Download Total Number of Days

UNIT 1 - POLYNOMIALS
Total Number of Days: 15 days (A and B days meet alternate days) Grade/Course: 11/Algebra 2
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ESSENTIAL QUESTIONS
How are the real solutions of a quadratic
equation related to the graph of the related
quadratic function?
What does the degree of a polynomial tell you
about its related polynomial function?
For a polynomial function, how are factors,
zeros and x-intercepts related?
For a polynomial function, how are factors and
roots related?
PACING
1
1 day
Q1
CONTENT
Unit 1 PreAssessment
1. Complex
number
system
SKILLS
 Complex number
system
 Quadratic Functions
with Complex
Solutions
 Functions
 Polynomials
Find the value of i raised
to a power.
Example 1: Evaluate i17.
ENDURING UNDERSTANDINGS
 A basis for the complex numbers is a number whose square is -1.
 Every quadratic equation has complex number solutions.
 Knowing the zeros of polynomial functions can help you understand the
behavior of its graph.
 The degree of a polynomial equation tells you how many roots the equation
has.
 You can use much of what you know about multiplying and dividing
fractions to multiply and divide rational expressions.
 When solving an equation involving rational expressions multiplying by the
common denominator can result in extraneous solutions.
RESOURCES
LEARNING
STANDARDS
Pearson
ACTIVITIES/ASSESSME
Pearson
(CCCS/MP)
OTHER
NTS
(e.g., tech)
N.CN.1, 2, 7, 9
Rewrite questions
A.SSE.1,
similar to the Unit 1 test.
A.APR.A.1,2,3
15 MC, 5 SR, 5 OE
MP 1-8
N.CN.1
Know there is a
complex number i
such that i2 = −1,
and every
complex number
has the form a +
bi with a and b
real.
Algebra 2
Student
Textbook
Section 4-8
Basic:
Problems 1-7
EXS: 8-46,
48, 50, 56,
http://www.suitc
aseofdreams.net/
Powers_i.htm#A1
Algebra Lab
Algebra 2
Student Textbook
Section 4-8 Solve It
http://www.regen
Page 248 or PowerAlgebra
tsprep.org/Regent
s/math/algtrig/A
TO6/powerlesson.
htm
(textbook website)
Algebra 2
Interactive Digital Path
Chapter 4
MP 2, 7
57, 73-89
Average:
Problems 1-7
EXS: 9-43
odd, 45-69,
73-89
BASIC
Using the Distributive
SKILLS
Property for problem
REVIEW
solving
PARCC/HSPA
PREP
Last
1/3 of
the
period.
A –CED.1
Create equations
and inequalities
in one variable
and use them to
solve problems.
MP 4, 2
Vocabulary
Support
PowerAlgebra
(textbook website)
Algebra 2
Other Resources
Teacher
Resources
Advanced:
Chapter 4
Problems 1-7
Additional
EXS: 9-43,
Vocabulary
45-72, 73-89
Support 4-8
Review of the WORKSHEET:
http://tullyschools.
distributive
org/hsteachers/dne
property
uman/IntegratedAlg
Algebra 1
ebra/IntegratedAlge
textbook pg
braNotes/01Septem
96 Problem
ber/008ChapterWo
rdProblems/Chapte
3 or
PowerAlgebr rWordProblems.pdf
a (textbook
website)
Algebra 1
Interactive
Digital Path
Chapter 2
Chapter 2-3
View
Instruction
Problem 3
Chapter 4-8 View
Solve it
Assessments
Quiz – Teacher created
 Students will create
the pattern of
powers of i.
 Questions on finding
the value of i raised
to a power.
Example: Half the sum
of six times a number
and eighteen is the same
as twice the number less
twenty.
2. Complex
number
system
Use the relation i2 = –1
and the commutative,
associative, and
distributive properties
to add, subtract, and
multiply complex
numbers.
Example 1:
Evaluate
(8 + 3i) + (–1 – 5i).
2 days
Q 2,3,4
Example 2:
Evaluate
(8 + 3i) – (–1 – 5i).
Example 3:
Evaluate
(8 + 3i)(–1 – 5i).
N.CN.2
Use Properties of
operations to add,
subtract, and
multiply complex
numbers
MP 2, 7
Algebra 2
Student
Textbook
Section 4-8
Basic:
Problems 1-7
EXS: 8-46,
48, 50, 56,
57, 73-89
Average:
Problems 1-7
EXS: 9-43
odd, 45-69,
73-89
Advanced:
Problems 1-7
EXS: 9-43,
45-72, 73-89
http://www.regents
prep.org/Regents/
math/algtrig/ATO6
/lessonadd.htm
Algebra Lab
PowerAlgebra (textbook
website)
Algebra 2 Textbook
Interactive Digital Path
Chapter 4
Chapter 4-8 View
Instruction Problems 3,
http://www.regents
3 Alternate, 4
prep.org/Regents/
http://www.regents
prep.org/Regents/
math/algtrig/ATO6
/multlesson.htm
math/algtrig/ATO6
/practicepageadd.ht
m
http://www.regents
prep.org/Regents/
math/algtrig/ATO6
/multprac.htm
Section A pg 34, Student
Activity 3, Powers of i
http://www.projectmaths.ie/
documents/teachers/tl_comp
lex_numbers.pdf
Assessment
Quiz - Teacher created
 One of each to add,
subtract, and
multiply complex
numbers.
BASIC
SKILLS
REVIEW
PARCC/HSPA
PREP
Last
1/3 of
the
period.
Factoring Trinomials
where a = 1
Example 1:
p2 + 13p + 40
Example 2:
n2 – 16n + 60
Example 3:
x2 – 14x + 48
Example 4:
x2 – 2x – 35
A.SSE.A.1a
Interpret parts of
an expression,
such as terms,
factors, and
coefficients.
MP 7
Extra
practice
Algebra 1
review
section 8-5
PowerAlgebra
(textbook
website)
Algebra 2
Interactive
Digital Path
Chapter 8
Chapter 8-5
View
Solve it
Instruction
Problems 1
to 5
Classwork
http://www.regents
prep.org/Regents/
math/ALGEBRA/AV
6/Ltri1.htm
http://www.youtub
e.com/watch?v=aYI
UQ-6IJu8
http://www.regents
prep.org/Regents/
math/ALGEBRA/AV
6/PracFact2.htm
Algebra Lab
TI-84 Activity
http://mathbits.com/MathBit
s/TISection/Algebra1/Factori
ng.htm
Homework
http://www.kutasoftware.co
m/FreeWorksheets/Alg1Wor
ksheets/Factoring%201.pdf
3. Quadratic
Functions
with
Complex
Solutions
Solve quadratic
equations using the
quadratic formula.
Example 1:
x2 – 2x + 10 = 0
Example 2:
x2 – 6x = –9
2 days
Q 5,6,7
N.CN.7
Solve quadratic
equations with
real coefficients
that have
complex
solutions.
MP 2, 7
Algebra 2
Textbook
TE Lesson 47 pg 240-244
Basic:
Problems 1-4
EXS: 11-42,
57-59, 67,
78-90
Average:
Problems 1-4
EXS: 11-37
odd, 39-69,
78-90
Advanced:
Problems 1-4
EXS: 11-37
odd, 39-77,
78-90
http://www.virtual
nerd.com/algebra2/quadratics/formu
ladiscriminant/quadr
aticformula/complexsolutions-quadraticformula-Example
Algebra Lab
Algebra 2
Solve It - Text pg 240 or
PowerAlgebra (textbook
website)
Algebra 2
Interactive Digital Path
Chapter 4
http://www.regents Chapter 4-7 View
prep.org/Regents/
Solve it
math/ALGEBRA/AE
5/indexAE5.htm
http://terzicmath.w
eebly.com/uploads/
5/7/3/3/5733011/
real-and-complexsolutions.pdf
Algebra Lab
Dynamic Activity at
same website as above
Assessment
Quiz - Teacher created
quiz – three questions –
all with complex
solutions including one
that can be solved by the
square root method.
BASIC SKILLS
REVIEW
PARCC/HSPA
PREP
Applications of Percents
Create equations
and inequalities
in one variable
and use them to
solve problems.
Last
1/3 of
the
period.
Algebra 2
text
Basic Review
Student Text
pg 972
Worksheet:
Application problems
http://teachers.s with sales discount,
duhsd.net/mlew markup, and sales tax.
is1/syllabus_file
s/PA7/Chapter
%209/PA7%20
Worksheetdiscounts_markups%203.pdf
5-6
ALL
MP 4,2
4. Functions
1 day
Q8,9,10
A –CED.1
Identify what parts of
equations represent.
Example 1:
C = M – x/100 * M
The equation above
represents the final cost
of an item after a
discount. Which part of
the formula is the
discount?
Example 2:
The expression P(1.05)2
gives the number of
dollars in an investment
account over years after
the initial amount is
invested. The account
earns a simple annual
interest.
a. What does 2 represent
N.CN.9
Know the
Fundamental
Theorem of
Algebra; show
that it is true for
quadratic
polynomials.
MP 2
1. C = P +
x
*P
100
The equation above
represents the final
cost of an item after
sales tax. Which
part of the formula
is the tax?
2. The expression
7000(1.02)t gives
the number of
dollars in an
investment account
over years after the
initial amount is
invested. The
account earns a
simple annual
interest.
a. What does 7000
represent in the
context of the
problem?
b. What does 1.02
Algebra Lab
Take some word
problems from the web
that are similar to the
ones on the test and
write questions about
the word problems.
Enrichment
Have students create
their own problems and
solutions.
in the context of the
problem?
b. What does 1.05
represent in the context
of the problem?
BASIC SKILLS
REVIEW
PARCC/HSPA
PREP
Example 3:
A 30-ounce solution that
is 25 percent acid has x
ounces of pure acid
added to it. The
following expression is
used to answer some
questions about the
mixture.
(0.25(30) + x)/(30 + x)
a. What does 30 + x
represent?
b. What does 0.25(30) +
x represent?
Applications of adding
fractions
Last
1/3 of
the
period.
Part of a MID UNIT
period TEST
Mid unit test to
determine areas of
weakness that need to
be addressed before the
represent in the
context of the
problem?
3. A 25-ounce
solution that is 55
percent acid has x
ounces of pure acid
added to it. The
following
expression is used
to answer some
questions about the
mixture.
0.55(25) + x
25 + x
a. What does 25 + x
represent?
b. What does
0.55(25) + x
represent?
7.EE.3
Solve multi-step reallife and mathematical
problems posed with
positive and negative
rational numbers in
any form (whole
numbers, fractions,
and decimals), using
tools strategically.
N.CN.1, 2, 7, 9
MP 7, 5
Algebra 2
Basic Review
Student Text
pg 973
Example 1
and Q 1, 2, 5
Teacher created
material.
Teacher created
material.
Example problem:
Paul practices a tenth of
an hour of basketball on
Friday, two and a
quarter hours of
basketball on Saturday,
and one and five-sixths
hours of basketball on
Sunday. How many
hours of basketball did
he practice altogether?
Test to determine skills
that need reteaching.
Use problems similar to
state unit test.
5. Polynomi
als
Write polynomial
expressions.
Example 1:
Rewrite the expression
6x + [2x/(x+5)] as one
rational expression that
is equivalent to the
expression for all x
values, where x ≠ –5.
2 days
Q11, 12
Example 2:
A box in the shape of a
rectangular prism has a
width that is 5 inches
greater than the height
and a length that is 2
inches greater than the
width. Write a
polynomial expression in
standard form for the
volume of the box.
Explain the meaning of
any variables used.
the pre-assessment that
have been covered.
A.SSE.1
Interpret expressions
that represent a
quantity in terms of
its context.
a. Interpret parts of
an expression, such
as terms, factors, and
coefficients.
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.
MP 3, 6
EXAMPLE 1
Basic/ELLS
Rewrite the
expression
3x + [2x/5]
as one
rational
expression
that is
equivalent to
the
expression
for all x
values.
EXAMPLE 2
Basic/ELLS
Regular
Rewrite the
expression
7x +
[5x/(x+8)] as
one rational
expression
that is
equivalent to
the
expression
for all x
values,
where x ≠ –8.
Enrichment
Example 2
Give questions
 Two questions to
similar to
answer similar to the
Example 2 but
basic and regular.
some have sides
that are less than  A third question
where students are
the height.
required to explain
These questions
how the process is
should also
similar to finding the
include some
common
with fractions
denominator of a
for the change.
regular fraction.
Enrichment
Give questions
similar to
Example 2.
Regular
Give questions
similar to
Example 2 but
some have sides
that are less than
the height.
Assessment
Example 1
 Two questions to
answer similar to the
basic and regular.

A third question
where students are
required to explain
how the process is
similar to finding the
common
denominator of a
regular fraction.
Rewrite the
expression
7x +
[5x/(x+8)] as
one rational
expression
that is
equivalent to
the
expression
for all x
values,
where x ≠ –8.
Last
1/3 of
the
period.
BASIC SKILLS
REVIEW
PARCC/HSPA
PREP
Polynomials
Solving equations using
the distributive property
and combining like
terms.

