections
between
arithmetic of
integers and
arithmetic of
polynomials

Use the
distributive
property
• Perform
arithmetic
operations on
polynomials
Factor
polynomials.
 Offer multiple
real world
examples such
as calculating
mortgage
payments

Use real word
Pearson 5-4
Pearson CB 95, 9-5
Pearson 4-4, 5-
A.C. = Additional Content
★=Modeling standards
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).
M.C.
factoring technique to factor
expressions completely
including expressions with
complex numbers


A.APR.3 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.
M.C.
A.APR.4 Prove Polynomial
identities and use them to
describe numerical
relationships. For example, the
polynomial identity (x2 + y2)2
= (x2 – y2)2 + (2xy)2 can be
used to generate Pythagorean
triples. A.C.
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). M.C.
19
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Algebra II Curriculum revised on June 16, 2014


7) Explain the relationship
between zeros and factors of
polynomials and use zeros
to construct a rough
graph of the function
defined by the polynomial.
S.C. = Supporting Content
context
examples.
Extend beyond
simplifying
expressions
Factor by
grouping
Have students
create their
own
expressions
that meets
specific criteria
and verbalize
how they can
be written and
re-written in
different forms
Pair or group
students to
share their
expressions
and re-write
one another’s
expressions
2) Create
experiences
with long
division of
polynomials
3, 6-1,
6-2, 6-3, 8-4
Pearson 4-5, 52, 5-6, CB 5-7
Pearson
CB 5-5
Pearson 4-4, 53, 6-1,
6-2, 6-3, 8-4
3) Graph
A.C. = Additional Content
★=Modeling standards
polynomial
functions in
factor form
A.APR.3 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.
M.C.
Suggested Performance Tasks:
 Exemplars
 Extended projects
 Math Webquests
 Writing in Math/Journal
20
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
Pearson 4-5, 52, 5-6, CB 5-7
Stage 2 – Assessment Evidence
Other Evidence:
 Classwork
 Exit Slips
 Homework
 Individual and group tests
 Open-ended questions
 Portfolio
 Quizzes
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
Stage 3 – Learning Plan
Lesson Format
7-10 min: Do Now/Journaling/Pretest (whole class)
Journaling
Pretest
Activate students’ prior knowledge
Can be a review of info
Pose EQ or provide relevant question / inquiry
Quick multiple choice format
related to EU
Not to be counted as a test grade
Share-out with several students
Review correct answers
10-15 min: Homework Review (whole class)
15-20 min: Mini Lesson/Content Presentation /Guided Practice (whole class)
Content Presentation
Guided Practice
Note taking of solutions to sample problems.
Clarify instructions for assignments and projects
Video or multi-media presentation
Teach specific skills (i.e. which problem solving skill is
appropriate, how to use rubrics)
30 min: Independent Practice (small group/independent)
Anchor Activity: major assignment that
Center Activities: variety of activities related to unit
everyone is responsible for completing
allowing some flexibility and choice for students to
complete
Word Wall activities, technology center with math
web quests, math centers
2 min: Transition back to seats for whole class
10 min: Closure/Assessment/Evaluation
Exit slip
Assign homework
21
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
Grade level: HS
UNIT NAME: Operations and Algebraic Thinking
District-Approved Text: Pearson
Unit #2
Stage 1 – Desired Results
Enduring Understandings/Goals:
 Algebraic expressions symbolize numerical relationships and can be manipulated in the same way as numbers.
 There is often an optimal method of manipulating equations and equalities.
Essential Questions:
 How can the properties of the real number system be useful when working with polynomials and rational expressions?
 In what ways can the problem be solved and why should one method be chosen over another?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
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.
Standard:
Student Learning
Suggested Instructional Strategies
Suggested
Objectives
Resources
N.RN.1 Explain how the
1. Use properties of integer
Pearson
definition of the meaning
exponents to explain and
Algebra Review p.225
of rational exponents
convert between
Concept Byte p.360
follows from extending the
expressions involving
Section 6-4
properties of integer
radicals and rational
exponents to those values,
exponents, using correct
allowing for a notation for
notation. For example,
radicals in terms of
we define 51/3 to be the
rational exponents. For
cube root of 5 because
example, we define 51/3 to
be the cube root of 5
22
we want (51/3)3 = 5(1/3)3
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
because we want (51/3)3 =
5(1/3)3 to hold, so (51/3)3
must equal 5. M.C.
to hold, so (51/3)3 must
equal 5.
N.RN.2 Rewrite
expressions involving
radicals and rational
exponents using the
properties of exponents.
M.C.
A.APR.6 Rewrite simple
2. Rewrite simple rational
rational expressions in
expressions in different
different forms; write
forms using inspection,
a(x)/b(x) in the form q(x)
long division, or, for the
+ r(x)/b(x), where a(x),
more complicated
b(x), q(x), and r(x) are
examples, a computer
polynomials with the
algebra system.
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.
S C.
A.REI.1 Explain each step 3. Solve simple rational and
in solving a simple
radical equations in one
equation as following from
variable, explain the
the equality of numbers
reasoning, and give
asserted at the previous
examples showing how
step, starting from the
extraneous solutions may
assumption that the
arise.
original equation has a
solution. Construct a
23
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014

