Mathematics Curriculum:
Algebra 2/2 Honors
1
Algebra 2 Mapping:
Dates
Math
September 4- October
24, 2014
5 Weeks
2 Weeks
Instruction Assessment/
Enrichment/
Unit 1
Asmnt
1/Unit 1
October 27 – December
22 2014
5 Weeks
2 Weeks
Instruction Assessment/
Enrichment/
Unit 2
Asmnt
2/Unit2
January 5 –Feb 27 2015
March 2 – Apr 24, 2014
Apr 27-June 19, 2014
5 Weeks
Instruction
5 Weeks
Instruction
5 Weeks
Instruction
Unit 3
2 Weeks
Assessment/
Enrichment/
Asmnt
3/Unit 3
Unit 4
2 Weeks
Assessment/
Enrichment/
Asmnt
4/Unit 4
Unit 3
2 Weeks
Assessment/
Enrichment/
Asmnt
5/Unit 5
Algebra 2 Unit Plan/Development:
Mathematics: Algebra 2
Standard


N.CN.7
A.REI.4.b
Description


Solve quadratic
equations with real
coefficients that have
complex solutions.
Solve quadratic
equations in one
variable. b. Solve
quadratic equations by
inspection (e.g., for x2
= 49), taking square
roots, completing the
square, the quadratic
formula and factoring,
as appropriate to the
initial form of the
equation. Recognize
when the quadratic
formula gives complex
solutions and write
them as a ± bi for real
numbers a and b.
Unit #1: Polynomials
9/4/14-10/24/14
Student Learning Objectives
Solve quadratic equations with real
coefficients that have complex
solutions.
Unit #1
Performance Tasks/Critical Thinking
Writing Task
1. If you are asked to write a
polynomial function of least
degree with zeros of 2 and sqrt
7, what would be the degree of
the polynomial? Explain.
2. You
are
designing
a
cylindrical, plastic glass with
an outside layer of water that,
when frozen, keeps the
contents of the glass cold. The
outer height of the glass should
be four times its outer radius,
and the thickness of the sides
and bottom of the glass should
be 1 cm. The glass is to hold
2
A.APR.2




A.SSE.2
A.APR.3A

Know and apply the
Remainder Theorem:
For a polynomial p(x)
and a number a, the
remainder on division
by x – a is p(a), so p(a)
= 0 if and only if (x –
a) is a factor of p(x).
Use the structure of an
expression to identify
ways to rewrite it. For
example, see x4 – y4 as
(x2)2 – (y2)2, thus
recognizing it as a
difference of squares
that can be factored as
(x2 – y2)(x2 + y2).
Identify
zeros
of
polynomials
when
suitable factorizations
are available, and use
the zeros to construct a
rough graph of the
function defined by the
polynomial.
Restructure by performing arithmetic
operations on polynomial/rational
expressions.
Use an appropriate factoring
technique to factor expressions
completely including expressions
with complex numbers.
140pi cubic centimeters of
liquid:
Critical Thinking
a. Why might you have
chosen 140pi cubic cm for
the capcity of the glass?
(1floz=29.537 cubic cm)
b. Write a function V1(x) for
the volume of liquid the
glass can hold. Substitute
140 pi for V1(x) and
rewrite
the
resulting
equation in standard form.
c. Use the rational zero
theorem to list the rational
possibilities for the outer
radius. Use a graphing
calculator to determine
which rational possibilities
for the outer radius are
reasonable.
d. Use the zero (or root)
feature of the calculator
and the equation from part
(b) to approximate the
outer radius of the glass to
the nearest whole number.
3


A.SSE.2
A.APR.3

Use the structure of an
expression to identify
ways to rewrite it. For
example, see x4 – y4 as
(x2)2 – (y2)2, thus
recognizing it as a
difference of squares
that can be factored as
(x2 – y2)(x2 + y2).
Identify
zeros
of
polynomials
when
suitable factorizations
are available, and use
the zeros to construct a
rough graph of the
function defined by the
polynomial.
Explain the relationship between
zeros and factors of polynomials and
use zeros to construct a rough graph
of the function defined by the
polynomial.
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.
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.
Use Properties of operations to add,
subtract, and multiply complex
numbers.