1 day
Q 13
Example 2:
(8x3 - 8x - 4) - (-16x6 +
9x3 - 6x2)
Example 3:
(-3x + 8) (-4x3 + 8x2 -
Teacher created
material.
Create equations
and inequalities
in one variable
and use them to
solve problems.
MP 4,2
A.APR.A.1
Arithmetic operations
with polynomials.
Example 1:
(-14x7 + 19x6 - 17) +
(5x5 - 10x4 + 18)
A –CED.1
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
Basic
(2r + 9r4) –
(8r - 7r2 +
4r4)
Regular
(3b3 + 8) –
(9b3 + 7 + b4)
+ (5b4 + 6)
Enrichment
(4b5 – 3b3 +
8) – (4b4 +
http://www.you
tube.com/watch
?v=hVCVW2cfcs
A
Example:
The perimeter of a
rectangle is 104m. The
length is 7m more than
twice the width.
What are the dimensions
of the rectangle?
http://www.mat
hsisfun.com/alge
bra/polynomials
-addingsubtracting.html
Algebra Lab
http://www.regentspre
p.org/Regents/math/AL
GEBRA/teachres/TRcub
es.htm
http://www.kut
asoftware.com/F
reeWorksheets/
Alg1Worksheets
/Adding+Subtra
cting%20Polyno
mials.pdf
http://www.regentspre
p.org/Regents/math/AL
GEBRA/AV2/indexAV2.h
tm
Assessment
2x + 12)
polynomials.
MP 3
9b3 + 7 + b) +
(5b2 + 6)
Verify results
http://educa
tion.ti.com/e
n/us/activity
/detail?id=B
E17AD49E4E
14CDA81B9B
A66A3587E1
0
BASIC SKILLS
REVIEW
PARCC/HSPA
PREP
Using the TI-84 to find
the roots of quadratics.
A.APR.3
Example 1
http://www.gle
ncoe.com/sec/m 
ath/algebra/alge
bra1/algebra1_0
4/study_guide/p 
dfs/alg1_pssg_G
063.pdf
Teacher created
material.
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.
Last
1/3 of
the
period.
MP 2
Polynomials
1 day
Q14
Determine the roots of
polynomial functions.
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.
MP 7
Algebra 2
Basic,
Regular,
Advance
Page 355
question 4
http://www.ck1
2.org/book/CK12-Algebra-I--Honors/r3/secti
on/7.9/
Two questions to
answer similar to the
basic and regular.
At least one should
not have like terms
in each expression.
http://mathbits.com/Ma
thBits/TISection/Algebr
a2/zerofunctions.htm
Students will be given
quadratics to find the
roots using the
calculator. Then
students will be given a
cubic and quartic to do
the same.
Algebra Lab
Algebra 2
Teachers Edition
pg 346
Performance Task 3
http://www.aug
ustatech.edu/ma 
th/molik/Polyno
mialFunctions.p 
df
Assessment
Given a graph,
determine the roots.
Given a polynomial
expression,
determine the roots.
Last
1/3 of
the
period.
BASIC SKILLS
REVIEW
PARCC/HSPA
PREP
Multiplying and
factoring perfect square
trinomials and
differences of squares.
A.APR.3
http://www.the
mathpage.com/a
lg/differencetwo-squares.htm
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.
MP 3
Polynomials
Difference of Squares
Difference of Cubes
Sum of Cubes
2 days
Q15
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.
MP 7
Last
1/3 of
the
period.
BASIC SKILLS
REVIEW
PARCC/HSPA
PREP
Write the equations of
lines.
A.CED.2
Create equations in
two or more
Algebra 2
Student
Textbook
Section 5-3
Basic:
Problems 1-4
EXS: 11-35
odd, 37, 38
Average:
Problems 1-4
EXS: 25-35
odd, 37, 38,
39-49 odd,
51-57 which
by class)
Advanced:
Problems 1-4
From
Average plus
58-60
Student
Textbook
Section 2-3 &
2-4
http://www.the
mathpage.com/a
lg/perfectsquaretrinomial.htm
http://www.mat
hsisfun.com/alge
bra/polynomials
-difference-twocubes.html
Example:
Multiply
(x + 9)(x – 9)
(x + 6)2
Factor
x2 – 100
9x2 – 24x + 16
Algebra Lab
Algebra 2
Teachers Edition
pg 346
Performance Task 3
http://www.mat
hsisfun.com/defi
nitions/differenc
e-ofsquares.html
Assessment
Given polynomials,
students will determine
if they are Difference of
Squares,
Difference of Cubes, Sum
of Cubes.
http://www.edu
cation.com/stud
yhelp/article/pre
Example:
What is the equation of
the line containing the
variables to
represent
relationships
between quantities;
graph equations on
coordinate axes with
labels
and scales.
MP 4, 2
Polynomials
Linear Factors and End
Behavior
1 day
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.
MP 7
Q16,17,
18
Last
1/3 of
the
BASIC SKILLS
REVIEW
PARCC/HSPA
PREP
Counting Principle
S.CP.9
Use permutations
Selected
problems
should be
determined
by the skills
of the class.
-calculus-helpslope-equationline/
http://www.edu
cation.com/stud
yhelp/article/pre
-calculus-helppre-calculuschapter-1/
Algebra 2
http://www.pur
Student
plemath.com/m
Textbook
odules/polyends
Section 5-1 & .htm
5-2
Basic:
Problems 1-4
EXS: pg 285
9-39 odd
Average:
Problems 1-4
EXS: pg 286
40-54
Advanced:
Problems 1-4
From
Average plus
pg 287 55-57
Student
Textbook
Section 11-1
points (0, −1) and (5, 1)?
Find an equation of the
line containing the point
(−1, −5) and parallel to
the line y = 2 x − 4.
Algebra Lab
Algebra 2
Teachers Edition
pg 280
Solve it or
PowerAlgebra (textbook
website)
Algebra 2
Interactive Digital Path
Chapter 5
Chapter 5-1 View
Solve it
Assessment
 Given a graph,
determine the roots.
 Given a polynomial
expression,
determine the roots
and describe the end
behavior.
http://www.regents Example:
prep.org/Regents/
A movie theater sells 3
math/ALGEBRA/AP
sizes of popcorn (small,
R1/PracCnt.htm
period.
and combinations
to compute
probabilities of
compound events
and solve
problems.
All: Problem
1
EXS: pg 678
9-11
medium, and large) with
3 choices of toppings (no
butter, butter, extra
butter). How many
possible ways can a bag
of popcorn be
purchased?
MP 2
Last
1/3 of
the
period.
Basic Skills
Mixed problem solving
PARCC/HSPA problems based on unit
Prep
basic skill review.
Teacher created
material.
Quiz on Basic Skills
Teacher created
material.
Test to determine skills
that need reteaching.
A.APR.3
S.CP.9
END UNIT
TEST
Part of a
period
A –CED.1, 2
A.SSE.A.1a
7.EE.3
End unit test to
determine areas of
weakness that need to
be addressed before the
state unit test.
A.SSE.1
A.APR.1, 3
Use problems similar to
the pre-assessment that
have been covered since
the mid-unit test.
INSTRUCTIONAL FOCUS OF UNIT
1. Use Properties of operations to add, subtract, and multiply complex numbers.
2.
Solve quadratic equations with real coefficients that have complex solutions.
3.
Show that the fundamental Theorem of Algebra is true for quadratic polynomials
4.
Interpret coefficients, terms, degree, powers (positive and negative), leading coefficients and monomials in polynomial and
rational expressions in terms of context.
5.
Restructure by performing arithmetic operations on polynomial/rational expressions.
6.
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.
7.
Use an appropriate factoring technique to factor expressions completely including expressions with complex numbers.
8.
Explain the relationship between zeros and factors of polynomials and use zeros to construct a rough graph of the function defined
by the polynomial.
PARCC FRAMEWORK/ASSESSMENT

PARCC EXEMPLARS: www.parcconline.org (copy & paste the url or link into search engine)
Complex Numbers: http://www.projectmaths.ie/documents/teachers/tl_complex_numbers.pdf
Polynomials: http://www.projectmaths.ie/students/stran4lc/student-activity-polynomial.pdf
1.

It is given that: 24 + 10𝑥 − 𝑥 2 = 𝑝 − (𝑥 − 5)2 . Find the value of p.
HSPA EXEMPLARS:
Number And Numerical Operations:
http://www.riverdell.org/cms/lib05/NJ01001380/Centricity/Domain/56/Number%20Sense%20Practice%20Problems.pdf
Question 81 - Candra had a gift card for $130. She spent $20.83 on Friday and $56.51 on Saturday using her gift card. Then, on Sunday she returned
an item she bought on Saturday, and $13.76 was credited back to her gift card. How much money is left on Candra's gift card on Monday?

Candra’s friend, Alex, also received a gift card. The amount on his gift card is 20% less than Candra’s. How much does Alex have on his gift
card.

If Alex bought three items and returned one to end up spending 75% of the balance of his card, create four transactions to reflect this.
Patterns And Algebra: http://mslaplantesmathclass.weebly.com/uploads/1/7/3/7/17373129/4.10.2013.pdf
Billie Sue's BBQ had their grand opening this year. The first month they did not turn a profit. However, each month thereafter, they have had steady
profits of $1,600 per month. If x represents the number of months they have profited, which of the following equations represents the amount of
profits after x months?
A. y = 1,600x

B. y = 1,600 – x
C. y = 1,600x + x
D. y = x + 1,600
To make low fat cottage cheese, milk containing 4% butterfat is mixed with 10 gallons of milk containing 1% butterfat to obtain a mixture
containing 2% butterfat. How many gallons of the richer milk is used? If the equation is (.02)(10 + x) = (.01)(10) + (.04)(x) explain how
each of the following relate to the original question.

a. What does (.02)(10 + x) represent?

b. What does (.01)(10) represent?

C. What does (.04)(x) represent?
21ST CENTURY SKILLS
(4Cs & CTE Standards)
9.4.D Business, Management & Administration Career Cluster
9.4.E Education & Training Career Cluster
9.4.F Finance Career Cluster
9.4.N Marketing Career Cluster
9.4.O Science, Technology, Engineering & Mathematics Career Cluster
9.4.P Transportation, Distribution & Logistics Career Cluster
9.4.12.D.2, 9.4.12.E.2, 9.4.12.F.2, 9.4.12.N.2, 9.4.12.O.2, 9.4.12.P.2
Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career opportunities.
9.4.12.D.4, 9.4.12.E.4
Solve mathematical problems and use the information to make business decisions and enhance business management duties.
9.4.12.F.4
Solve mathematical problems to obtain information for decision-making in financial settings.
9.4.12.N.4
Solve mathematical problems to obtain information for marketing decision-making.
9.4.12.O.15
Prepare science, technology, engineering, and mathematics material in oral, written, or visual formats to provide information to an intended audience and to
fulfill the specific communication needs of that audience.
9.4.H(5) Biotechnology Research and Development
9.4.12.H.(5).2
Apply biochemistry, cell biology, genetics, mathematics, microbiology, molecular biology, organic chemistry, and statistics concepts to conduct effective
biotechnology research and development.
9.4.O(1) Engineering and Technology
9.4.12.O.(1).1
Apply the concepts, processes, guiding principles, and standards of school mathematics to solve science, technology, engineering, and mathematics
problems.
9.4.12.O.(1).7
Use mathematics, science, and technology concepts and processes to solve problems in projects involving design and/or production (e.g., medical,
agricultural, biotechnological, energy and power, information and communication, transportation, manufacturing, and construction).
9.4.O(2) Science and Mathematics
9.4.12.O.(2).1
Develop an understanding of how science and mathematics function to provide results, answers, and algorithms for engineering activities to solve problems
and issues in the real world.
9.4.12.O.(2).2
Apply science and mathematics when developing plans, processes, and projects to find solutions to real world problems.
9.4.12.O.(2).3
Assess the impact that science and mathematics have on society when used to develop projects or products.
9.4.12.O.(2).4
Use scientific and mathematical problem-solving skills and abilities to develop realistic solutions to assigned projects, and illustrate how science and
mathematics impact problem-solving in modern society.
9.4.12.O.(2).6
Demonstrate the knowledge and technical skills needed to obtain and succeed in a chosen scientific and mathematical field.
MODIFICATIONS/ACCOMMODATIONS


APPENDIX
(Teacher resource extensions)
1. E-Text, Interactive Digital Resources, Teacher Resources
Login at https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true
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.
SLO 6 Communicate the precise answer to a real-world problem.
7. Look for and make use of structure.
SLO 5 Identify structural similarities between integers and polynomials.
SLO 7 Identify expressions as single entities, e.g. the difference of two squares.
8. Look for and express regularity in repeated reasoning.
SLO 6 Arrive at the formula for finite geometric series by reasoning about how to get from one term in the series to the next.
All of the content presented in this course has connections to the standards for mathematical practices.
* This course includes exponential and logarithmic functions as modeling tools. (PARCC Model Content Frameworks)
UNIT 2 – Expressions and Equations (1)
Total Number of Days: 16 days (A and B days meet alternate days) Grade/Course: 11/Algebra 2