Write rational expressions in
different forms

Begin with simple, one step
equations and require students to
write out a justification for each
step used to solve the equations
Ensure that students are
proficient with solving simple
rational and radical equations that
have no extraneous solutions
before moving on to equations

S.C. = Supporting Content
A.C. = Additional Content
Pearson
5-4, 8-6
Pearson
6-5, 8-6
★=Modeling standards
viable argument to justify
a solution method. M.C.

A.REI.2 Solve simple
rational and radical
equations in one variable,
and give examples
showing how extraneous
solutions may arise. M.C.
3. Solve simple rational and
radical equations in one
variable, explain the
reasoning, and give
examples showing how
extraneous solutions may
arise.



A.REI.6 Solve systems of
linear equations exactly
24
4. Solve systems of linear
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
that result in quadratics and
possible solutions that need to be
eliminated
Provide visual examples of radical
and rational equations with
technology so that students can
see the solutions as the
intersections of two functions and
further understand how
extraneous solutions do not fit the
model
Pearson
Begin with simple, one step
equations and require students to 6-5, 8-6
write out a justification for each
step used to solve the equations
Ensure that students are
proficient with solving simple
rational and radical equations that
have no extraneous solutions
before moving on to equations
that result in quadratics and
possible solutions that need to be
eliminated.
Provide visual examples of radical
and rational equations with
technology so that students can
see the solutions as the
intersections of two functions and
further understand how
extraneous solutions do not fit the
model.
Pearson
A.C. = Additional Content
★=Modeling standards
equations and simple
systems consisting of a
linear and a quadratic
equation in two variables,
algebraically and
graphically.
A.REI.7 Solve a simple
4. Solve systems of linear
system consisting of a
equations and simple
linear equation and a
systems consisting of a
quadratic equation in two
linear and a quadratic
variables algebraically and
equation in two variables,
graphically. For example,
algebraically and
find the points of
graphically.
intersection between the
line y = –3x and the circle
x2 + y2 = 3. A.C.
A.SSE.3 Choose and
5. Write equivalent
produce an equivalent
expressions for
form of an expression to
exponential functions
reveal and explain
using the properties of
properties of the quantity
exponents.
represented by the
expression.★
c. Use the properties of
exponents to transform
expressions for
exponential functions. For
example the expression
1.15t can be rewritten as
(1.151/12)12t ≈ 1.01212t to
reveal the approximate
equivalent monthly
interest rate if the annual
rate is 15%. M.C.
3-1, 3-2, 3-3, 4-9
and approximately (e.g.,
with graphs), focusing on
pairs of linear equations in
two variables. A.C.
25
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
Pearson
3-1, 3-2, 3-3, 4-9
Pearson
1-1
A.C. = Additional Content
★=Modeling standards
FIF.4 For a function that
6. Interpret key features of
models a relationship
graphs and tables in
between two quantities,
terms of the quantities,
interpret key features of
and sketch graphs
graphs and tables in terms
showing key features
of the quantities, and
given a verbal description
sketch graphs showing
of the relationship. Key
key features given a
features include:
verbal description of the
intercepts; intervals
relationship. Key features
where the function is
include: intercepts;
intervals where the
function is increasing,
decreasing, positive, or
negative; relative
maximums and
minimums; symmetries;
end behavior; and
periodicity.★ M.C.
increasing, decreasing,
positive, or negative;
relative maximums and
minimums; symmetries;
end behavior; and
periodicity. ★
FIF.8 Write a function
defined by an expression
in different but equivalent
forms to reveal and
explain different
properties of the function.
S.C.
7. Rewrite a function in
different but equivalent
forms to identify and
explain different
properties of the
function.
G.PE.2 Derive the
equation of a parabola,
given a focus and
directrix. A.C.
8. Derive the equation of a
parabola given a focus
and directrix.
26
Pearson
2-3, 2-5, 4-1, 4-2, 4-3,
5-1, 5-8, Concept Byte
p.459, 13.1, 13.4, 13.5


