Curriculum Guide
for
Algebra II
North Arlington Public Schools
North Arlington Public Schools
Content Area: Algebra II
Target Course/Grade level: 11
Unit Title: Polynomial, Rational, and Radical Relationships
Essential Questions: How do use Polynomial, Rational, and Radical Relationships?
Unit Overview: This unit develops the structural similarities between the system of polynomials and the system of integers. Students draw on analogies between
polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property. Students connect multiplication of
polynomials with multiplication of multi-digit integers, and division of polynomials with long division of integers. Students identify zeros of polynomials,
including complex zeros of quadratic polynomials, and make connections between zeros of polynomials and solutions of polynomial equations. The unit
culminates with the fundamental theorem of algebra. Rational numbers extend the arithmetic of integers by allowing division by all numbers except 0. Similarly,
rational expressions extend the arithmetic of polynomials by allowing division by all polynomials except the zero polynomial. A central theme of this unit is that
the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.
Standards/
CPI’s
N.CN.1
N.CN.7
N.CN.8 (+)
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
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.CN.2 Use the relation
i2= –1 and the commutative,
associative, and distributive
properties to add, subtract, and
multiply complex numbers.
“Use addition of complex numbers in real
life”. Electricity – circuit components - Find
the impedance of the circuit.
Class discussion.
Teacher directed
inquiry.
Example 3 p. 277 in
textbook
Solve quadratic equations with real
coefficients that have complex
solutions.
Students will solve quadratic equations,
distinguish between real and complex
solutions, and interpret the graphs of the
functions.
Class discussion.
Check student
solutions.
http://www.purplemath.c
om/modules/complex3.ht
m
Extend polynomial identities to the
complex numbers. For example,
rewrite x2+ 4 as (x + 2i)(x – 2i).
Students will explore factoring over the set of
complex numbers by viewing the cool math
website.
Class discussion.
Teacher-made
worksheets.
Quiz
on material.
http://www.coolmath.com
/algebra/10-complexnumbers/02-factoringthe-sum-of-two-squares01.htm
Content Area: Algebra II
Target Course/Grade level: 11
Unit Title: Polynomial, Rational, and Radical Relationships
Essential Questions: How do use Polynomial, Rational, and Radical Relationships?
Standards/
CPI’s
N.CN.9 (+)
A.SSE.1
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Know the Fundamental Theorem of
Algebra; show that it is true for
quadratic polynomials.
Interpret expressions that represent a
quantity in terms of its
context.★
a. Interpret parts of an
expression, such as terms,
factors, and coefficients.
Powerpoint presentation of the Theorem –
Find the number of solutions to given
equations.
Students will use exponential equations to
solve real-world problems involving
compound interest. As a project/writing
assignment students will be required to
research bank interest rates and analyze the
effects of compounding interest quarterly,
daily, and continuously.
b. Interpret complicated
expressions by viewing one or
more of their parts as a single
entity. For example, interpret
P(1+r)n as the product of P
and a factor not depending on
P.
3
Evidence of Learning
Formative and
Summative measures
Class discussion.
Review student
responses. Teachermade quiz.
Evaluation of student
projects.
Resources Books, articles,
text, etc.
http://www.classzone.com
/cz/books/algebra_2_2007
_na/resources/application
s/PowerPoint/Chapter_05
/Alg2CH0507example1.p
ps
Teacher-made handouts
for project.
Content Area: Algebra II
Target Course/Grade level: 11
Unit Title: Polynomial, Rational, and Radical Relationships
Essential Questions: How do use Polynomial, Rational, and Radical Relationships?
Standards/
CPI’s
A.SSE.2
A.SSE.4
A.APR.1
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
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)
Identify quadratic forms of polynomials and
use them to factor even powers of polynomials.
Assess student
responses to guided
practice problem #
5,6,7 on page 355.
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.★
Example
A defense contractor doubles its production
every year after producing 1000 units in the
first year. Let S10 be the production after 10
years. Write S10 as a finite geometric series.
Class discussion.
Assessment of student
responses on
worksheet.
http://faculty.atu.edu/mfi
nan/2924/cal92.pdf
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.
Real-World Problem involving multiplication
of polynomials: Find the length of the wire
supporting a tree.
Discussion of You
Tube video.