A.SSE.4


N.CN.1
N.CN.2


Know there is a
complex number i
such that i2 = −1,
and every complex
number has the form
a + bi with a and b
real.
Use the relation i2 =
–1
and
the
commutative,
associative,
and
distributive
e.
The thickness of the glass
(1cm)
includes
the
thickness of the plastic and
the space for water. Write
a function V2(x) for the
volume of the sides and
bottom of the glass. Use
your answer from part (d)
to approximate this volume
to the nearest whole
number.
4
properties
subtract,
multiply
numbers.
to
add,
and
complex
Algebra 2
Standard


N.RN.1,
N.RN.2




A.REI.1
A.REI.2

Description
Explain how the
definition of the
meaning of rational
exponents follows
from extending the
properties of integer
exponents to those
values, allowing for
a notation for
radicals in terms of
rational exponents.
For example, we
define 51/3 to be the
cube root of 5
because we want
(51/3)3 = 5(1/3)3
to hold, so (51/3)3
must equal 5.
Rewrite expressions
involving radicals
and rational
exponents using the
properties of
exponents.
Explain each step in
solving a simple
equation as
following from the
equality of numbers
Unit #2: Expressions and Equations
10/27/14-12/22/14
Student Learning Objectives
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.
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.
Unit #2
Performance Tasks/Critical Thinking
Writing Task
1. Why do students often think it is not
possible to multiply or divide two
radicals with different indices? How
do rational exponents help you to
multiply or divide two radicals with
different indices? Write/present two
examples to support your answer.
2.
Your school is putting on a prom
fashion show and you are in charge
of building a platform to serve as a
stage. The main part of the stage is a
rectangle and the runway is a square.
5


A.SSE.3
F.IF.4
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.
 Understand solving
equations as a
process of reasoning
and explain the
reasoning. Solve
simple rational and
radical equations in
one variable, and
give examples
showing how
extraneous solutions
may arise.
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 be
rewritten as (1.151/12)12t ≈
1.01212t to reveal the
approximate equivalent
monthly interest rate if the
annual rate is 15%.
For a function that models a
relationship between two
The length and width of the main
part of the stage is 3 times and 2
times the side length of the runway,
respectively:
a. Write a function A1 (x) for the
area of the main part of the stage
and a function A2 (x) for the area
of the runway.
b. Write a function A(x) for the
area of the entire stage.
c. Graph the function A. How can
you use the graph to explain why
the inverse of A is not a
function?
Write equivalent expressions for exponential
functions using the properties of exponents.
d.
e.
f.
Writing
How can you restrict the domain
of A so that A-1 is a function?
Why does this restriction make
sense in the context of the
problem?
Find the inverse of A, assuming
that its domain is restricted as
you described in part (d). what
information can you obtain from
the inverse function?
You have 700 square feet of
plywood to make the stage floor.
Use the inverse from part € to
find the dimensions of the
runway and the main part of the
stage.
Interpret key features of graphs and tables in
terms of the quantities, and sketch graphs
6
quantities, interpret key
features of graphs and tables
in terms of the quantities, and
sketch graphs showing key
features given a verbal
description of the relationship.
Key features include:
intercepts; intervals where the
function is increasing,
decreasing, positive, or
negative; relative maximums
and minimums; symmetries;
end behavior; and periodicity.
Algebra 2
Standard
A.REI.11
F.BF.2
Description
Explain why the xcoordinates of the points
where the graphs of the
equations y = f(x) and y =
g(x) intersect are the solution
nsof the equation f(x) = g(x);
find the solutions
approximately, e.g., using
technology to graph the
functions, make tables of
values, or find successive
approximations. Include cases
where f(x) and/or g(x) are
linear, polynomial, rational,
absolute value,
exponential, and logarithmic
functions.
Write arithmetic and
geometric sequences both
recursively and with an
explicit formula, use them to
model situations, and translate
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.
Unit #3: Expressions and Equations Cont.
& Modeling Functions
1/5/15-2/27/15
Student Learning Objective
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.
Unit #3
Performance Tasks/Critical Thinking
Writing Task
1. In the definition of a logarithm, b
can be any positive number except 1.
Explain why this constraint means y
must be positive. Give two examples
to support your answer, one where x
is negative and one where x is a
fraction between 0 and 1.
2.
In 1995, a home builder builds the
exact same model of house in two
different cities in two different states.
The table shows the value of each
house v1 and v2 for t years after
7
between the two forms.