M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
Use the process of factoring and
completing the square in a
quadratic function to show zeros,
extreme value, and symmetry of
the graph and interpret this in
terms of a context.
Use the properties of exponents
to interpret expressions for
exponential functions
Pearson 2-4, 4-2, 59, 6-8,
7-2, 7-3, CB
7.5
Pearson 10-2, 10-6
Parabolas
A.C. = Additional Content
★=Modeling standards
Suggested Performance Tasks:
 Exemplars
 Extended projects
 Math Webquests
 Writing in Math/Journal
Stage 2 – Assessment Evidence
Other Evidence:
 Classwork
 Exit Slips
 Homework
 Individual and group tests
 Open-ended questions
 Portfolio
 Quizzes
Stage 3 – Learning Plan
Lesson Format
7-10 min: Do Now/Journaling/Pretest (whole class)
Journaling
Pretest
Activate students’ prior knowledge
Can be a review of info
Pose EQ or provide relevant question / inquiry
Quick multiple choice format
related to EU
Not to be counted as a test grade
Share-out with several students
Review correct answers
10-15 min: Homework Review (whole class)
15-20 min: Mini Lesson/Content Presentation /Guided Practice (whole class)
Content Presentation
Guided Practice
Note taking of solutions to sample problems.
Clarify instructions for assignments and projects
Video or multi-media presentation
Teach specific skills (i.e. which problem solving skill is
appropriate, how to use rubrics)
30 min: Independent Practice (small group/independent)
Anchor Activity: major assignment that
Center Activities: variety of activities related to unit
everyone is responsible for completing
allowing some flexibility and choice for students to
complete
Word Wall activities, technology center with math
web quests, math centers
2 min: Transition back to seats for whole class
27
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
10 min: Closure/Assessment/Evaluation
Exit slip
Assign homework
UNIT NAME: Expressions and Equations(2)
Grade level: HS
District-Approved Text: Pearson
Unit #3
Stage 1 – Desired Results
Enduring Understandings/Goals:
 Equations, verbal descriptions, graphs and table provide insights into the relationships between quantities
Essential Questions:
 How can the relationship between quantities best be represented?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
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.
Standard:
Student Learning
Suggested Instructional
Suggested
Objectives
Strategies
Resources
28
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
A.REI.11
Explain why the xcoordinates 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.★
M.C.
F.BF.2
Write arithmetic and
geometric sequences
both recursively and
29
Pearson
3-1, 5-3, 7-5,
1)Find approximate
solutions for the
intersections of functions
and explain why the xcoordinates 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) involving
linear, polynomial,
rational, absolute value,
and exponential
functions.
2) Write arithmetic and
geometric sequences both
recursively and with an explicit
formula, use them to model
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
Concept Byte 7-6 p.484,
8-6