Assessment of student
responses on
worksheet.
http://www.youtube.com/
watch?v=bES9eYNG7EI
&feature=related
Students will explore applying the remainder
Class discussion.
4
Ex. 4 p. 355 of textbook
Content Area: Algebra II
Target Course/Grade level: 11
Unit Title: Polynomial, Rational, and Radical Relationships
Essential Questions: How do use Polynomial, Rational, and Radical Relationships?
Standards/
CPI’s
A.APR.2
A.APR.3
A.APR.4
A.APR.5 (+)
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Evidence of Learning
Formative and
Summative measures
theorem over the set of polynomials by viewing Assessment of student
Know and apply the Remainder
responses on
Theorem: For a polynomial p(x) and the cool math website.
worksheet.
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.
Know and apply the Binomial
Theorem for the expansion
of (x + y)n in powers of x and y for a
positive integer n, where x and y
are any numbers, with coefficients
determined for example by Pascal’s
Triangle.
Students will construct rough graphs of
polynomials by utilizing the zeros of
polynomials for small values of x.
Class discussion.
Assessment of student
responses on
worksheet.
Resources Books, articles,
text, etc.
http://www.purplemath.c
om/modules/remaindr.ht
m
http://www.mathsisfun.co
m/algebra/polynomialsremainder-factor.html
Students will work on proving polynomial
identities using teacher made worksheets.
Class discussion.
Assessment of student
responses on
worksheet.
http://math2.org/math/al
gebra/polynomials.htm
Students will work on Pascal’s Triangle and
apply it to the expansion of any binomial.
Class discussion.
Review student
responses. Teachermade quiz.
http://www.purplemath.c
om/modules/binomial2.ht
m
Students will practice and work with long and
synthetic divisions.
Class discussion.
Check student
solutions.
http://calc101.com/webM
athematica/longdivide.jsp
5
Content Area: Algebra II
Target Course/Grade level: 11
Unit Title: Polynomial, Rational, and Radical Relationships
Essential Questions: How do use Polynomial, Rational, and Radical Relationships?
Standards/
CPI’s
A.APR.6
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
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. Students will learn the properties of rational
expressions. They will understand closure
properties under addition, and subtraction.
A.APR.7 (+)
A.REI.2
A.REI.11
Understand that rational expressions
form a system analogous to the
rational numbers, closed under
addition, subtraction, multiplication,
and division by a nonzero rational
expression; add, subtract, multiply,
and divide rational expressions.
Students will review LCD and use it to solve
simple rational equations.
Solve simple rational and radical
equations in one variable, and give
examples showing how extraneous
solutions may arise.
Students will use a graphing utility to find the
intersection points of two curves and relate Iit
to the solution of f(x) = g(x) .
6
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Class discussion.
Check student
solutions.
http://www.algebralab.or
g/lessons/lesson.aspx?file
=Algebra_rational_opera
tions.xml
Class discussion.
Assessment of student
responses on
worksheet.
http://hotmath.com/hotm
ath_help/topics/extraneou
s-solutions.html
Class discussion.
Assessment of student
responses on
worksheet.
http://www.purplemath.c
om/modules/intrcept.htm
Content Area: Algebra II
Target Course/Grade level: 11
Unit Title: Polynomial, Rational, and Radical Relationships
Essential Questions: How do use Polynomial, Rational, and Radical Relationships?
Standards/
CPI’s
F.IF.7
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
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.★
Graph functions expressed
symbolically and show key features
of the graph, by hand in simple cases
and using technology for more
complicated cases.★
Students will use a graphing utility to graph
sophisticated functions. They will learn how
adjust the window setting to obtain the best
view.
c. Graph polynomial functions,
identifying zeros when
suitable factorizations are
available, and showing end
behavior.
7
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Class discussion.
Assessment of student
responses on
worksheet.
Graphing Calculator
Teacher-made handouts
for project (Funny
Faces).
Class discussion.
Assessment of student
responses on
worksheet.
Graphing Calculator
Teacher-made handouts
for project
Content Area: Algebra II
Target Course/Grade level: 11
Unit Title: Trigonometric Functions
Essential Questions: How do we us Trigonometric Functions?
Unit Overview: Building on their previous work with functions, and on their work with trigonometric ratios and circles in Geometry, students now use the
coordinate plane to extend trigonometry to model periodic phenomena.