F.IF.4
F.IF.7


For a function that
models a relationship
between two
quantities, interpret
key features of
graphs and tables in
terms of the
quantities, and
sketch graphs
showing key features
given a verbal
description of the
relationship. Key
features include:
intercepts; intervals
where the function is
increasing,
decreasing, positive,
or negative; relative
maximums and
minimums;
symmetries; end
behavior; and
periodicity.
Graph functions
expressed
symbolically and
show key features of
the graph, by hand in
simple cases and
using technology for
1995:
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.
Time, t
2
4
6
8
10
Value, v1 260 275 279 285 287
(thousands)
Value, v2 210 250 300 361 420
(thousands)
a. Use a graphing calculator to draw
two scatterplots, one of Lnv1 vs t and
another of ln v2 vs t in the same
viewing window.
b. Use a graphing calculator to draw
two scatter plots one of ln v2 vs t and
another of v2 vs ln t, in the same
viewing window.
c. Based on your results from (a) and
(b), does the exponential function or
a power function better fit each set of
original data?
d. Describe how to verify your answer
for part (c) using a graphing
calculator.
e. Find a model for the value of each
house.
f. Estimate the value of each house in
2002 to the nearest thousand.
g. Approximately how many years
would it take the value of the first
house, to reach 300,000? Determine
the solution algebraically.
8
more complicated
cases.
e. Graph exponential
and logarithmic
functions, showing
intercepts and end
behavior, and
trigonometric
functions, showing
period, midline, and
amplitude,
Find inverse functions.
a. Solve an equation of
the form f(x) = c for
a simple function f
that has an inverse
and
write
an
expression for the
inverse.
For
example, f(x) =2 x3
or f(x) = (x+1)/(x–1)
for x ≠ 1
F.BF.4
Algebra 2
Standard



N.Q.2
F.IF.4
F.IF.7


Description
Define appropriate
quantities for the
purpose of
descriptive
modeling.
For a function that
models a relationship
between two
quantities, interpret
key features of
Determine the inverse function for a simple
function that has an inverse and write an
expression for it.
h.
i.
Unit #4: Modeling with Functions Cont.
3/2/15-4/24/15
Student Learning Objective
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.
Critical thinking
Determine the year when the values
of the two houses were equal.
Describe how you can find the
solution
graphically
and
algebraically. Explain why using an
algebraic method would be more
difficult than in part (g).
Critical Thinking
Describe the rate of change in the
value of each house. What factors
may have affected the values of the
two houses.
Unit #4
Performance Tasks/Critical Thinking
A standard beverage can has a volume of 21.7
cubic inches:
a. Use the formula for the volume of a
cylinder to write an equation that
gives the height h of a can in terms of
its radius.
b. Write an equation that gives the
can’s surface area S in terms of its
radius r by substituting the
expression for h from part (a) into the
9