S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
with an explicit formula,
use them to model
situations, and translate
between the two forms.
★ M.C.
F.BF.4
Find inverse functions.
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. For example,
situations, and translate
between the two forms.★
Pearson
6-7, 7-3
3)Determine the inverse
function for a simple function
that has an inverse and write
an expression for it.
f(x) =2 x3 or f(x) =
(x+1)/(x–1) for x
A.C.
F.IF.4
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.
b. Graph square root,
cube root, and
piecewise-defined
functions, including
step functions and
absolute value
functions.
e. Graph exponential
30
4)Graph functions
expressed
symbolically and
show key features of
the graph (including
intercepts, intervals
where the function is
increasing,
decreasing, positive,
or negative; relative
maximums and
minimums;
symmetries; end
behavior; and
periodicity) by hand
in simple cases and
using technology for
more complicated
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014


Use a set of given
characteristics to sketch the
graph of a function
Examine a table of related
quantities and identify
features in the table , such
as intervals on which the
interval increases, decreases
, or exhibits periodic
behavior
S.C. = Supporting Content
Pearson
2-3, 2-5, 4-1, 4-2, 4-3, 51, 5-8, CB 7-3, 13-1, 134, 13-5
2-3, 2-4, CB 2-4, 2-6, 27, 4-1, 4-2, 5-1, 5-2, 5-8,
6-8, 7-2, CB 8-2, 8-3
CB 2-4, 2-7, 2-8, 6-8
5-1, 5-2, 5-9
CB 8-2
7-1, 7-2, 7-3, CB 7-5, 134, 13-5, 13-6, 13-7, 13-8
A.C. = Additional Content
★=Modeling standards
and logarithmic
functions, showing
intercepts and end
behavior, and
trigonometric
functions, showing
period, midline, and
amplitude. S.C.
N.Q.2 Define
appropriate quantities
for the purpose of
descriptive modeling.
S.C.
F.LE.5
Interpret the
parameters in a linear or
exponential function in
terms of a context. A.C.
F.TF.1
Understand radian
measure of an angle as
the length of the arc on
the unit circle subtended
by the angle. A.C.
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
31
cases.
5)Interpret the parameters in
a linear or exponential
function in terms of a context.
6) Uses the radian measure of
an angle to find the length of
the arc in the unit circle
subtended by the angle and
find the measure of the angle
given the length of the arc.
7)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) and use
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
Pearson 13-3
Pearson
13-4, 13-5, 13-6
A.C. = Additional Content
★=Modeling standards
measures of angles
traversed
counterclockwise around
the unit circle. A.C.
F.TF.8
Prove the Pythagorean
identity sin 2 (θ) +
cos2(θ) = 1 and use it to
find sin(θ), cos(θ), or
tan(θ) given sin(θ),
cos(θ), or tan(θ) and
the quadrant of the
angle. A.C.
F.TF.5
Choose trigonometric
functions to model
periodic phenomena
with specified
amplitude, frequency,
and midline.★ A.C.
the Pythagorean identity (sin
θ )2 + (cos θ )2 = 1 to find sin
θ , cos θ , or tan θ , given sin
θ , cos θ , or tan θ , and the
quadrant of the angle.
7)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) and use
the Pythagorean identity (sin
θ )2 + (cos θ )2 = 1 to find sin
θ , cos θ , or tan θ , given sin
θ , cos θ , or tan θ , and the
quadrant of the angle.
8)Choose trigonometric
functions to model periodic
phenomena with specified
amplitude, frequency, and
midline. ★
Suggested Performance Tasks:
 Exemplars
 Extended projects
 Math Webquests
 Writing in Math/Journal
32
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
Pearson
14-1
Pearson
13-4, 13-5, 13-6, 13-7
Stage 2 – Assessment Evidence
Other Evidence:
 Classwork
 Exit Slips
 Homework
 Individual and group tests
 Open-ended questions
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
 Portfolio
 Quizzes
Stage 3 – Learning Plan
Lesson Format
7-10 min: Do Now/Journaling/Pretest (whole class)
Journaling
Pretest
Activate students’ prior knowledge
Can be a review of info
Pose EQ or provide relevant question / inquiry
Quick multiple choice format
related to EU
Not to be counted as a test grade
Share-out with several students
Review correct answers
10-15 min: Homework Review (whole class)
15-20 min: Mini Lesson/Content Presentation /Guided Practice (whole class)
Content Presentation
Guided Practice
Note taking of solutions to sample problems.
Clarify instructions for assignments and projects
Video or multi-media presentation
Teach specific skills (i.e. which problem solving skill is
appropriate, how to use rubrics)
30 min: Independent Practice (small group/independent)
Anchor Activity: major assignment that
Center Activities: variety of activities related to unit
everyone is responsible for completing
allowing some flexibility and choice for students to
complete
Word Wall activities, technology center with math
web quests, math centers
2 min: Transition back to seats for whole class
10 min: Closure/Assessment/Evaluation
Exit slip
Assign homework
33
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
UNIT NAME: Modeling with Functions
Grade level: HS
District-Approved Text: Pearson
Unit #4
Stage 1 – Desired Results
Enduring Understandings/Goals:
 Trigonometric functions are useful for modeling periodic phenomena
Essential Questions:
 When does a function best model a situation?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
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.
Standard:
Student Learning
Suggested Instructional
Objectives
Strategies
FIF.6 Calculate and
1. Estimate, calculate
 Given a table of values,
interpret the average
and interpret the
such as the height of a
rate of change of a
average rate of
plant overtime, students
function (presented
change of a function
estimate the rate of plant
symbolically or as a
presented
growth
table) over a specified
symbolically, in a
 Provide students with
interval. Estimate the
table, or graphically
many examples of
rate of change from a
over a specified
functional relationships,
graph.★ M.C.
interval.★
both linear or non-linear