Standards/
CPI’s
F.TF.1
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Understand radian measure of an
angle as the length of the arc on
the unit circle subtended by the angle
Stringing Along with Radians
Students will learn the meaning of
radians by physically transferring
the measurement of the radius onto
the circle. Students will also
discover the relationship between
Evidence of Learning
Formative and
Summative measures
Students will solve
real-life application
problems to
demonstrate their
understanding and
knowledge of circular
functions.
Resources Books, articles,
text, etc.
http://www.nsa.gov/acade
mia/_files/collected_learni
ng/high_school/trigonomet
ry/stringing_along_radians.
pdf
radian and degree measurement
and explore applications
F.TF.2
F.TF.5
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.
Choose trigonometric functions to
model periodic phenomena
with specified amplitude, frequency,
and midline.★
“Life-size unit circle activity”
Using garland and premade cards students will
create a unit circle on the floor and will find
points around the circle.
See how sounds of music are related to
trigonometric functions. What does change of
amplitude do? How about frequency?
Class discussion.
Teacher-made quiz.
Class discussion of
video.
Best, Current Strategies
for Increasing Student
Learning – by Kitty
Morgan
http://www.youtube.com/w
atch?v=5k_Fzmn3CJo
Content Area: Algebra II
Target Course/Grade level: 11
Unit Title: Trigonometric Functions
Essential Questions: How do we us Trigonometric Functions?
Standards/
CPI’s
F.TF.8
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
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
The Reciprocal, Quotient, and Pythagorean
Identities
9
Evidence of Learning
Formative and
Summative measures
Class discussion using
white boards.
Teacher-made quiz.
Resources Books, articles,
text, etc.
http://www1.teachertube.co
m/viewVideo.php?video_i
d=212378&title=The_Reci
procal__Quotient__and_Py
thagorean_Identiti
Content Area: Algebra II
Functions
Target Course/Grade level: 11
Unit Title: Modeling with
Essential Questions: How and why do we make models of functions?
Unit Overview: In this unit students synthesize and generalize what they have learned about a variety of function families. They extend their work with
exponential functions to include solving exponential equations with logarithms. They explore the effects of transformations on graphs of diverse functions,
including functions arising in an application, in order to abstract the general principle that transformations on a graph always have the same effect regardless of
the type of the underlying function. They identify appropriate types of functions to model a situation, they adjust parameters to improve the model, and they
compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit. The description of modeling as
“the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions” is at the heart of
this unit. The narrative discussion and diagram of the modeling cycle should be considered when knowledge of functions, statistics, and geometry is applied in a
modeling context.
Standards/
CPI’s
A.CED.1
A.CED.2
A.CED.3
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
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.
Create equations in two or more
variables to represent relationships
between quantities; graph equations
on coordinate axes with labels and
scales.
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.
For example, represent inequalities
Students will complete a dating/relationship
table, graph, and respond to questions and
make predictions.
All Tied Up In Knots
Solving a System of Equations by
Graphing
Linear programming problems:
Purple Math Website
Evidence of Learning
Formative and
Summative measures
Class discussion using
white boards.
Teacher-made
worksheets.
Resources Books, articles,
text, etc.
http://www.purplemath.co
m/modules/linprog2.htm
Graph equations on
white board grids.
Discuss graphs.
http://www.algebralab.co
m/activities/activity.aspx
?file=Science_AllTiedUp
InKnots.xml
Class discussion.
Teacher-guided
inquiry.
http://www.purplemath.co
m/modules/linprog3.htm
Content Area: Algebra II
Functions
Target Course/Grade level: 11
Unit Title: Modeling with
Essential Questions: How and why do we make models of functions?
Standards/
CPI’s
A.CED.4
F.IF.4
F.IF.5
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
describing nutritional and cost
constraints on combinations of
different foods.
Rearrange formulas to highlight a
“The Language of Physics” Activity:
quantity of interest, using the same
Manipulating equations, modeling
reasoning as in solving equations. For phenomenon to fit the real world.
example, rearrange Ohm’s law V =
IR to highlight resistance R.
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.★
See Polynomial Graphs – End Behavior
11
Class discussion.
Student worksheets.
Manipulating
Equations.docx
using white board
grids.