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.
Graph functions
expressed
symbolically and
show key features of
the graph, by hand in
simple cases and
using technology for
more complicated
cases.
b. Graph square root,
cube root, and
piecewise-defined
functions, including
step functions and
absolute value
functions.
e. Graph exponential
and logarithmic
functions, showing
intercepts and end
behavior,
c.
d.
e.
formula for the surface area of a
cylinder.
Rewrite your equation from part (b)
as ta quotient of two polynomials.
Do you expect the graph of S(r) to
have a horizontal asymptote?
Explain.
Use a graphing calculator and its
minimum feature to find the
minimum value of S. what are the
dimensions r and h of the can that
uses the least material?
Compare your result from part (d)
with the dimensions of an actual
beverage can, which has a radius of
1.25 inches and a height of 4.42
inches.
10
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.
Estimate, calculate and interpret the average
rate of change of a function presented
symbolically, in a table, or graphically over a
specified interval.
F.IF.8
Write a function defined by
an expression in different but
equivalent forms to reveal and
explain different properties of
the function.
Rewrite a function in different but equivalent
forms to identify and explain different
properties of the function.
f.
g.
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.
Writing
Why might the manufacturer choose
not to make the beverage can with
the least amount of material
possible?
Critical Thinking
Is it possible to make the beverage
container shaped like a prism with a
square base using less material than
it takes to make the cylindrical can
with minimal surface area? Explain.
Construct a function that combines standard
function types using arithmetic operations to
model a relationship between two quantities.
11
Algebra 2
Standards
S.IC.1
Description
Understand statistics as a
process for making inferences
about population parameters
based on a random sample
from that population.
Unit 5: Inference and Conclusions from
Data
4/27/15-6/19/15
Student Learning Objective
Make
inferences
about
population
parameters based on a random sample from
that population.
S.IC.2
Decide if a specified model is
consistent with results from a
given data-generating process,
e.g., using simulation. For
example, a model says a
spinning coin falls heads up
with probability 0. 5. Would a
result of 5 tails in a row cause
you to question the model?
Determine if the outcomes and properties of
a specified model are consistent with results
from a given data-generating process using
simulation.
S.IC.3
Recognize the purposes of
and differences among sample
surveys, experiments, and
observational studies; explain
how randomization relates to
each.
Identify different methods and purposes for
conducting sample surveys, experiments, and
observational studies and explain how
randomization relates to each.
S.IC.4
Use data from a sample
survey to estimate a
population mean or
proportion; develop a margin
of error through the use of
simulation models for random
sampling.
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.
Unit #5
Performance Tasks/Critical Thinking
Writing Task
1. Explain the difference between the
measures of central tendency and a
measure of dispersion. Give a reallife example of when it might be
preferable to represent a data set
using the median or mode, instead of
the mean. Explain your reasoning.
2. The student council at your school is
responsible for surveying the
students to determine whether they
would prefer the school to offer
study halls and limited electives or
no study halls and a broad range of
electives. Because 1740 students
attend your school, the council
decides to survey a sample of the
students.
a. A student council member suggests
that the four representatives from
each class (grades 9-12) be surveyed
during the next student council
meeting. Identify the type of sample
described. Then tell if the sample is
biased. Explain your reasoning.
b. How
many
students
would
participate in the survey described in
part (a)? Calculate the margin of
error for a survey with this sample
size. Is it acceptable, why or why
not?
c. The student council would like the
survey to have a margin of error of
12
d.
e.


S.IC.5
S.IC.6


Use data from a
randomized experiment
to compare two
treatments; use
simulations to decide if
differences between
parameters are
significant.
Evaluate reports based
on data.
no more than +/-2% and include no
more than one quarter of the student
body. Is this possible? If not,
explain why and find the least
margin of error to the nearest percent
that can be achieved by surveying
one quarter of the student body?
Writing
Describe how the student council
might achieve an unbiased random
sample of one quarter of the student
body.
Critical Thinking
The student council administers the
survey as described in part (d). 46%
of the students want study halls and
limited electives, and 54% of the
students want no study halls and a
broad range of electives. From this
survey, can the school determine
which option the student body
prefers? Explain
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.
13