ESENTIAL QUESTIONS
What are the operations that apply to all function?
How can Geometric and Analytic representations be
used to describe the behavior of the function?
How are algebraic, numeric, and graphic
representations of functions related?
How does representing functions graphically help you
solve a system of equations?
How does writing equivalent equations help you solve a
system of equations?
What does the degree of a polynomial tell you about its
related polynomial function?
For a polynomial function, how are factors, zeros and xintercepts related?
For a polynomial function, how are factors and roots
related?
PACING
1
CONTENT
Unit 2 PreAssessment
SKILLS
 Exponents and
Radicals
 Rational expression
 Equations in one
ENDURING UNDERSTANDINGS
 You can add, subtract, multiply, and divide functions based on how
you perform these operations for real numbers. One difference,
however, is that you must consider the domain of each function.
 To solve a system of equations, find a set of values that replace the
variables in the equations and make each equation true.
 You can solve a system of equations by writing equivalent systems
until the value on one variable is clear. Then substitute to find the
values of the other variables.
 You can factor many quadratic trinomials into products of two
binomials.
 To find the zeros of a quadratic function, you must set the equation
equal to zero..
 A polynomial function has distinguishing “behaviors”. You can look
at its algebraic form and know something about its graph. You can
look at its graph and know something about its algebraic form.
 Knowing the zeros of polynomial functions can help you understand
the behavior of its graph.
 You can divide polynomials using steps that are similar to the long
division steps that you use to divide whole numbers.
 The degree of a polynomial equation tells you how many roots the
equation has.
RESOURCES
LEARNING
STANDARDS
ACTIVITIES/ASSESSME
OTHER
(CCCS/MP)
Pearson
NTS
(e.g., tech)
N.RN.1, 2
Rewrite questions similar
A.APR.6
to the Unit 2 test.
A.REI.1,6
15 MC, 5 SR, 5 OE
A.SSE.3
1. Exponents
and
Radicals.
2
variable
F.IF.4
 System of Equations
 Equivalent Expressions
 Key features of graphs
1. Solve exponential
N.RN.1
equations.
Explain how the
Ex:
definition of the
1 𝑥
meaning of rational
If (53 ) = 5, what is the
exponents follows
value of x? Explain your
from extending the
reasoning.
properties of
integer exponents
2. Rewrite radical
to those values,
expression in
allowing for a
exponential forms:
notation for
radicals in terms of
Ex:
rational exponents.
Rewrite the
3
expression 5√125 as a N.RN.2
power of 5.
Rewrite
expressions
involving radicals
and rational
exponents using
the properties of
exponents.
MP 1, 8
Algebra 2
Student
Textbook
Section 6-1
Basic:
Problems
1-4
EXS: 10-30,
33-37, 5667
Average:
Problems
1-4
EXS: 11-29
odd, 31-48,
56-67
Advanced:
Problems
1-4
11-29 odd,
31-67
Student
Textbook
Section 6-4
Basic:
Problems
Interactive
Digital Path 61 Roots and 86-1 Radical
Expressions
PowerAlgebra
(textbook
website)
Algebra 2
Interactive
Digital Path
Chapter 6
Chapter 6-1
View
Solve it
Dynamic
Activity
6-4 Rational
Exponents
PowerAlgebra
(textbook
website)
Algebra 2
Interactive
Digital Path
Chapter 6
Chapter 6-4
View
Dynamic
Algebra Lab
Algebra 2
Student Textbook
Section 6-1 Concept Byte
Page 360
Algebra Lab
Student Textbook
Section 6-4 Solve It
Page 381 or on web at
PowerAlgebra (textbook
website)
Algebra 2
Interactive Digital Path
Chapter 6
Chapter 6-4 View
Solve it
Assessment
Three question quiz:
Two calculation questions
similar to the Examples
shown.
One reasoning question
requiring a written
response that shows a
student understands how
the exponent power
relates to the radical.
1-6
EXS: 10-67,
72-82 E,
56-67, 98119
Activity
Average:
Problems
1-6
EXS: 11-65
odd, 67-90,
98-119
Advanced:
Problems
1-6
11-65 odd,
67-119
Basic Skills
PARCC/HSPA
Last 1/3 Prep
of the
period.
2. Rational
expression
3
Simplify radical
expressions
N-RN.A.2
Dividing Polynomials
using long or synthetic
method.
A.APR.6
Ex: Divide
2
A) 4x + 2x + 1 , where
x -2
x ¹ 2?
B) Simplify
Rewrite expressions
involving radicals and
rational exponents
using the properties of
exponents.
MP 4
Rewrite rational
expressions.
Rewrite simple
rational
expressions in
different forms;
write a(x)/b(x) in
the form q(x) +
Student
Textbook
Section 5-4
Basic:
Problems
1-5
EXS: 9-41,
43, 48, 50,
67-85
Teacher
created
material.
This will be a review of
the process to simplify
radicals. This skill will be
applied in the next test
prep.
Interactive
Digital Path 54 Dividing
Polynomials
Algebra Lab
Student Textbook
Section 5-4 Solve It Page
303 or on the web at
http://www.pea
rsonsuccessnet.c
om/snpapp/lear
n/navigateIDP.d
o?method=vlo&i
nternalId=13111
2100000061&is
Html5Sco=false
http://www.pearsonsuccessne
t.com/snpapp/learn/navigateI
DP.do?method=vlo&internalId
=131112100000061&isHtml5
Sco=false
Algebra Lab
x 2 - 3x - 10
x2 - 5x + 6
¸ 2
2
2 x - 11x + 5 2 x - 7 x + 3
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.
MP 1, 2, 3, 6
Average:
Problems
1-5
EXS: 9-39
odd, 40-62,
67-85
Advanced:
Problems
1-5
EXS: 9-39
odd, 40-66,
67-85
Student
Textbook
Section 8-4
Basic:
Problems
1-4
EXS: 8-27,
31-33, 37,
50-67
Average:
Problems
1-4
EXS: 9-35
odd, 27-44,
50-67
Advanced:
Problems
1-4
EXS: 9-25
odd, 27-67
Interactive
Digital Path 84 Rational
Expressions
http://www.pea
rsonsuccessnet.c
om/snpapp/lear
n/navigateIDP.d
o?method=vlo&i
nternalId=13111
2100000094&is
Html5Sco=false
Student Textbook
Section 8-4 Solve It
Page 527 or on web at
http://www.pearsonsuccessne
t.com/snpapp/learn/navigateI
DP.do?method=vlo&internalId
=131112100000094&isHtml5
Sco=false
Click on Solve It Tab
Assessment
Three question quiz:
Two calculation questions
similar to the Examples
shown.
One reasoning question
requiring a written
response where students
will discuss the processes
of long and synthetic
division.
Basic Skills
PARCC/HS
PA Prep
Problem solving with
radicals.
3. Equations
in One
variable
Solving radical
Equations
Last 1/3
of the
period.
2
EX: solve for x
5 - 2 x + 5 = 12
N-RN.A.2
Rewrite
expressions
involving radicals
and rational
exponents using
the properties of
exponents.
MP 4
A.REI.1
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.
A.REI.2
Understand solving
equations as a
process of
reasoning and
explain the
Student
Textbook
Section 65
Basic:
Problems
1-5
EXS: 9-47,
57-60, 6365
Average:
Problems
1-5
EXS: 9-43
odd 45-67,
73-96
Advanced:
Problems
1-5
EXS: 9-43
odd, 45-72
Teacher
created
material.
Three part open ended
question where students
will find the width, area,
and area of a shaded
region where the answers
must be written in radical
form.
Interactive
Digital Path 65 Solving
Square Root
and Other
Radical
Expressions
Algebra Lab
Student Textbook
Section 6-5 Solve It Page
390 or on the web at
http://www.pea
rsonsuccessnet.c
om/snpapp/lear
n/navigateIDP.d
o?method=vlo&i
nternalId=13111
2100000075&is
Html5Sco=false
http://www.pearsonsuccessne
t.com/snpapp/learn/navigateI
DP.do?method=vlo&internalId
=131112100000075&isHtml5
Sco=false
Assessment
Three question quiz:
 Two calculation
questions similar to
the Example shown.
 One reasoning
question requiring a
written response
where students will
discuss why the
solution normally has
± in front of it and in
what situations it is
not needed.
Basic Skills
PARCC/HS
PA Prep
Solving radical word
problems.
Last 1/3
of the
period.
Part of a
period
MID UNIT
TEST
4. System of
Equations
Mid unit test to
determine areas of
weakness that need to
be addressed before the
state unit test.
1. Solve system of linear
equations by graphing.
EX:
3
1
y  x 3
2
1
1
y 
x
6
3
reasoning. Solve
simple rational and
radical equations in
one variable, and
give Examples
showing how
extraneous
solutions may
arise.
N-RN.A.2
Rewrite
expressions
involving radicals
and rational
exponents using
the properties of
exponents.
MP 3
N.RN.1, 2
A.APR.6
A.REI.1, 2
A.REI.6
Solve systems of
linear equations
exactly and
approximately (e.g.,
with graphs),
focusing on pairs of
linear equations in
two variables.
Student
Textbook
Section 3-1
Basic:
Problems
1-4
EXS: 7-28,
30-36 even,
38-43, 53-
Teacher
created
material.
Example: A shop needs
to make a frame where
the height is 1/2 its
width. It is to be enlarged
to have an area of 60.5
square inches. What will
be the dimensions of the
enlargement?
Teacher
created
material.
Test to determine skills
that need reteaching.
Interactive
Digital Path 31 Solving
Systems Using
Tables and
Graphs
http://www.pea
rsonsuccessnet.c
om/snpapp/lear
n/navigateIDP.d
o?method=vlo&i
Algebra Lab
Student Textbook
Section 3-1 Solve It Page
134 or on the web at
http://www.pearsonsuccessne
t.com/snpapp/learn/navigateI
DP.do?method=vlo&internalId
=131112100000075&isHtml5
Sco=false
Algebra Lab
2. Solve the system of
equations algebraically.
EX:
2 x  3y  8
4 x  2y  10
3. Solve system of
equations graphically
and algebraically.
EX:
y = 2x + 5
y = x 2 + 4x - 10
A.REI.7
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.
MP 6
67
Average:
Problems
1-4
EXS: 7-27
odd 29-47,
53-67
Advanced:
Problems
1-4
EXS: 7-27
odd, 29-52
Student
Textbook
Section 3-2
Basic:
Problems
1-5
EXS: 10-43,
53-57, 6780
Average:
Problems
1-5
EXS: 11-41
odd, 43-61,
67-80
Advanced:
Problems
1-5
EXS: 11-41
nternalId=13111
2100000036&is
Html5Sco=false
Interactive
Digital Path 32 Solving
Systems
Algebraically
http://www.pea
rsonsuccessnet.c
om/snpapp/lear
n/navigateIDP.d
o?method=vlo&i
nternalId=13111
2100000037&is
Html5Sco=false
Section 3-1 Dynamic
Activity on the web at
http://www.pearsonsuccessne
t.com/snpapp/learn/navigateI
DP.do?method=vlo&internalId
=131112100000075&isHtml5
Sco=false
Algebra Lab
Student Textbook
Section 3-2 Solve It Page
142 or on the web at
http://www.pearsonsuccessne
t.com/snpapp/learn/navigateI
DP.do?method=vlo&internalId
=131112100000037&isHtml5
Sco=false
Algebra Lab
Section 3-2 Dynamic
Activity on the web at
http://www.pearsonsuccessne
t.com/snpapp/learn/navigateI
DP.do?method=vlo&internalId
=131112100000037&isHtml5
Sco=false
odd, 43-66,
67-80
Basic Skills
PARCC/HSPA
Prep
Problem Solving with
Systems of Linear
Equations
Last 1/3
of the
period.
5. Equivalent
Expression
s.
Use properties of
exponents to simplify
exponential functions.
Ex: Simplify the
following function
()
f x = 3x × 23x+2
2
A.REI.6
Solve systems of
linear equations
exactly and
approximately (e.g.,
with graphs),
focusing on pairs of
linear equations in
two variables.
MP 4,2
A.SSE.3
Choose and
produce an
equivalent form of
an expression to
reveal and explain
properties of the
quantity
represented by the
expression.
c. Use the
properties of
exponents to
transform
expressions for
exponential
functions. For
Example the
expression 1.15t can
Student
Textbook
Section 6-4
Basic:
Problems
1-6
EXS: 10-67,
72-82 E,
56-67, 98119
Average:
Problems
1-6
EXS: 11-65
odd, 67-90,
98-119
Advanced:
Problems
Teacher
created
material.
Example:
Interactive
Digital Path 64 Rational
Exponents
Algebra Lab
Student Textbook
Section 6-4 Solve It
Page 381 or on web at
http://www.pea
rsonsuccessnet.c
om/snpapp/lear
n/navigateIDP.d
o?method=vlo&i
nternalId=13111
2100000073&is
Html5Sco=false
http://www.pearsonsuccessne
t.com/snpapp/learn/navigateI
DP.do?method=vlo&internalId
=131112100000073&isHtml5
Sco=false
Interactive
Digital Path 65 Solving
Square Root
and Other
Radical
Expressions
http://www.pea
rsonsuccessnet.c
At Pinho’s, Sam bought 2
donuts and 5 muffins
spending $14.25. Amy
bought 3 donuts and 2
muffins spending $9. How
much do they charge for a
donut? How much for a
muffin?
Click on Dynamic Activity
Tab
Algebra Lab
Student Textbook
Section 6-5 Solve It Page
390 or on the web at
http://www.pearsonsuccessne
t.com/snpapp/learn/navigateI
DP.do?method=vlo&internalId
=131112100000075&isHtml5
Sco=false
be rewritten as
(1.151/12)12t ≈
1.01212t to reveal
the approximate
equivalent monthly
interest rate if the
annual rate is 15%.
MP 4, 3
1-6
11-65 odd,
67-119
Student
Textbook
Section 6-5
om/snpapp/lear
n/navigateIDP.d
o?method=vlo&i
nternalId=13111
2100000075&is
Html5Sco=false
Assessment
Two question quiz:
 Two calculation
questions similar to
the Example shown.
Basic:
Problems
1-5
EXS: 9-47,
57-60, 6365
Average:
Problems
1-5
EXS: 9-43
odd 45-67,
73-96
Advanced:
Problems
1-5
EXS: 9-43
odd, 45-72
Basic Skills
PARCC/HSPA
Prep
Last 1/3
of the
period.
Multiplying with
scientific notation.
N-RN.A.2
Rewrite
expressions
involving radicals
and rational
exponents using
the properties of
exponents.
Teacher
created
material.
Example: The speed of
light is approximately
3 x 10 8 m/s. How far
does light travel in
6.0 x 101 seconds?
6. Key
features of
graphs
End behavior of a
function.
EX: Find the end
behavior of the function
f(x)=x4 – 4 x3 + 3 x + 25.
2
MP 3, 8
F.IF.4
For a function that
models a
relationship
between two
quantities,
interpret key
features of graphs
and tables in terms
of the quantities,
and sketch graphs
showing key
features given a
verbal description
of the relationship.
MP 4, 2
Last 1/3 Basic Skills
of the PARCC/HSPA
period. Prep
Mixed problem solving
problems based on unit
basic skill review.
N-RN.A.2
A.REI.6
Student
Textbook
Section 5-1
Basic:
Problems
1-4
EXS: 8-39,
40-50 Even,
58-71
Average:
Problems
1-4
EXS: 9-39,
40-54 Even,
58-71
http://hotmath.c
om/hotmath_hel
p/topics/endbehavior-of-afunction.html
Interactive
Digital Path 51 Polynomial
Functions
http://www.pea
rsonsuccessnet.c
om/snpapp/lear
n/navigateIDP.d
o?method=vlo&i
nternalId=13111
2100000075&is
Html5Sco=false
Advanced:
Problems
1-4
EXS: 9-39
odd, 40-71
67
Page 283
Teacher
created
material.
Algebra Lab
Student Textbook
Section 5-1 Solve It
Page 280 or on web at
http://www.pearsonsuccessne
t.com/snpapp/learn/navigateI
DP.do?method=vlo&internalId
=131112100000073&isHtml5
Sco=false
Assessments
Three question quiz:
 Two questions similar
to the Example shown.
 One reasoning
question requiring a
written response
where students will
discuss how they can
sometimes determine
the roots visually.
Quiz on Basic Skills
END UNIT
TEST
Part of a
period
End unit test to
determine areas of
weakness that need to
be addressed before the
state unit test.
A.REI.6, 7
A.SSE.3
F.IF.4
Teacher
created
material.
Test to determine skills
that need reteaching.
INSTRUCTIONAL FOCUS OF UNIT
1. Use properties of integer exponents to explain and convert between expressions involving radicals and rational exponents, using
correct notation. 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.
2. Rewrite simple rational expressions in different forms using inspection, long division, or, for the more complicated Examples, a
computer algebra system.
3. Solve simple equations in one variable and use them to solve problems, justify each step in the process and the solution and in the
case of rational and radical equations show how extraneous solutions may arise.
4. Solve systems of linear equations and simple systems consisting of a linear and a quadratic equation in two variables, algebraically
and graphically.
Write equivalent expressions for exponential functions using the properties of exponents.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.
PARCC FRAMEWORK/ASSESSMENT

PARCC EXEMPLARS: www.parcconline.org (copy & paste the url or link into search engine)
Complex Numbers: http://www.projectmaths.ie/documents/teachers/tl_complex_numbers.pdf
Polynomials: http://www.projectmaths.ie/students/stran4lc/student-activity-polynomial.pdf
It is given that: 24 + 10𝑥 − 𝑥 2 = 𝑝 − (𝑥 − 5)2 . Find the value of p.