Teacher-made quiz.
http://www.purplemath.co
m/modules/polyends.htm
Content Area: Algebra II
Functions
Target Course/Grade level: 11
Unit Title: Modeling with
Essential Questions: How and why do we make models of functions?
Standards/
CPI’s
F.IF.6
F.IF.7
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Relate the domain of a function to its
graph and, where applicable, to the
quantitative relationship it describes.
For example, if the function h(n)
gives the number of person-hours it
takes to assemble n engines in a
factory, then the positive integers
would be an appropriate domain for
the function.★
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.★
Graph functions expressed
symbolically and show key features
of the graph, by hand in simple cases
and using technology for more
complicated cases.★
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Domain and Range Activity:
“All about Trees” relating the height of a tree
over time.
Class discussion.
Teacher-made quiz.
All About Trees.pdf
Ranger Activity - "Walk the Line"
The students will be using the CBR's and
graphing calculators to model their
movements while "walking the line".
Evaluate students
modeling of the
function using the
motion detectors.
Walk_the_Line.doc
Students investigate functions with several
representations: verbal, number line,
graphical, and tabular.
Find the growth rate of student enrollment at
your high school based on past data and use
the result to predict future enrollment.
Class discussion.
Evaluation of student
projects.
http://illuminations.nctm.
org/LessonDetail.aspx?i
d=L621
12
Content Area: Algebra II
Functions
Target Course/Grade level: 11
Unit Title: Modeling with
Essential Questions: How and why do we make models of functions?
Standards/
CPI’s
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
b. Graph square root, cube root,
and piecewise-defined
functions, including step
functions and absolute value
functions
F.IF.8
e. Graph exponential and
logarithmic functions,
showing intercepts and end
behavior, and trigonometric
functions, showing period,
midline, and amplitude.
Write a function defined by an
expression in different but equivalent
forms to reveal and explain different
properties of the function.
F.IF.9
Using a graphing calculator, graph a
quadratic function in standard form, vertex
form, and intercept form. Find the vertex in
each form.
Class discussion.
Teacher-made quiz.
White boards.
Making the Most of Your Space
Class discussion using
white boards.
You are the manager of a band that has
been hired to perform at a party, and you
want to create the largest dance floor
possible for the attendees. If you only have
a given length of rope to delineate the
space, how can you make the most of your
space?
13
Graphing utilities.
http://www.algebralab.com
/activities/activity.aspx?file
=Science_MakingTheMost
OfYourSpace.xml
Content Area: Algebra II
Functions
Target Course/Grade level: 11
Unit Title: Modeling with
Essential Questions: How and why do we make models of functions?
Standards/
CPI’s
F.BF.1
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
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.
Write a function that describes a
relationship between two
quantities.*
F.BF.3
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..
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
“Population and Supply” Activity:
Using a graphing calculator to combine two
functions.
Class discussion.
Student hand-outs.
http://www.algebralab.com
/activities/activity.aspx?file
=Science_MakingTheMost
OfYourSpace.xml
Graph a family of functions and observe the
effects of changing the parameters a, h, and k
to compare f(x) with f(x) with f( ax-h) + k.
Students will graph by hand and using
graphing utilities.
Class discussion.
Student worksheets.
http://docs.google.com/view
er?a=v&q=cache:hR8DHJg
YbmUJ:www.letu.edu/peopl
e/stevearmstrong/Math120
3/Lesson%25205.1.ppt+co
mbining%2Bfunctions&hl=e
n&gl=us&pid=bl&srcid=AD
GEEShDz0AtbOXHQRhjxC
o3ikHnW6NYVaYdPwRyAKHlww6xkJH
VRxDIfTRTXlwgjKdBeo3BUy
i1xKr8G0T0hHGSjgYLxA2jvq1CaYFeUNAVzVgE25aksIIW57O3u99NXVbkCF1&sig=AHIEtbR
ZhXyKr7bCc-l9xdKB9irQNPpvg
14
Content Area: Algebra II
Functions
Target Course/Grade level: 11
Unit Title: Modeling with
Essential Questions: How and why do we make models of functions?
Standards/
CPI’s
F.BF.4
F.LE.4
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
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.
Find inverse functions.
a. Solve an equation of the form f(x)
= c for a simple function 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.
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.
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Students will graph a linear function using a
table of values, reverse the domain and range,
graph the new function on the same set of
axes, and compare the graphs.