34
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
Suggested
Resources
Pearson 2-5, 4-1, 4-2,
CB 4-3, 5-8
A.C. = Additional Content
★=Modeling standards
FIF.9 Compare
properties of two
functions each
represented in a
different way
(algebraically,
graphically,
numerically in tables,
or by verbal
descriptions). For
example, given a
graph of one
quadratic function
and an algebraic
expression for
another, say which
has the larger
maximum. S.C.
F.BF.1. Write a
function that
describes a
relationship between
two quantities.*
b. Combine
standard function
types using arithmetic
operations. For
example, build a
function that models
the temperature of a
cooling body by
adding a constant
function to a
35
2. Analyze and compare

properties of two
functions when each is
represented in a
different form
(algebraically,
graphically,
numerically in tables,
or by verbal
descriptions).
Compare a graph of one
quadratic function and an
algebraic expression for
another and say which has
the larger maximum
3. Construct a function
that combines
standard function
types using arithmetic
operations to model a
relationship between
two quantities.★
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
Pearson 2-4, 4-2, 5-9, 7-3
Pearson 2-2, 2-5, 4-2, 5-2, 6-6,
7-2, 8-2, 8-3
A.C. = Additional Content
★=Modeling standards
decaying exponential,
and relate these
functions to the
model. ★ M.C.
FBF.3 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.
A.C.
F.LE.4 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
36
4. Identify and illustrate
(using technology) an
explanation of the
effects 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.
5. 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.
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
Pearson 2-6, 2-7, 4-1, 5-9, 8-2

Allow students to work
with a single parent
function and examine
numerous parameter
changes to make
generalizations.