HSPA EXEMPLARS:
Number And Numerical Operations:
http://www.riverdell.org/cms/lib05/NJ01001380/Centricity/Domain/56/Number%20Sense%20Practice%20Problems.pdf
Question 81 - Candra had a gift card for $130. She spent $20.83 on Friday and $56.51 on Saturday using her gift card. Then, on Sunday she returned
an item she bought on Saturday, and $13.76 was credited back to her gift card. How much money is left on Candra's gift card on Monday?

Candra’s friend, Alex, also received a gift card. The amount on his gift card is 20% less than Candra’s. How much does Alex have on his gift
card.

If Alex bought three items and returned one to end up spending 75% of the balance of his card, create four transactions to reflect this.
Patterns And Algebra: http://mslaplantesmathclass.weebly.com/uploads/1/7/3/7/17373129/4.10.2013.pdf
Billie Sue's BBQ had their grand opening this year. The first month they did not turn a profit. However, each month thereafter, they have had steady
profits of $1,600 per month. If x represents the number of months they have profited, which of the following equations represents the amount of
profits after x months?
A. y = 1,600x

B. y = 1,600 – x
C. y = 1,600x + x
D. y = x + 1,600
To make low fat cottage cheese, milk containing 4% butterfat is mixed with 10 gallons of milk containing 1% butterfat to obtain a mixture
containing 2% butterfat. How many gallons of the richer milk is used? If the equation is (.02)(10 + x) = (.01)(10) + (.04)(x) explain how
each of the following relate to the original question.

a. What does (.02)(10 + x) represent?

b. What does (.01)(10) represent?

C. What does (.04)(x) represent?
21ST CENTURY SKILLS
(4Cs & CTE Standards)
9.4.D Business, Management & Administration Career Cluster
9.4.E Education & Training Career Cluster
9.4.F Finance Career Cluster
9.4.N Marketing Career Cluster
9.4.O Science, Technology, Engineering & Mathematics Career Cluster
9.4.P Transportation, Distribution & Logistics Career Cluster
9.4.12.D.2, 9.4.12.E.2, 9.4.12.F.2, 9.4.12.N.2, 9.4.12.O.2, 9.4.12.P.2
Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career opportunities.
9.4.12.D.4, 9.4.12.E.4
Solve mathematical problems and use the information to make business decisions and enhance business management duties.
9.4.12.F.4
Solve mathematical problems to obtain information for decision-making in financial settings.
9.4.12.N.4
Solve mathematical problems to obtain information for marketing decision-making.
9.4.12.O.15
Prepare science, technology, engineering, and mathematics material in oral, written, or visual formats to provide information to an intended audience and to
fulfill the specific communication needs of that audience.
9.4.H(5) Biotechnology Research and Development
9.4.12.H.(5).2
Apply biochemistry, cell biology, genetics, mathematics, microbiology, molecular biology, organic chemistry, and statistics concepts to conduct effective
biotechnology research and development.
9.4.O(1) Engineering and Technology
9.4.12.O.(1).1
Apply the concepts, processes, guiding principles, and standards of school mathematics to solve science, technology, engineering, and mathematics problems.
9.4.12.O.(1).7
Use mathematics, science, and technology concepts and processes to solve problems in projects involving design and/or production (e.g., medical,
agricultural, biotechnological, energy and power, information and communication, transportation, manufacturing, and construction).
9.4.O(2) Science and Mathematics
9.4.12.O.(2).1
Develop an understanding of how science and mathematics function to provide results, answers, and algorithms for engineering activities to solve problems
and issues in the real world.
9.4.12.O.(2).2
Apply science and mathematics when developing plans, processes, and projects to find solutions to real world problems.
9.4.12.O.(2).3
Assess the impact that science and mathematics have on society when used to develop projects or products.
9.4.12.O.(2).4
Use scientific and mathematical problem-solving skills and abilities to develop realistic solutions to assigned projects, and illustrate how science and
mathematics impact problem-solving in modern society.
9.4.12.O.(2).6
Demonstrate the knowledge and technical skills needed to obtain and succeed in a chosen scientific and mathematical field.
MODIFICATIONS/ACCOMMODATIONS
APPENDIX
(Teacher resource extensions)
E-Text, Interactive Digital Resources, Teacher Resources
Login at https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true
Mathematical Practices
1. Make sense of problems and persevere in solving them.
SLO 3 Use problems that involve may givens of the need to be composed or decomposed before they can be solved
2. Reason abstractly and quantitatively.
SLO 5 Using properties of exponents to determine if two expressions are equal.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics. *
5. Use appropriate tools strategically.
SLO 6 Use graphing technically when available.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
All of the content presented in this course has connections to the standards for mathematical practices.
* This course includes exponential and logarithmic functions as modeling tools. (PARCC Model Content Frameworks)
UNIT 3 – Expressions and Equations (2)
Total Number of Days: 16 days (A and B days meet alternate days) Grade/Course: 11/Algebra 2