Class discussion.
Student worksheets.
Logger Pro graphing
utility
Small Group Activity
"Modeling Exponential Growth"
Part I
Students will complete a dating/relationship
table, graph, and respond to questions and
make predictions.
Part II
Class discussion.
Student worksheets.
TI NSPIRE
Students will use an online graphing calculator
to "discover" transformations of exponential
functions.
Class discussion.
Student worksheets.
http://www.uen.org/Lesso
nplan/preview.cgi?LPid=
19846
15
Content Area: Algebra II
Functions
Target Course/Grade level: 11
Unit Title: Modeling with
Essential Questions: How and why do we make models of functions?
Standards/
CPI’s
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
16
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Content Area: Algebra II
Target Course/Grade level: 11
Unit Title: Inferences and Conclusions from Data
Essential Questions: How do make inferences and draw conclusions from data?
Unit Overview: In this unit, students see how the visual displays and summary statistics they learned in earlier grades relate to different types of data and to
probability distributions. They identify different ways of collecting data—including sample surveys, experiments, and simulations—and the role that randomness
and careful design play in the conclusions that can be drawn.
Standards/
CPI’s
S.ID.4
S.IC.1
S.IC.2
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Evidence of Learning
Formative and
Summative measures
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.
Students will learn the properties of a normal
distribution also known as the 68/95/99 rule,
and test whether or not a data set may be
approximated by a bell shape curve.
Class discussion.
Student worksheets
Understand statistics as a process for
making inferences about population
parameters based on a random
sample from that population.
Students will understand that the mean is a
good estimator of a population parameter
through sampling distributions.
Class discussion.
Student worksheets
Students will understand the law of large
numbers.
Class discussion.
Student worksheets
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?
Resources Books, articles,
text, etc.
http://www.math.uakron
.edu/amc/DataAnalysis_
Statistics/OldDataStat/IB
LDeviationSD.pdf
http://www.home.ubalt.e
du/ntsbarsh/Businessstat/opre504.htm#rgoodq
uali
http://illuminations.nctm.
org/LessonDetail.aspx?i
d=L621
Content Area: Algebra II
Target Course/Grade level: 11
Unit Title: Inferences and Conclusions from Data
Essential Questions: How do make inferences and draw conclusions from data?
Standards/
CPI’s
S.IC.3
S.IC.4
S.IC.5
S.IC.6
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Recognize the purposes of and
differences among sample surveys,
experiments, and observational
studies; explain how randomization
relates to each.
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.
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Students will understand the differences
between experimental and observational
studies.
Class discussion.
Evaluation of student
projects
http://serc.carleton.edu/
sp/library/datasim/exam
ples/cokepepsi.html
Students will learn the proper sample sizes
required for certain margin of error through
estimating population parameters.
Class discussion.
Student worksheets
http://www.rad.jhmi.edu
/jeng/javarad/samplesize
/
Class discussion.
Student worksheets
Compare the average
height of males and
females in your school.
Use data from a randomized
experiment to compare two
treatments; use simulations to decide
if differences between parameters are
significant.
Students will compute the sample statistics for
two different treatments and use the result to
compare whether or not there is a significant
difference between the population parameters.
Evaluate reports based on data.
Students will understand how to relate a pvalue to decision making.
18
Class discussion.
Evaluation of student
projects
http://www.aei.org/files/
2011/11/02/-assessingthe-compensation-ofpublicschoolteachers_19282337242.
pdf
Content Area: Algebra II
Target Course/Grade level: 11
Unit Title: Inferences and Conclusions from Data
Essential Questions: How do make inferences and draw conclusions from data?
Standards/
CPI’s
S.MD.6 (+)
S.MD.7 (+)
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Use probabilities to make fair
decisions (e.g., drawing by lots, using
a random number generator).
Analyze decisions and strategies
using probability concepts (e.g.,
product testing, medical testing,
pulling a hockey goalie at the end of
a game).
Students will understand probability
distribution and it’s applications in decision
making.
Using probability concepts to compute the
odds of winning , life insurance , and business
Decisions.
19
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Class discussion.
Student worksheets
http://www.purplemath.c
om/modules/probability.h
tm
Class discussion.
Student worksheets
http://illuminations.nctm.
org/LessonDetail.aspx?i
d=L621