Use visual approaches to
identify the graphs of
even and odd functions

Use technology to solve
exponential equations
Use technology to
evaluate logarithms

S.C. = Supporting Content
Pearson 7-5, 7-6
A.C. = Additional Content
★=Modeling standards
technology.
S.IC.2 Decide if a
specified model is
consistent with
results
from a given data
generating process,
e.g.,
using simulation. For
example, a model
says a
spinning coin falls
heads
up with probability 0.
5.
Would a result of 5
tails in
a row cause you to
question the model?
S.C. ★
S.IC.3 Recognize the
purposes of and
differences among
sample surveys,
experiments, and
observational studies;
explain how
randomization relates
to each. M.C. ★
37
6. Determine if the outcomes
and properties of a specified
model are consistent with
results from a given datagenerating process using
simulation.
7. Identify different methods
and purposes for
conducting sample
surveys, experiments, and
observational studies and
explain how
randomization relates to
each. ★
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014

Use simulations to decide if a
specified model is consistent
with results from a given
data-generating process
Pearson CB 11-3

Pearson 11-8

Use sample surveys,
experiments, and
observational studies
Explain how
randomization relates to
each.
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
S.IC.1 Understand
statistics as a process
for
making inferences
about
population
parameters
based on a random
sample from that
population. S.C. ★
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.C. ★
Use simulations provide
opportunities for students to
clearly distinguish between a
population parameter which
is constant, and a sample
statistic which is a variable.
Use sample surveys,
experiments, and
observational studies
Simulate random sampling
Pearson 11-8
Pearson 11-8, CB 11-10a
S.IC.5 Use data from 9. Use data from a

a randomized
randomized experiment to
experiment to
compare two treatments
compare two
and use simulations to
treatments; use
decide if differences
simulations to decide
between parameters are
if differences between
significant; evaluate
parameters are
reports based on data. ★
significant. M.C. ★
use simulations to decide if
differences between
parameters are significant.
Pearson 11-10b
S.IC.6 Evaluate
reports based on
experiments, and
observational studies
Pearson 11-6, 11-7, 11-8
38
8. 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. ★