ESENTIAL QUESTIONS
How does representing functions graphically
help you solve a system of equations?
For a polynomial function, how are factors,
zeros and x-intercepts related?
How do you model a quantity that changes
regularly over time by the same percentage?
How can you model periodic behavior?
PACING
CONTENT
SKILLS
ENDURING UNDERSTANDINGS
 To solve a system of equations, find a set of values that replace the variables in
the equations and make each equation true.
 A polynomial function has distinguishing “behaviors”. You can look at its
algebraic form and know something about its graph. You can look at its graph
and know something about its algebraic form.
 Periodic behavior is behavior that repeats over intervals of equal length.
 An angle with a full circle of rotation measure 2π radians.
RESOURCES
STANDARDS
LEARNING
OTHER
ACTIVITIES/ASSESSMENTS
(CCCS/MP)
Pearson
(e.g., tech)
1
Unit 3 PreAssessment
Systems of equations
Arithmetic
Sequences
Geometric Sequences
Inverse of functions.
Functions and their
graphs.
Exponential
functions.
Radian Measures
Trig
A.REI.11
F.BF.2
F.BF.4
F.IF.4
F.IF.7
F.LE.5
F.TF.1
F.TF.2
F.TF.8
F.TF.5
1. Systems of
equations
Determine the
solution from the
graph of the system.
A.REI.11
SECTION 4-9
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
Basic:
Problem 1
Pg 262
Q 8 – 13
EXAMPLE 1:
What is the solution
set?
2
EXAMPLE 2:
For the functions a
and b defined below,
sketch a graph
Rewrite questions similar to
the Unit 2 test.
15 MC, 5 SR, 5 OE
Average:
Problem 1
Pg 262 - 263
Q 8 – 13, 41 46
Advanced:
Problem 1
Pg 262 - 263
Q 8 – 13, 41 –
46, 53-55
Understand
that where
the graphs
intersect is
the solution.
Understand
that when
looking at the
table of values
in the
graphing
calculator the
solutions are
where all the
y values are
the same.
Algebra Lab
Concept Byte pg 477
Questions 1 – 3
Algebra Lab
Concept Byte pg 484-485
Questions 1 – 12
Algebra Lab
Teacher created worksheets
with systems of two
different types of equations
including:
Rational with linear.
Square root with absolute
value.
Last
1/3 of
the
period.
Basic Skills
PARCC/HSPA
Prep
without the use of a
calculator and use
the graph to identify
the solution set to
a(x) = b(x).
a(x) = 4/x
b(x) = 1/2x + 1
EXAMPLE 3:
For the functions
defined above, fill in
the tables of values.
Then give the
solution set
to g(x) = h(x).
Explain your answer.
g(x) = √𝑥 − 4
h(x) = | x – 6 |
Patterns in
mathematics
functions.
Then have students make
up some of their own. They
should graph them and
determine the solution set.
If the solution set is not easy
to find, students should
adjust the parameters of the
problem until it is.
MP 1, 4, 5
8.NS.1
Know that
numbers that are
not rational are
called irrational.
Understand
informally that
every number has
a decimal
expansion; for
rational numbers
show that the
decimal expansion
repeats eventually,
and convert a
decimal expansion
which repeats
eventually into a
Algebra Lab
http://en.wikib
ooks.org/wiki/
SA_NC_Doing_In
vestigations/Ch
apter_6#Numbe
r_Patterns_Activ
ity_1
After covering the patterns,
have students create their
own pattern, then write a
question and solution.
http://wwwrohan.sdsu.edu
/~ituba/math3
03s08/mathide
as/mmi10_01_0
2.pdf
This should also include a
paragraph or two in writing
where students can explain
they understand the
process.
rational number.
2. Arithmetic
Sequences
2
Basic Skills
PARCC/HSPA
Prep
Last
1/3 of
the
period.
MP
Write the explicit and F.BF.2
recursive form of an
arithmetic sequence. Write arithmetic
and geometric
EXAMPLE:
sequences both
recursively and
Julia makes $2.00 an with an explicit
hour for first hour of formula, use them
work, $4.00 her
to model
second hour, $6.00
situations, and
her third hour and so translate between
on. How much
the two forms.
money will she earn
on her 12th hour of
MP 3
work?
Write a recursive and
explicit rule for this
problem.
Combinations and
S.CP.9
Permutations
Use permutations
and combinations
to compute
probabilities of
compound events
and solve
problems.
Section 9-2
Basic:
Problems 1-4
EXS: 7-25, 3135, 49-53, 61,
75-88
http://www.alge
bralab.org/lesso
ns/lesson.aspx?fi
le=algebra_ariths
eq.xml
Algebra Lab
Solve it pg 572 also on
http://www.pearsonsuccessnet.c
om/snpapp/learn/navigateIDP.d
o?method=vlo&internalId=13111
2100000100&isHtml5Sco=false
Dynamic Activity also on
same web site.
Average:
Problems 1-4
EXS: 7-25 odd,
26-62, 75-88
Advanced
Problems 1-4
EXS: 7-25 odd,
26-88
http://www.mat
hsisfun.com/com
binatorics/combi
nationspermutations.ht
ml
Example:
Permutation:
In how many ways can 4 of
7 different kinds of bushes
be planted along a
http://www.rege walkway?
ntsprep.org/Reg
ents/math/algtri
g/ATS5/Lcomb.h
tm
Combination:
How many ways are there to
select 3 bracelets from a box
of 20?
3. Geometric
Sequences
2
Write the explicit and F.BF.2
recursive form of a
geometric sequence. Write arithmetic
EXAMPLE:
and geometric
sequences both
A ball is dropped,
recursively and
and for each bounce
with an explicit
after the first bounce, formula, use them
the ball reaches a
to model
height that is a
situations, and
constant percent of
translate between
the preceding height. the two forms.
After the first
bounce, it reaches a
MP 4, 2
height of 30 feet, and
after the third
bounce it reaches a
height of 10.8 feet.
Section 9-3
Basic:
Problems 1-4
EXS: 7-31, 3644 even, 4850, 59, 63-81
http://www.alge
bralab.org/lesso
ns/lesson.aspx?fi
le=Algebra_GeoS
eq.xml
Algebra Lab
Solve it pg 580 also on
http://www.pearsonsuccessnet.c
om/snpapp/learn/navigateIDP.d
o?method=vlo&internalId=13111
2100000102&isHtml5Sco=false
Dynamic Activity also on
same web site.
Average:
Problems 1-4
EXS: 7-31 odd,
32-59, 63-81
Advanced:
Problems 1-4
EXS: 7-31 odd,
32-62, 63-81
Write an explicit rule
for the height after
the nth bounce, an,
where n represents
the bounce number.
Last
1/3 of
the
period.
Basic Skills
PARCC/HSPA
Prep
Simple probability
S.MD.6
Use probabilities
to make fair
decisions (e.g.,
drawing by lots,
using
a random number
generator).
http://www.mat
hsisfun.com/dat
a/probability.ht
ml
Example:
There are five balls in a bag:
2 red, 2 blue, and 1 white.
What is the probability of
randomly choosing a red
ball?
4. Geometric
Sequences
Write the recursive
formula of a
geometric sequence
in visual form.
Example:
2
Write a recursive
formula for the
pattern shown.
Basic Skills
PARCC/HSPA
Prep
Last
1/3 of
the
period.
Dependent and
Independent Events
F.BF.2
Write arithmetic
and geometric
sequences both
recursively and
with an explicit
formula, use them
to model
situations, and
translate between
the two forms.
S.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.
http://www.skw
irk.com.au/p-c_s12_u-223_t599_c2236/VIC/5/Patt
erns-numberandgeometric/Patter
ns-andalgebra/Patterns
-andalgebra/Maths/
http://www.mat
hsisfun.com/dat
a/probability.ht
ml
Example:
You throw a die twice. What
is the probability of
throwing a six and then a
second six? Are these
independent or dependent
events?
A bowl contains 4 peaches
and 4 apricots. Maxine
randomly selects one, puts it
back, and then randomly
selects another. What is the
probability that both
selections were apricots?
5. Inverse of
functions.
Find the inverse of a
given function.
EXAMPLES:
Write an expression
for the inverse of f(X)
= 4x + 3.
7
What is the inverse
function for
x 2
, where
3
2
f(x) =
x0?
F.BF.4
Section 6-7
Determine the
inverse function
for a simple
function that has
an inverse and
write an
expression for it.
Basic:
Problems 1-6
EXS: 8-43, 4854 even, 65,
75-95
MP 4
Average:
Problems 1-6
EXS: 9-41 odd,
42-67, 75-95
Advanced:
Problems 1-6
EXS: 9-42-74,
75-95
Section 7-3
2
4
find
x–3
f 1  x  , where x > 3.
If f(x) =
Basic:
Problems 1-5
EXS:12-47,
58-61, 72-76
even, 85-98
Average:
Problems 1-5
EXS:13-43
odd, 44-79,
85-98
Advanced:
Problems 1-5
EXS:13-43,
odd, 44-84,
85-98
http://www.alge
bralab.org/lesso
ns/lesson.aspx?fi
le=Algebra_Funct
ionsRelationsInv
erses.xml
http://www.mat
hworksheetsgo.c
om/sheets/algeb
ra-2/functionsandrelations/inverse
-functionsworksheet.php
Basic Skills
PARCC/HSPA
Prep
Mutually exclusive
and non-mutually
exclusive events.
Last
1/3 of
the
period.
6. Functions
and their
graphs.
Describing key
features of functions.
EXAMPLE 1:
2
Describe each of the
following key
features of the graph
of
f(x) = (x – 4)(x –
3)2(x + 1)3
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.
F.IF.4
For a function that
models a
relationship
between two
quantities,
interpret key
features of graphs
and tables in
terms of the
quantities, and
sketch graphs
showing key
features given a
verbal description
of the relationship.
Key features
include: intercepts;
intervals where the
function is
http://www.nuts
hellmath.com/te
xtbooks_glossary
_demos/demos_c
ontent/alg2_com
pound_probabilit
y.html
http://www.mat
hsisfun.com/dat
a/probabilityevents-mutuallyexclusive.html
USE THE
FOLLOWING
SECTIONS2-3
2-5, 4-1, 4-2,
4-3, 5-1, 5-8,
13-1, 13-4,
13-5
Section 5-1
Basic:
Problems 1-4
EXS: 8-39, 4050, even, 51,
58-71
Average:
Problems 1-4
EXS: 9-39 odd,
40-54, 58-71
Advanced:
Example:
A pair of dice is
rolled. What is the
probability that the sum of
the numbers rolled is either
7 or 11?
A pair of dice is
rolled. What is the
probability that the sum of
the numbers rolled is either
an even number or a
multiple of 3?
http://www.you
tube.com/watch?
v=GALfCd-2XRQ
Algebra Lab
Concept Byte pp 459-460
http://learni.st/
users/S33572/b
oards/2366reading-andinterpretinggraphs-commoncore-standard-912-f-if-4
Algebra Lab
Concept Byte pp 477
http://olhs.olentangy.k12.oh.us/t
eachers/kevin_streib/Algebra%2
0I
The above web site has the
solution keys to some really
good questions on this topic.
However, the original
worksheets are not
available.
Example 2:
Use the graph of the
function f to answer
the following
questions.
For what values of x
is f < 0?
increasing,
decreasing,
positive, or
negative; relative
maximums and
minimums;
symmetries; end
behavior; and
periodicity.
Problems 1-4
9-39 odd, 4071
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
exponential and
logarithmic
functions, showing
intercepts and end
behavior, and
trigonometric
functions, showing
period, midline,
and amplitude.
Average:
Problems 1-5
13-35 odd,
36-47, 50-76
MP 6, 4
Section 8-3
Basic:
Problems 1-5
EXS: 13-42,
50-76
Advanced:
Problems 1-5
EXS: 13—35
odd, 36-49,
50-76
USE THE
FOLLOWING
SECTIONS
7-1, 7-2, 7-3,
13-4, 13-5,
13-6, 13-7,
13-8
Basic Skills
PARCC/HSPA
Prep
Geometric
Probability
S.MD.7
Analyze decisions
and strategies
using probability
concepts (e.g.,
product testing,
medical testing,
pulling a hockey
goalie at the end of
a game).
Last
1/3 of
the
period.
7. Exponenti
al
functions.
Modeling with
exponential
functions.
EXAMPLE:
2
The population, in
thousands, of a
certain city can be
modeled by the
function
P t   180 0.94
0.25t
where t is the
number of years
since 2000. What
was the population of
the city in the year
2000? What is the
rate of change of the
city’s population?
http://www.mat
hsisfun.com/dat
a/probabilityevents-mutuallyexclusive.html
F.LE.5
Section 7-2
Interpret the
parameters in a
linear or
exponential
function in terms
of a context.
Basic:
Problems 1-5
EXS: 7-33, 35,
38-40 even,
44-62
MP 1, 2, 6, 5
,
http://www.nuts
hellmath.com/te
xtbooks_glossary
_demos/demos_c
ontent/alg2_com
pound_probabilit
y.html
Average:
Problems: 1-5
EXS: 7-29 odd,
31-41, 44-62
Advanced:
Problems 1-5
EXS: 7-29 odd,
31-62
http://www.alge
bralab.org/lesso
ns/lesson.aspx?fi
le=Algebra_Expo
nentsApps.xml
http://www.ope
ntextbookstore.c
om/precalc/1.3/
Chapter%204.pd
f
Example:
Find the probability that a
randomly chosen point in
the figure lies in the shaded
region. Give all
answers in fraction and
percent forms.
Algebra Lab
Solve it pg 442 also found
on
http://www.pearsonsuccessnet.c
om/snpapp/learn/navigateIDP.d
o?method=vlo&internalId=13111
2100000082&isHtml5Sco=false
Dynamic activity on same
site as above.
Last
1/3 of
the
period.
Basic Skills
PARCC/HSPA
Prep
Measures of Central
Tendency
8. Radian
Measures
Measuring angles
with radians.
EXAMPLE:
Convert as required.
60° =
3 =
1
5
radian
degrees
T.TF.1
Section 13-3
Understand radian
measure of an
angle as the length
of the arc on the
unit circle
subtended by the
angle.
Basic:
Problems 1-4
EXS: 6-34, 3549, 54-68
http://www.rege
ntsprep.org/Reg
ents/math/ALGE
BRA/AD2/measu
re.htm
http://www.keswick.hs.yrdsb.edu
.on.ca/DeptResources/Math/MBF
3CWebsite/Resources/Statistics/
MeasureofCentralTendencyPracti
ce.pdf
http://www.mat
hwarehouse.com
/trigonometry/r
adians/convertdegee-toradians.php
Algebra Lab
Solve it pg 844 also found
on
http://www.pearsonsuccessnet.c
om/snpapp/learn/navigateIDP.d
o?method=vlo&internalId=13111
2100000140&isHtml5Sco=false
Average:
Problems 1-4
7-33 odd, 3550, 54-68
Advanced:
Problems 1-4
7—33 odd,
35-53, 54-68
Last
1/3 of
the
period.
Basic Skills
PARCC/HSPA
Prep
Bar and circle graphs
http://www.mat
hsisfun.com/dat
a/bargraphs.html
http://www.mat
hsisfun.com/dat
a/piecharts.html
Algebra Lab
Pg 982
http://nces.ed.gov/nceskids/crea
teagraph/default.aspx
9. Trig
functions
Use trig identities to
solve problems.
EXAMPLE:
1
If sinθ = 5/7 and cosθ
< 0, then in which
quadrant does the
terminal side of θ lie
when it is placed in
standard position?
What are the values
of cosθ and tanθ ?
Explain your
reasoning and show
your work.
T.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.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.
USE THE
FOLLOWING
SECTIONS
Section 13-4
Section 13-5
Section 13-6
Section 14-1
http://www.ope
ntextbookstore.c
om/precalc/1.3/
Chapter%205.pd
f
Algebra Lab
Solve it pg 851 also found
on
http://www.pearsonsuccessnet.c
om/snpapp/learn/navigateIDP.d
o?method=vlo&internalId=13111
2100000141&isHtml5Sco=false
Dynamic activity on same
site as above.
Algebra Lab
Solve it pg 861 also found
on
http://www.pearsonsuccessnet.c
om/snpapp/learn/navigateIDP.d
o?method=vlo&internalId=13111
2100000143&isHtml5Sco=false
Dynamic activity on same
site as above.
Last
1/3 of
the
period.
Basic Skills
PARCC/HSPA
Prep
Descriptive Statistics
and Histograms
10. Periodic
functions
Modeling trig
functions.
EXAMPLE:
The amount of
daylight, in hours per
day, can be
approximated by the
function
𝑑(𝑡) =
1
75 25
2𝜋
(𝑡
− cos⁡(
5
7
365
+ 9)9))
where t is the
number of days since
the most recent
January 1 (including
January 1). Using this
approximation, what
are the maximum
and minimum
amounts of daylight
throughout the year?
Maximum: _________
Minimum: _________
http://www.mat
hsisfun.com/dat
a/histograms.ht
ml
T.TF.5
Choose
trigonometric
functions to model
periodic
phenomena with
specified
amplitude,
frequency, and
midline.
USE THE
FOLLOWING
SECTIONS
13-4
13-5
13-6
13-7
http://www.ope
ntextbookstore.c
om/precalc/1.3/
Chapter%206.pd
f
Algebra Lab
Pg 983
http://nces.ed.gov/nceskids/crea
teagraph/default.aspx
Algebra Lab
Solve it pg 868 also found
on
http://www.pearsonsuccessnet.c
om/snpapp/learn/navigateIDP.d
o?method=vlo&internalId=13111
2100000144&isHtml5Sco=false
Dynamic activity on same
site as above.
Algebra Lab
Solve it pg 875 also found
on
http://www.pearsonsuccessnet.c
om/snpapp/learn/navigateIDP.d
o?method=vlo&internalId=13111
2100000145&isHtml5Sco=false
Dynamic activity on same
site as above.
END UNIT
TEST
Part of a
period
End unit test to
determine areas of
weakness that need
to be addressed
before the state unit
test.
A.REI.11
F.BF.2
F.BF.4
F.IF.4
F.IF.7
F.LE.5
F.TF.1
F.TF.2
F.TF.8
F.TF.5
Teacher
created
material.
Test to determine skills that
need reteaching.
Use problems similar to the
pre-assessment that have
been covered since the midunit test.
INSTRUCTIONAL FOCUS OF UNIT








Find approximate solutions for the intersections of functions and 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) involving linear, polynomial, rational, absolute value, and exponential functions.
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Determine the inverse function for a simple function that has an inverse and write an expression for it.
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 cases.
Interpret the parameters in a linear or exponential function in terms of a context.
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.
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.
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
PARCC FRAMEWORK/ASSESSMENT

21ST CENTURY SKILLS
(4Cs & CTE Standards)
9.4.D Business, Management & Administration Career Cluster
9.4.E Education & Training Career Cluster
9.4.F Finance Career Cluster
9.4.N Marketing Career Cluster
9.4.O Science, Technology, Engineering & Mathematics Career Cluster
9.4.P Transportation, Distribution & Logistics Career Cluster
9.4.12.D.2, 9.4.12.E.2, 9.4.12.F.2, 9.4.12.N.2, 9.4.12.O.2, 9.4.12.P.2
Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career opportunities.
9.4.12.D.4, 9.4.12.E.4
Solve mathematical problems and use the information to make business decisions and enhance business management duties.
9.4.12.F.4
Solve mathematical problems to obtain information for decision-making in financial settings.
9.4.12.N.4
Solve mathematical problems to obtain information for marketing decision-making.
9.4.12.O.15
Prepare science, technology, engineering, and mathematics material in oral, written, or visual formats to provide information to an intended audience and to
fulfill the specific communication needs of that audience.
9.4.H(5) Biotechnology Research and Development
9.4.12.H.(5).2
Apply biochemistry, cell biology, genetics, mathematics, microbiology, molecular biology, organic chemistry, and statistics concepts to conduct effective
biotechnology research and development.
9.4.O(1) Engineering and Technology
9.4.12.O.(1).1
Apply the concepts, processes, guiding principles, and standards of school mathematics to solve science, technology, engineering, and mathematics
problems.
9.4.12.O.(1).7
Use mathematics, science, and technology concepts and processes to solve problems in projects involving design and/or production (e.g., medical,
agricultural, biotechnological, energy and power, information and communication, transportation, manufacturing, and construction).
9.4.O(2) Science and Mathematics
9.4.12.O.(2).1
Develop an understanding of how science and mathematics function to provide results, answers, and algorithms for engineering activities to solve problems
and issues in the real world.
9.4.12.O.(2).2
Apply science and mathematics when developing plans, processes, and projects to find solutions to real world problems.
9.4.12.O.(2).3
Assess the impact that science and mathematics have on society when used to develop projects or products.
9.4.12.O.(2).4
Use scientific and mathematical problem-solving skills and abilities to develop realistic solutions to assigned projects, and illustrate how science and
mathematics impact problem-solving in modern society.
9.4.12.O.(2).6
Demonstrate the knowledge and technical skills needed to obtain and succeed in a chosen scientific and mathematical field.
MODIFICATIONS/ACCOMMODATIONS

APPENDIX
(Teacher resource extensions)
E-Text, Interactive Digital Resources, Teacher Resources
Login at https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
SLO 7 Make connections between the unit circle and trigonometric functions.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics. *
5. Use appropriate tools strategically.
6. Attend to precision.
SLO 7 Use precise language to explain why trigonometric functions are radian measures of angles traversed counter-clockwise
around the unit circle.
7. Look for and make use of structure.
SLO 3 Use the structure of a function to determine if it has an inverse.
8. Look for and express regularity in repeated reasoning.
All of the content presented in this course has connections to the standards for mathematical practices.
* This course includes the exponential and logarithmic functions as modeling tools. (PARCC Model Content Frameworks)
UNIT 4
MODELING WITH FUNCTIONS
Total Number of Days: 14 days (A and B days meet every other day) Grade/Course: 11/Algebra 2



ESENTIAL QUESTIONS
What are the different types of functions?
How can Geometric and Analytic
representations be used to describe the
behavior of the function?
How are exponential functions and logarithmic
functions related?
PACING
1
1
CONTENT
SKILLS
Unit 4 Pre-  Equation of parabola
Assessmen  Graphing functions
t
 Average rate of change
 Writing functions
 Compare graphs of
different functions
 Combine functions
 Transformations of
graphs
 Exponential and
logarithmic models
1.
Write the equation of
Equation
parabolas using the
of
distance formula.
Parabola
EX:
Q1
Find the equation of a
parabola with focus (0,4)
ENDURING UNDERSTANDINGS
 There are sets of functions, called families, in which each function is a
transformation of a special function called the parent.
 You can use logarithms to solve exponential equations; and conversely, you
can use exponents to solve logarithmic properties.
 You can translate periodic functions in the same way that you translate
other functions.
RESOURCES
LEARNING
STANDARDS
Pearson
ACTIVITIES/ASSESS
Pearson
(CCCS/MP)
OTHER
MENTS
(e.g., tech)
G.PE.2
Rewrite questions
N.Q.2
similar to the Unit 4
F.IF.4, 6, 7, 8, 9
test.
F.BF.1, 3
F.LE.4
G.PE.2
Section 10-2
Derive the equation of a
parabola given a focus
and directrix.
Basic:
Problems 1-5
EXS: 7-33,
38-42 even,
45, 55, 59-69
http://www.m
athwarehouse.
com/quadratic
/parabola/foc
us-anddirectrix-ofparabola.php
http://swh.spr
ALGEBRA LAB
Solve it! Pg 622 and
on Interactive Digital
Path
Here’s Why It Works
Activity (paper
folding)
and directrix y = -3
Average:
Problems 1-5
EXS: 7-33
odd, 34-55,
59-69
ingbranchisd.c
om/LinkClick.a
spx?fileticket=
WxTPGm3oaY%3D&tabi
d=16646
Advanced:
Problems 1-5
EXS: 7-33
odd, 34-69
Last
1/3 of
the
period.
1
Basic
Skills
PARCC/HS
PA Prep
Distance Formula
G.SRT.4
Prove theorems about
triangles. Theorems
include: a line parallel to
one side of a triangle
divides the other two
proportionally, and
conversely; the
Pythagorean Theorem
proved using triangle
similarity.
1.
Equation
of
Parabola
Write the equation of
parabolas in vertex form.
G.PE.2
Section 10-2
Derive the equation of a
parabola given a focus
and directrix.
Q2
Find the equation of a
parabola with focus (0,4)
and directrix x = -3
Basic:
Problems 1-5
EXS: 7-33,
38-42 even,
45, 55, 59-69
EX:
http://www.y
outube.com/w
atch?v=PuqdjX
yBavY
Average:
Problems 1-5
EXS: 7-33
odd, 34-55,
http://www.m
athwarehouse.
com/geometry
/parabola/sta
ndard-andvertexform.php
Teachers Edition pg
623
ASSESSMENT
• Identify the parts
of a parabola
• Explain how the
distance formula
relates to this
• Find an equation
using the distance
formula
Example:
A 50 feet ladder is
placed 35 feet away
from a wall. The
distance from the
ground straight up to
the top of the wall is
60 feet. Check
whether the ladder
reaches the top of
the wall?
ALGEBRA LAB
Dynamic Activity on
Interactive Digital
Path
ASSESSMENT
• Find the equation
of two parabolas
in vertex form.
• One should open
up or down and
the other open left
or right.
59-69
Advanced:
Problems 1-5
EXS: 7-33
odd, 34-69
Last
1/3 of
the
period.
Basic
Skills
PARCC/HS
PA Prep
Real Number Systems
2.
Graphing
Functions
Graph square root, cube
root, and piecewise-defined
functions, including step
functions and absolute
value functions.
N.Q.2
Define appropriate
quantities for the
purpose of descriptive
modeling.
EX 1:
You are given the graph
below; create a word
problem that matches the
information labeled on the
graph.
F.IF.4
For a function that
models a relationship
between two quantities,
interpret key features of
graphs and tables in
terms of the quantities,
and sketch graphs
showing key features
given a verbal description
Q 3, 4, 5
2
N.Q.2
Define appropriate
quantities for the
purpose of descriptive
modeling.
http://www.m
athsisfun.com/
decimalfractionpercentage.ht
ml
Section CB 24
http://www.m
athsisfun.com/
sets/functionfloorceiling.html
Page 90 & 91
Examples 1-5
http://www.m
EXS: 1
athsisfun.com/
sets/functionspiecewise.html
http://www.m
athsisfun.com/
sets/functionexponential.ht
ml
http://a4a.lear
nport.org/foru
• At least on should
open in the
negative direction.
• Explain how the
focus and directrix
will give a clue as
to what direction
the parabola
opens in.
Example:
Which of the
following is NOT a
correct statement?
a) 63% of 63 is less than
63.
b) 115% of 63 is more
than 63.
c) 1/3% of 63 is the same
as 1/3 of 63.
d) 100% of 63 is equal to
63.
ALGEBRA LAB
Worksheets for
practice available on
http://www.ciclt.net/ul/
okresa/MATHEMATICS%
20II%20Unit%205%20St
ep%20and%20Piecewise
%20Functions.pdf
ASSESSMENT
Quiz - Graph a step,
piecewise, and
exponential function
OR
• Use a project to
assess where
students do the
EX 2:
The amount of snow in mm
during a major snow storm
is given by the function
h(x) below, where x is the
time in hours,

0  x  10
2

 3 
10 
h x    x 
10  x  30
10
3 



30  x  50
8



Graph the function h(x)
on the coordinate plane
below.
Describe the change in
the height of the snow
on the ground during
the 50-hour period.
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.
b. Graph square root,
cube root, and piecewisedefined functions,
including step functions
and absolute value
functions.
e. Graph exponential and
logarithmic functions,
showing intercepts and
end behavior.
MP 6, 4
m/topics/piec
ewisefunction-cellphoneactivity?xg_sou
rce=activity
http://www.re
gentsprep.org/
Regents/math
/ALGEBRA/AE
7/ExpDecayL.h
tm
same thing but
with more
detailed
explanation.
Last
1/3 of
the
period.
2
Basic
Skills
PARCC/HS
PA Prep
Conversions
N.Q.2
Define appropriate
quantities for the
purpose of descriptive
modeling.
3. Average Calculate the average rate
rate of
of change for a function.
change
EX 1:
Q 6, 7, 8
Find the average rate of
change for the function f(x)
= 5(3)x on intervals of
length1, starting at 0. What
do you observe about the
rate of change?
EX 2:
A data set with equally
spaced inputs is given.
x
Last
1/3 of
the
period.
Basic
Skills
PARCC/HS
PA Prep
2 3 5
1 1 3
y
2 6 2
Direct Variation
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.
Textbook:
Page 336 Q
20-23
Page 337 Q
35
Page 760 Q
17
http://www.y
outube.com/w
atch?v=XKCZn
5MLKvk
Example:
Average%20R
ate%20of%20
Change/Avera
ge%20Rate%2
0of%20Change
.pdf
http://earthmath.kennes
aw.edu/main_site/revie
w_topics/rate_of_change.
htm
http://www.y
outube.com/w
atch?v=iJ_0nP
UUlOg
http://www.y
outube.com/w
atch?v=iJ_0nP
UUlOg&feature
=youtu.be
MP 1, 4, 5, 7
Change 75 km/hr to
m/min. Show your
process.
ASSESSMENT
Quiz – Rate of
Change from a table
and another from a
graph.
7
4
2
A.CED.1
Create equations and
inequalities in one
variable and use them to
solve problems. Include
equations arising from
linear and quadratic
functions, and simple
rational and exponential
functions.
Lesson 2-2
Pg 71-72
Q 25, 26, 34
http://courses.
dcs.its.utexas.e
du/speedwayfiles/highscho
ol/ASKME/sha
red/template.p
hp?moviePath
=../ALG-1A04321/flash/u
nit02/u02tu08
propDire/&mo
vieName=u02t
u08propDire.s
wf
Example:
The exchange rate
from U.S. dollars to
British pound
sterling (£) was
approximately $1.79
to £1 in 2004.
Write and solve a
direct variation
equation to
determine how many
pounds sterling you
would receive in
exchange for US$90.
4. Writing
functions
Q 9, 10, 11
Write and explain a
function to represent
quantity.
F.IF.8
EX 1:
Write a function for the
volume of the following
shape.
Write a function defined
by an expression in
different but equivalent
forms to reveal and
explain different
properties of the
function.
MP 7
r
h
2
EX 2:
The density, D, of the water
in the ocean is related to
the pressure, p, underwater
and the height, ℎ of the
water column in meters by
𝑝
the function 𝐷 = 𝑔ℎ where
g is the acceleration due to
gravity. (Facts: Density of
sea seawater is about 1025
kg/m3, and g is about 10
m/s2)
Textbook:
Page 414
http://www.so
phia.org/volu
me-ofcompositefigures-3/volume-ofcompositefigures-tutorial
Algebra Lab (for
Example 1)
For the geometric
composite figures,
have students find
the volume of the
composites to start.
http://www.so
phia.org/volu
me-ofcompositefigures-3/volume-ofcompositefigures--5tutorial
http://map.ma
thshell.org/ma
terials/downlo
ad.php?fileid=
684
http://www.m
athwarehouse.
com/geometry
/parabola/sta
ndard-tovertexform.php
Then have students
look at the original
formulas for each
and combine the
formulas without the
numbers from the
problem.
Last have students
use literal equations
to rewrite the
combined formulas
for other variables.