9. Use data from a

randomized experiment to
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
data. M.C. ★
compare two treatments
and use simulations to
decide if differences
between parameters are
significant; evaluate
reports based on data.★
Stage 2 – Assessment Evidence
Suggested Performance Tasks:
 Exemplars
 Extended projects
 Math Webquests
 Writing in Math/Journal
39
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
Other Evidence:
 Classwork
 Exit Slips
 Homework
 Individual and group tests
 Open-ended questions
 Portfolio
 Quizzes
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
Stage 3 – Learning Plan
Lesson Format
7-10 min: Do Now/Journaling/Pretest (whole class)
Journaling
Pretest
Activate students’ prior knowledge
Can be a review of info
Pose EQ or provide relevant question / inquiry
Quick multiple choice format
related to EU
Not to be counted as a test grade
Share-out with several students
Review correct answers
10-15 min: Homework Review (whole class)
15-20 min: Mini Lesson/Content Presentation /Guided Practice (whole class)
Content Presentation
Guided Practice
Note taking of solutions to sample problems.
Clarify instructions for assignments and projects
Video or multi-media presentation
Teach specific skills (i.e. which problem solving skill is
appropriate, how to use rubrics)
30 min: Independent Practice (small group/independent)
Anchor Activity: major assignment that
Center Activities: variety of activities related to unit
everyone is responsible for completing
allowing some flexibility and choice for students to
complete
Word Wall activities, technology center with math
web quests, math centers
2 min: Transition back to seats for whole class
10 min: Closure/Assessment/Evaluation
Exit slip
Assign homework
40
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
UNIT NAME: Inference and Conclusions from Data
Grade level: HS
District-Approved Text: Pearson
Unit #5
Stage 1 – Desired Results
Enduring Understandings/Goals:
 Statisticians design experiments based on random sample and analyze the data to estimate the important properties of a
population and make informed judgments
 The rule of probability can lead to more valid and reliable predictions about the likelihood of an event occurring.
Essential Questions:
 How can a population be described when it is large?
 How is probability used to make informed decision about uncertain events?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
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.
Standard:
Student Learning
Suggested Instructional
Suggested
Objectives
Strategies
Resources
S.CP.1 Describe events as
subsets of a sample space
(the set of outcomes)
using characteristics (or
categories) of the
outcomes, or as unions,
intersections, or
41
1. Describe events as
subsets of a sample space
(the set of outcomes) using
characteristics (or
categories) of the
outcomes, or as unions,
intersections, or
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
complements of other
events (“or,” “and, ”not”).
A.C.
S.CP.2 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. A.C.
S.CP.3 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. A.C.
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
42
complements of other
events (“or,” “and,””not”).
2. Use two-way frequency
tables to determine if
events are independent and
to calculate and
approximate conditional
probability.
Pearson 11-3
2. Use two-way frequency
tables to determine if
events are independent and
to calculate and
approximate conditional
probability.
Pearson 11-4
2. Use two-way frequency
tables to determine if
events are independent and
to calculate and
approximate conditional
probability.
Pearson 11-4
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
way table as a sample
space to decide if events
are independent and to
approximate conditional
probabilities. For example,
collect data from a random
sample of students in your
school on their favorite
subject among math,
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. A.C.
S.CP.5 Recognize and
explain the concepts of
conditional probability and
independence in
everyday language and
everyday situations. For
3. Use everyday language
to explain independence
and conditional probability
in real-world situations.
Pearson 11-3, 11-4
S.CP.6 Find the
conditional probability of A
4. Find the conditional
probability of A given B as
Pearson 11-4
example, compare the
chance of having lung
cancer if you are a smoke
with the chance of being a
smoker if you have lung
cancer. A.C.
43
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
given B as the fraction of
B’s outcomes that also
belong to A, and interpret
the answer in terms of the
model. A.C.
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.C.
44
the fraction of B’s outcomes
that also belong to A and
apply the addition [P(A or
B) = P(A) + P(B) – P(A and
B)] rule of probability in a
uniform probability model;
interpret the results in
terms of the model.
4. Find the conditional
probability of A given B as
the fraction of B’s outcomes
that also belong to A and
apply the addition [P(A or
B) = P(A) + P(B) – P(A and
B)] rule of probability in a
uniform probability model;
interpret the results in
terms of the model.
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
Pearson 11-3
A.C. = Additional Content
★=Modeling standards
Stage 2 – Assessment Evidence
Suggested Performance Tasks:
Other Evidence:
9. Exemplars
 Classwork
10. Extended projects
 Exit Slips
11. Math Webquests
 Homework
12. Writing in Math/Journal
 Individual and group tests
 Open-ended questions
 Portfolio
 Quizzes
Stage 3 – Learning Plan
Lesson Format
7-10 min: Do Now/Journaling/Pretest (whole class)
Journaling
Pretest
Activate students’ prior knowledge
Can be a review of info
Pose EQ or provide relevant question / inquiry
Quick multiple choice format
related to EU
Not to be counted as a test grade
Share-out with several students
Review correct answers
10-15 min: Homework Review (whole class)
15-20 min: Mini Lesson/Content Presentation /Guided Practice (whole class)
Content Presentation
Guided Practice
Note taking of solutions to sample problems.
Clarify instructions for assignments and projects
Video or multi-media presentation
Teach specific skills (i.e. which problem solving skill is
appropriate, how to use rubrics)
30 min: Independent Practice (small group/independent)
Anchor Activity: major assignment that
Center Activities: variety of activities related to unit
everyone is responsible for completing
allowing some flexibility and choice for students to
complete
Word Wall activities, technology center with math
web quests, math centers
2 min: Transition back to seats for whole class
45
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards
10 min: Closure/Assessment/Evaluation
Exit slip
Assign homework
46
M.C. = Major Content
Algebra II Curriculum revised on June 16, 2014
S.C. = Supporting Content
A.C. = Additional Content
★=Modeling standards