Last
1/3 of
the
period.
Part of a
period
2
Basic
Skills
PARCC/HS
PA Prep
Find the gravity, g,
given the density and
the pressure.
Indicate the type of
proportionality, direct
or inverse, that relates
height to pressure and
density.
EX 3:
Rewrite the equation of the
parabola f (x) = 2x 2 + x - 3 ,
in vertex form and find the
vertex.
Proportional Division
MID UNIT
TEST
Mid unit test to determine
areas of weakness that
need to be addressed
before the state unit test.
5.
Compare
graphs of
different
functions
Compare properties of two
functions each represented
in a different way
(algebraically, graphically,
numerically in tables, or by
A.CED.1
Create equations and
inequalities in one
variable and use them to
solve problems. Include
equations arising from
linear and quadratic
functions, and simple
rational and exponential
functions.
G.PE.2
N.Q.2
F.IF.4, 6, 7, 8
F.IF.9
Compare properties of
two functions each
represented in a different
http://www
.cimt.plymo
uth.ac.uk/pr
ojects/mepr
es/book8/b
k8i7/bk8_7i
3.htm
Teacher
created
material.
Page 860 Q
1-8
http://a4a.lear
nport.org/page
/comparingfunctions
http://a4a.lear
Example:
If three students
share $180 in the
ratio 1 : 2 : 3, how
much is the largest
share?
Test to determine
skills that need
reteaching.
Algebra Lab
Give students
different graphs to
function. Have them
Q 12, 13,
14
verbal descriptions)
EX 1:
Compare the graph of the
two parabolas:
- The graph of f is a
parabola with
vertex (0,0) and
focus (6,0).
-
g:y =
1 2
x
4
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.3
EX 2:
Compare the following
graph to the function
()
g(x) = 2cos x + 1. Include
maximum, minimum,
amplitudes, and periods.
y
x
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.
MP 1, 3, 5, 6, 8
nport.org/page
/comparingfunctions
graph them on the
graphing calculator
and sketch them by
hand.
Have students
describe the
characteristics of
each graph then
compare the
characteristics
across the different
graphs.
Assessment
Give students
different graphs to
function and ask
them to list some key
characteristics. Then
have them compare
pairs of functions.
Last
1/3 of
the
period.
1
Basic
Skills
PARCC/HS
PA Prep
Angles with parallel lines
6.
Combine
functions
Write a function that
combines two relations or
more.
Q 15, 16,
17, 18
EX:
Write a function that gives
the area A, as a function of
x for a square and 2
semicircles:
G.CO.9
Prove theorems about
lines and angles.
Theorems include:
vertical angles are
congruent; when a
transversal crosses
parallel lines, alternate
interior angles are
congruent and
corresponding angles are
congruent; points on a
perpendicular bisector of
a line segment are exactly
those equidistant from
the segment’s endpoints.
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.
http://www.re
gentsprep.org/
Regents/math
/geometry/GP
8/Lparallel.ht
m
Example:
What is the value
of x?
http://www.m
athwarehouse.
com/geometry
/angle/parallel
-lines-cuttransversal.ph
p
http://scc.scds
b.edu.on.ca/St
udents/onlinec
ourses/Sacche
tto/AFIC%20w
eb%20page/p
df%20files/78%20Applicati
ons%20of%20
Logs%20&%2
0Exp.pdf
http://www.purplemath.
com/modules/quadprob.
htm
http://www.nlreg.com/c
ooling.htm
Assessment
Four questions, one
of each related to the
unit test questions.
Last
1/3 of
the
period.
Basic
Skills
PARCC/HS
PA Prep
7.
Transform
ation of
graphs
Q 19, 20,
21
2
Triangle congruence.
EX:
Explain the differences
between the two functions:
f(X) = x2
g(X) = 3x2+4
G.CO.10
Prove theorems about
triangles. Theorems
include: measures of
interior
angles of a triangle sum
to 180°; base angles of
isosceles triangles are
congruent; the segment
joining midpoints of two
sides of a triangle is
parallel to the third side
and half the length; the
medians of a triangle
meet at a point.
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.
MP 3, 5, 8
http://www.re
gentsprep.org/
Regents/math
/geometry/GP
4/Ltriangles.ht
m
Example problem:
ΔABC ≅ ΔDEF as
shown. Find x.
http://www.re
gentsprep.org/
Regents/math
/geometry/GP
4/PracCon2.ht
m
Section 7-2
Basic:
Problems 1-5
EXS: 7-333,
35, 38-40
even, 44-62
Average:
Problems 1-5
EXS: 7-29
odd, 31-41,
44-62
Advanced:
Problems 1-5
EXS: 7-29
odd, 31-62
https://teache
r.ocps.net/theo
dore.klenk/ma
thwebpage/me
dia/calchorizo
ntalandvertical
stretches.pdfh
ow
http://www.y
outube.com/w
atch?v=kFw3X
U0wisU
Algebra Lab
Give students
different functions to
graph the horizontal
and vertical stretch
and shrink.
Students should
come up with a set of
rules so they
understand what
changes in the
function create what
changes in the graph.
Assessment
Quiz – three
questions similar to
the unit test.
Last
1/3 of
the
period.
Basic
Skills
PARCC/HS
PA Prep
Angles in circles
8.
Exponenti
al and
logarithmi
c models
Solve exponential
equations using logarithms.
Q 22, 23,
24
2
EX:
What is the value of x that
satisfy the equation:
32x = 12
G.C.2
Identify and describe
relationships among
inscribed angles, radii,
and chords. Include the
relationship between
central, inscribed, and
circumscribed angles;
inscribed angles on a
diameter are right angles;
the radius of a circle is
perpendicular to the
tangent where the radius
intersects the circle.
F.LE.4
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.
MP 4
Section 7-5
Basic:
Problems 1-6
EXS: 7-45,
46-54 even,
60, 61, 84100
Average:
Problems 1-6
EXS: 7-45
odd, 46-78,
84-100
Advanced:
Problems 1-6
EXS: 7-45
odd, 46-83,
84-100
http://www.re
gentsprep.org/
Regents/math
/geometry/GG
2/CylinderPag
e.htm
Example problem:
A cylinder and a cone
each have a radius of
3 cm. and a height of
8 cm. What is the
ratio of the volume
of the cone to the
volume of the
cylinder?
http://www.e
du.gov.on.ca/e
ng/studentsuc
cess/lms/files/
tips4rm/mhf4
u_unit_5.pdf
Algebra Lab
Instruction problem
1 from Interactive
Digial Path Lesson 75.
http://www.youtube.co
m/watch?v=5R5mKpLsf
Yg
Last
1/3 of
the
period.
Part of a
period
Basic
Skills
PARCC/H
SPA Prep
Mixed problem solving
problems based on unit
basic skill review.
A –CED.1, 2
A.SSE.A.1a
7.EE.3
A.APR.3
S.CP.9
Teacher
created
material.
Quiz on Basic Skills
END UNIT
TEST
End unit test to determine
areas of weakness that
need to be addressed
before the state unit test.
A.REI.6, 7
A.SSE.3
F.IF.4
Teacher
created
material.
Test to determine
skills that need
reteaching.
INSTRUCTIONAL FOCUS OF UNIT








Derive the equation of a parabola given a focus and directrix.
Graph functions that model relationships between two quantities, 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 cases.
Estimate, calculate and interpret the average rate of change of a function presented symbolically, in a table, or graphically over a specified interval.
Rewrite a function in different but equivalent forms to identify and explain different properties of the function.
Analyze and compare properties of two functions when each is represented in a different form (algebraically, graphically, numerically in tables, or by verbal
descriptions).
Construct a function that combines standard function types using arithmetic operations to model a relationship between two quantities.
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.
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.
PARCC FRAMEWORK/ASSESSMENT
OVERVIEW
 http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsAlgII_Nov2012V3_FINAL.pdf
 http://www.parcconline.org/sites/parcc/files/ESTableAlgebra2EOYforPARCC_FinalV2.pdf
EXAMPLES
 https://sites.google.com/site/jacobsmathdepartment/parcc-assessments
 http://www.parcconline.org/samples/mathematics/high-school-mathematics
21ST CENTURY SKILLS
(4Cs & CTE Standards)
9.4.D Business, Management & Administration Career Cluster
9.4.E Education & Training Career Cluster
9.4.F Finance Career Cluster
9.4.N Marketing Career Cluster
9.4.O Science, Technology, Engineering & Mathematics Career Cluster
9.4.P Transportation, Distribution & Logistics Career Cluster
9.4.12.D.2, 9.4.12.E.2, 9.4.12.F.2, 9.4.12.N.2, 9.4.12.O.2, 9.4.12.P.2
Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career opportunities.
9.4.12.D.4, 9.4.12.E.4
Solve mathematical problems and use the information to make business decisions and enhance business management duties.
9.4.12.F.4
Solve mathematical problems to obtain information for decision-making in financial settings.
9.4.12.N.4
Solve mathematical problems to obtain information for marketing decision-making.
9.4.12.O.15
Prepare science, technology, engineering, and mathematics material in oral, written, or visual formats to provide information to an intended audience and to
fulfill the specific communication needs of that audience.
9.4.H(5) Biotechnology Research and Development
9.4.12.H.(5).2
Apply biochemistry, cell biology, genetics, mathematics, microbiology, molecular biology, organic chemistry, and statistics concepts to conduct effective
biotechnology research and development.
9.4.O(1) Engineering and Technology
9.4.12.O.(1).1
Apply the concepts, processes, guiding principles, and standards of school mathematics to solve science, technology, engineering, and mathematics
problems.
9.4.12.O.(1).7
Use mathematics, science, and technology concepts and processes to solve problems in projects involving design and/or production (e.g., medical,
agricultural, biotechnological, energy and power, information and communication, transportation, manufacturing, and construction).
9.4.O(2) Science and Mathematics
9.4.12.O.(2).1
Develop an understanding of how science and mathematics function to provide results, answers, and algorithms for engineering activities to solve problems
and issues in the real world.
9.4.12.O.(2).2
Apply science and mathematics when developing plans, processes, and projects to find solutions to real world problems.
9.4.12.O.(2).3
Assess the impact that science and mathematics have on society when used to develop projects or products.
9.4.12.O.(2).4
Use scientific and mathematical problem-solving skills and abilities to develop realistic solutions to assigned projects, and illustrate how science and
mathematics impact problem-solving in modern society.
9.4.12.O.(2).6
Demonstrate the knowledge and technical skills needed to obtain and succeed in a chosen scientific and mathematical field.
MODIFICATIONS/ACCOMMODATIONS
TEXTBOOK RELATED MATERIALS
 Guided Instruction – Virtual Nerd Videos available on the Interactive Digital Path (see Appendix for login site)
 Algebra 2 Companion – Vocabulary worktext to be used as the lesson is taught
 Reteaching Worksheet – Simplified explanations of the concepts with additional practice
TOOLS
 Graphing Calculators where applicable
 Manipulatives where applicable
 Graphic Organizers
 Sketching the problem where applicable
 Interactive web sites
 You Tube
STRATEGIES
 Highlight important ideas
 Pair or group activities
 Visual and graphic depictions of the problem
 Peer tutoring
 Formative assessments to determine need




Frequent feedback to students
Appropriate pacing of the material
Allow adequate processing time
Monitor student work and responses
TEACHER WEB SITES FOR IDEAS
http://nichcy.org/research/ee/math
http://www.cehd.umn.edu/nceo/presentations/NCTMLEPIEPStrategiesMathGlossaryHandout.pdf
http://floridarti.usf.edu/resources/format/pdf/Classroom%20Cognitive%20and%20Metacognitive%20Strategies%20for%20Teachers_Revised_SR_09.08.10.p
df
http://www2.edc.org/accessmath/resources/strategiestoollist.pdf
http://www.glencoe.com/sec/teachingtoday/subject/intervention_strategies.phtml
APPENDIX
(Teacher resource extensions)
E-Text, Interactive Digital Resources, Teacher Resources
Login at https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true
Mathematical Practices
1. Make sense of problems and persevere in solving them.
SLO 6 Use more complex real-world context than those use in Algebra I.
2. Reason abstractly and quantitatively.
SLO 3 Interpret the rate of change in context.
SLO 8 Convert between exponential and logarithmic models
3. Construct viable arguments and critique the reasoning of others.
SLO 4 Justify why two different forms of a function are equivalent.
4. Model with mathematics. *
5. Use appropriate tools strategically.
SLO 7 Use technology when available.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
All of the content presented in this course has connections to the standards for mathematical practices.
* This course includes the exponential and logarithmic functions as modeling tools. (PARCC Model Content Frameworks)
UNIT 5
Inference and Conclusions from Data
Total Number of Days: 11 days (A and B days meet every other day) Grade/Course: 11/Algebra 2


ESENTIAL QUESTIONS
How can we gather, organize and display data to

communicate and justify results in the real world?
How can we analyze data to make inferences and/or 
predictions, based on surveys, experiments,
probability and observational studies?

PACING
1
CONTENT
SKILLS
Unit 5 Pre-  Sample space, events
Assessment
outcomes, unions,
intersections and
complements
 Independent events
 Conditional probability and
independence
 The definition of conditional
probability.
 Random sample, statistic,
parameter, population and
sample
 The meaning of theoretical
and experimental statistics
 Survey, an experiment, and
an observational study
ENDURING UNDERSTANDINGS
You can describe and compare sets of data using various statistical
measures, depending on what characteristics you want to study.
Standard deviation is a measure of how far the numbers in a data set
deviate from the mean.
You can get good statistical information about population by studying
a sample of the population.
RESOURCES
LEARNING
STANDARDS
Pearson
ACTIVITIES/ASSE
Pearson
(CCCS/MP)
OTHER
SSMENTS
(e.g., tech)
S.CP.1, 2, 5, 6
Rewrite questions
S.IC.1, 2, 3, 4, 5, 6
similar to the Unit
4 test.
 Mean, proportion and
margin of error
 Conduct an experiment or
simulation and the meaning
of significance
Describe the union and
intersection of events, and the
complement of an event.
1
1. Sample
space,
events
outcomes,
unions,
EX:
intersectio
ns and
complemen
ts
Q 1,2
Use the calendar above to list
the outcomes in the events “a
date after April 15 and not on a
Monday or Saturday”
Last
1/3 of
the
period.
1
S.CP.1
NONE
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”).
Find:
List the
outcomes of
multiple
events
MP 2, 4
Basic Skills
PARCC/HS
PA Prep
3D Geometry
G.GMD.3
Use volume formulas
for cylinders,
pyramids, cones, and
spheres to solve
problems.
2.
Independe
nt events
Justify that two events are
S.CP.2
independent through the use of Understand that two
probability rules.
events A and B are
ALGEBRA 1
TEXT CB 125
http://www.y
outube.com/
watch?v=2Rx
W3UWpi2c
http://www.v
irtualnerd.co
m/commoncore/hssstatisticsprobability/H
SS-CPconditionalprobabilityrules/A/1/sa
mple-spacedefinition
http://www.virtualne
rd.com/commoncore/hss-statisticsprobability/HSS-CPconditionalprobabilityrules/A/2/dependentindependent-eventsExample
http://www.
mathopenref.
com/cubevol
ume.html
Example:
If a cube has a
volume of
64cu.cm, the
length of ONE edge
would =
A. 6 cm. B. 4 cm. C.
8 cm. D. 16 cm.
http://www.y
outube.com/
watch?v=WD
P_O3msUXk
http://www.illustrati
vemathematics.org/ill
ustrations/950
Q 3,4,5
EX:
50 g
100
g
200
g
Total
independent if the
probability of A and B
occurring together is
Tea Packe Instan Tota the product of their
bag
t19
tea t4tea l probabilities, and use
3
s
34
0
59
this characterization to
16
determine if they are
24
100 independent.
Use the frequency table above
to find the probability that a
person buys:
a) Instant tea
b) 100g
tea
c) 200 g Tea bags
c) 50g
packet tea
EX 2: The table below shows
the enrollment in art and
biology classes at a small
school.
Enrolled
in
Biology
classes
Did not
enroll
in biology
classes
Enrolled
in
Art
classes
Did not
enroll
in art
classes
x
54
45
81
What is the value of x if the
events “selected student is
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.
S.CP.4
Construct and
interpret two-way
frequency tables of
data when two
categories are
associated with each
object being classified.
Use the two-way table
Section 11-4
Problems 14
Basic:
EXS: 8-26,
34-49
Average:
EXS: 9-19
odd, 20-31,
34-49
Advanced:
EXS: 9-19
odd, 20-49
http://www.cpalms.o
rg/RESOURCES/URLr
esourcebar.aspx?Reso
urceID=vRQBCoxzGfo
=D
enrolled in Art classes” and
“selected student is enrolled in
Biology classes” are
independent? Show your work.
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.
MP 2, 4
Last
1/3 of
the
period.
Basic Skills
PARCC/HS
PA Prep
Maximize Area
G.MG.3
Apply geometric
methods to solve
design problems (e.g.,
designing
an object or structure
to satisfy physical
constraints or
minimize cost;
working with
http://cims.n
yu.edu/~kiryl
/Calculus/Sec
tion_4.5-Optimization
%20Problems
/Optimization
_Problems.pdf
Example:
John has 100 feet
of fencing and
wants to fence off
the largest
possible space.
John says a circle
would be best, but
his cousin Jack
says a square
typographic grid
systems based on
ratios).
3.
Conditional
probability
and
independe
nce.
Recognize conditional
probability and independence
in everyday situations.
EX 1:
Q 6,7,8
1
A checkerboard has 64 sectors
of equal size, with 32 white
sectors and 32 black sectors.
When throwing a coin on the
board, the coin is equally likely
to land on a white sector or a
black sector. A boy throws a
coin four times and lands on
black. He guesses that the next
time the coin will land on
black. Is his guessing accurate?
Why or why not?
would give you the
largest space. Who
is correct? Draw
diagrams, show
work, and explain
your solution.
S.CP.5
Sect 11-4
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.
Problems 14
MP 2, 4
Basic:
EXS: 8-26,
34-49
Average:
EXS: 9-19
odd, 20-31,
34-49
Advanced:
EXS: 9-19
odd, 20-49
http://www.youtube.c
om/watch?v=tbBW2V
VFgso
EX 2:
There are 6 black pens and 8
blue pens in a jar. If you take a
pen without looking and then
take another pen without
replacing the first. Explain why
the two events are not
independent. Describe the
change that could make them
independent.
Last
1/3 of
the
period.
1
Basic Skills
PARCC/HS
PA Prep
3D Geometry
G.GMD.3
Use volume formulas
for cylinders,
pyramids, cones, and
spheres to solve
problems.
4. The
definition
of
conditional
probability.
Compute the probability of A
or B using the Addition Rule
for probability.
S.CP.6
Section 11-3
Problems 15
Q 9,10,11
A bag contains 4 red, 2 blue, 6
green, and 8 white marbles.
What is the probability of
selecting a white marble at
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.
EX 1:
http://www.v
irtualnerd.co
m/prealgebra/peri
meter-areavolume/volu
me/volumeExamples/cyli
nder-heightfrom-volume
Basic:
EXS: 9-37,
45-62
Average:
Example:
Mr. Braunsdorf
has a circular
above ground
swimming pool. If
the 20 ft diameter
pool holds 1256
ft3 of water, how
deep is it? (Use 7r
= 3.14)
http://www.mathgoo
dies.com/lessons/vol
6/addition_rules.html
random from this bag, not
replacing the marble, and then
selecting another white
marble? Round your answer to
the nearest tenth of a percent
if necessary.
EX 2:
Last
1/3 of
the
period.
1
S.CP.7
EXS: 9-29
odd, 31-42,
45-62
Apply the Addition
Rule, P(A or B) = P(A) + Advanced:
P(B) – P(A and B), and EXS: 9-29
interpret the answer in odd, 31-62
terms of the model.
You shuffle a standard deck of
playing cards and choose a
card at random. What is the
probability that you choose a
face card (jack, queen, king, or
a club)?
MP 1, 2
Basic Skills
PARCC/HS
PA Prep
Midpoint Formula
5. Random
sample,
statistic,
parameter,
Make inferences about a
population from a random
sample
G.MG.3
Apply geometric
methods to solve
design problems (e.g.,
designing
an object or structure
to satisfy physical
constraints or
minimize cost;
working with
typographic grid
systems based on
ratios).
S.IC.1
Section 11-7
Understand statistics
as a process for
Problems 13
http://www.s
ophia.org/ap
plying-themidpointformula-withoneendpoint/app
lying-themidpointformula-withone-endpointtutorial
Example:
Given: M (-1,-2) is
the midpoint of AB
where A is (-4,2).
Find the
coordinates of the
other endpoint, B.
http://www.sophia.or
g/standard-deviationtutorial
population
and sample
Q 12,13
EX:
making inferences
about population
The points scored in each game parameters based on a
played by the boys’ and girls’
random sample from
basketball teams last season
that population.
are given,
MP 1, 2
Boys Team: 56, 81, 80, 75, 48,
65, 90, 66, 70, 70
Girls Team: 60, 72, 61, 58, 78,
65, 66, 55, 65, 73
1
Basic Skills
PARCC/HS
PA Prep
Shaded Region
6. The
meaning of
theoretical
and
Design a simulation that
models a desired event
EX:
Average:
EXS: 7-13
odd, 14-21,
24-37
Advanced:
EXS: 7-13
odd, 14-37
Interpret the data as to which
team is more consistent in
their scoring (use the standard
deviation).
Last
1/3 of
the
period.
Basic:
EXS: 6-13,
15, 17, 20,
21, 24-27
G.MG.3
Apply geometric
methods to solve
design problems (e.g.,
designing
an object or structure
to satisfy physical
constraints or
minimize cost;
working with
typographic grid
systems based on
ratios).
S.IC.2
Section 11-2
Decide if a specified
model is consistent
Problem 1,
2, 3, 5
http://www.o
nlinemathlear
ning.com/are
a-shadedregion.html
Example:
Find the area of a
given shaded
region.
http://www.sophia.or
g/standard-deviationtutorial
experiment
al statistics Suppose we throw a coin 10
times, and we only see heads 3
Q 14, 15
times. What can we say about
the fairness of this coin?
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?
MP 2, 4
Last
1/3 of
the
period.
1
Basic:
EXS: 8-28,
31-35, 3751
Average:
EXS: 9-27
odd 28-35,
37-51
Advanced:
EXS: 9-27
odd, 28-36,
37-51
Basic Skills
PARCC/HS
PA Prep
Scientific Notation
N.Q.3
Choose a level of
accuracy appropriate
to limitations on
measurement
when reporting
quantities.
7. Survey,
an
experiment
, and an
observatio
nal study
Recognize a survey, an
experiment and an
observational study
S.IC.3
Section 11-8
Recognize the
purposes of and
differences among
sample surveys,
experiments, and
observational studies;
explain how
Problem 1-3
Q 16, 17,18
EX:
Jason is interested in finding
the number of students who
would be willing to donate $10
http://www.c
hem.tamu.edu
/class/fyp/m
athrev/mrscnot.html
Basic:
EXS: 6-12,
15-19, 23,
26-38
Example:
The speed of light
is approximately
299.8 million
meters per second.
What is that speed
in scientific
notation form?
http://www.regentsp
rep.org/Regents/math
/algtrig/ATS1/StatSur
veylesson.htm
or an hour of time to help a
local food bank? Explain how
can randomization be applied?
randomization relates
to each.
MP 1, 2
Average:
EXS: 7-11
odd, 15-19,
21-23, 2638
Advanced:
EXS: 7-11
odd, 16-19,
23, 24, 2638
Last
1/3 of
the
period.
2
Basic Skills
PARCC/HS
PA Prep
Ordering Rational Numbers
8. Mean,
proportion
and margin
of error
EX:
The midterm scores for 20
random students (in a class of
100):
Q 19,20
82 45 37 98 100 74 87 89 63
76 75 61 43 99 86 75 92 65 80
86
Estimate the mean score of all
students and identify the range
of scores within 2 standard
deviations of the mean.
N.Q.3
Choose a level of
accuracy appropriate
to limitations on
measurement
when reporting
quantities.
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.
MP 1, 2
http://www.e
tap.org/demo
/Algebra1/les
son2/instruct
ion4tutor.htm
l
Section 11-7
Problem 1-3
Basic:
EXS: 6-13,
15, 17, 20,
21, 24-27
Average:
EXS: 7-13
odd, 14-21,
24-37
Advanced:
EXS: 7-13
odd, 14-37
Example:
Arrange the
following numbers
in order from
LEAST to
GREATEST: 1/3,
2/5, 0.6, 0.125
http://psy2.ucsd.edu/
~dhuber/ch5_hays.pd
f
http://www.regentsp
rep.org/Regents/math
/algtrig/ATS1/Disper
sion.htm
Last
1/3 of
the
period.
2
Basic Skills
PARCC/HS
PA Prep
Angles
9. Conduct
an
experiment
or
simulation
and the
meaning of
significanc
e
Decide if the differences
between parameters are
significant
EX:
Q 21, 22
G.MG.3
Apply geometric
methods to solve
design problems (e.g.,
designing
an object or structure
to satisfy physical
constraints or
minimize cost;
working with
typographic grid
systems based on
ratios).
S.IC.5
(Use
Algebra 1
Text
Resources
Section 124)
Use data from a
randomized
experiment to
compare two
treatments; use
simulations to decide if Section 11-6
differences between
parameters are
significant.
Problem 1-5
S.IC.6
1. The heights, in millimeters, of
10 seedlings from 2 seed types
are shown.
Seed A: 56, 61, 48, 51, 59, 65,
http://www.f
reemathhelp.c
om/felizanglestriangle.html
Evaluate reports based
on data.
MP 1, 2
Basic:
EXS: 7-23,
25, 30-43
Average:
EXS: 7-15
Example:
If A is a right
angle, and m B =
43o, then m C =
http://www.regentsp
rep.org/Regents/math
/algtrig/ATS1/Central
Tendency.htm
49, 71, 69, 64
Seed B: 55,63, 58, 47, 61, 46,
53, 47, 41, 59
Make box-and-whisker plots
comparing the samples. Which
seed type is, on average, taller?
END UNIT
Part of a TEST
period
End unit test to determine
areas of weakness that need to
be addressed before the state
unit test.
odd, 16-27,
30-43
Advanced:
EXS: 7-15
odd, 16-43
S.CP. 1-7
S.IC.1-6
Teacher
created
material.
Test to determine
skills that need
reteaching.
INSTRUCTIONAL FOCUS OF UNIT
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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”).
Use two-way frequency tables to determine if events are independent and to calculate/approximate conditional probability.
Use everyday language to explain independence and conditional probability in real-world situations.
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.
Make inferences about population parameters based on a random sample from that population.
Determine if the outcomes and properties of a specified model are consistent with results from a given data-generating process using simulation.
Identify different methods and purposes for conducting sample surveys, experiments, and observational studies and 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.
Use data from a randomized experiment to compare two treatments and use simulations to decide if differences between parameters are significant;
evaluate reports based on data.
PARCC FRAMEWORK/ASSESSMENT
OVERVIEW
 http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsAlgII_Nov2012V3_FINAL.pdf
 http://www.parcconline.org/sites/parcc/files/ESTableAlgebra2EOYforPARCC_FinalV2.pdf
EXAMPLES
 https://sites.google.com/site/jacobsmathdepartment/parcc-assessments
 http://www.parcconline.org/samples/mathematics/high-school-mathematics
21ST CENTURY SKILLS
(4Cs & CTE Standards)
9.4.D Business, Management & Administration Career Cluster
9.4.E Education & Training Career Cluster
9.4.F Finance Career Cluster
9.4.N Marketing Career Cluster
9.4.O Science, Technology, Engineering & Mathematics Career Cluster
9.4.P Transportation, Distribution & Logistics Career Cluster
9.4.12.D.2, 9.4.12.E.2, 9.4.12.F.2, 9.4.12.N.2, 9.4.12.O.2, 9.4.12.P.2
Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career opportunities.
9.4.12.D.4, 9.4.12.E.4
Solve mathematical problems and use the information to make business decisions and enhance business management duties.
9.4.12.F.4
Solve mathematical problems to obtain information for decision-making in financial settings.
9.4.12.N.4
Solve mathematical problems to obtain information for marketing decision-making.
9.4.12.O.15
Prepare science, technology, engineering, and mathematics material in oral, written, or visual formats to provide information to an intended audience and
to fulfill the specific communication needs of that audience.
9.4.H(5) Biotechnology Research and Development
9.4.12.H.(5).2
Apply biochemistry, cell biology, genetics, mathematics, microbiology, molecular biology, organic chemistry, and statistics concepts to conduct effective
biotechnology research and development.
9.4.O(1) Engineering and Technology
9.4.12.O.(1).1
Apply the concepts, processes, guiding principles, and standards of school mathematics to solve science, technology, engineering, and mathematics
problems.
9.4.12.O.(1).7
Use mathematics, science, and technology concepts and processes to solve problems in projects involving design and/or production (e.g., medical,
agricultural, biotechnological, energy and power, information and communication, transportation, manufacturing, and construction).
9.4.O(2) Science and Mathematics
9.4.12.O.(2).1
Develop an understanding of how science and mathematics function to provide results, answers, and algorithms for engineering activities to solve
problems and issues in the real world.
9.4.12.O.(2).2
Apply science and mathematics when developing plans, processes, and projects to find solutions to real world problems.
9.4.12.O.(2).3
Assess the impact that science and mathematics have on society when used to develop projects or products.
9.4.12.O.(2).4
Use scientific and mathematical problem-solving skills and abilities to develop realistic solutions to assigned projects, and illustrate how science and
mathematics impact problem-solving in modern society.
9.4.12.O.(2).6
Demonstrate the knowledge and technical skills needed to obtain and succeed in a chosen scientific and mathematical field.
MODIFICATIONS/ACCOMMODATIONS
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APPENDIX
(Teacher resource extensions)
E-Text, Interactive Digital Resources, Teacher Resources
Login at https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true
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Probability concepts: http://www.marlboro.edu/academics/study/mathematics/courses/probability
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Probability and statistics problems: http://learn.tkschools.org/mwilkinson/Algebra%20II/alg2%20Chapter%2012%20Notes.pdf
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
SLO 6 Compare theoretical and empirical data.
3. Construct viable arguments and critique the reasoning of others.
SLO 7 Explain when and why you would use a sample survey, experiment, or an observational study; develop the meaning of
statistical significance.
4. Model with mathematics.*
5. Use appropriate tools strategically.
6. Attend to precision.
SLO 9 Examine the scope and nature of conclusions drawn in the reports.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
All of the content presented in this course has connections to the standards for mathematical practices.
*This course includes the exponential and logarithmic functions as modeling tools. (PARCC Model Content Frameworks)