Download Algebra II - Harrison County Schools

Harrison County Schools
Curriculum Guide for Math Department
Course Name: _Algebra II______ Grade Level Targeted: _10-11______ Unit (s): ___________
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
Key Vocabulary
Activities
and
Assessments
Number Operations
 How do you solve
real-world problems
by simplifying real
number expressions?
 What is the difference
between an arithmetic
and geometric
sequence?
MA-11-1.3.1
Students will solve realworld problems to
specified accuracy
levels by simplifying
real number
expressions involving
addition, subtraction,
multiplication, division,
absolute value, integer
exponents, roots
(square, cube), and
factorials. DOK - 2
MA-11-1.3.2
Students will:
 describe and
extend arithmetic
and geometric
Addition, subtraction,
multiplication, division,
absolute value, integer
exponents, roots,
square root, cube root,
factorial, distributive
property, commutative
property, associative
property
Simplify expressions with
 Absolute values
 Exponents
 Roots
 Factorials
Solve geometric problems using perimeter & Pythagorean
Theorem.
Applying combinations & permutations to real world
situations.
Arithmetic sequence,
geometric sequence,
finite sequence, infinite
sequence, common
difference, common
 Using a list of various sequences (algebraic,
geometric and other), have students determine the
next 2 terms and finally, a formula for the nth
term.
Essential Questions
toward
Course Objectives
 What are the rules for
determining specific
terms of a given
sequence?
 How do sequences
apply to the real
world?
Kentucky
Core Content
Version 4.1
sequences;
determine a
specific term of a
sequence given
an explicit
formula;
 determine an
explicit rule for
the nth term of an
arithmetic
sequence; and
 apply sequences
to solve realworld problems.
DOK - 3

MA-11-1.3.2a
Students will write an
explicit rule for the nth term
of a geometric sequence.
MA-11-1.3.2b
Students will recognize and
solve problems that can be
modeled using a finite
geometric series, such as
home mortgage problems
and other compound
interest problems.
Key Vocabulary
ratio, explicit rule, nth
term, summation
notation
Explicit rule, nth term,
geometric sequence
Geometric series,
recursive, compound
interest
Activities
and
Assessments
 Describe an arithmetic sequence including
common difference and initial term.
 Describe and geometric sequence including
common difference and initial term.
 Use sequences to solve real-world problems such
as:
 Bouncing ball
 Perimeters and areas of squares
 Interest
 Dilation
 Volume
 Linear measurement
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
Key Vocabulary
Activities
and
Assessments
Transformations of
Shapes
 How do you perform
geometric
transformations using
matrices?
MA-11-3.2.1
Students will describe
properties of and apply
geometric
transformations within a
plane to solve real-world
problems.
DOK - 3
Use matrices on geometric figures
 translations & dilations
 rotations & reflections
Data Representations
 How do you analyze
and interpret results
and draw conclusions
based on a set of data?
 How do you organize
and display statistical
models of data?
MA-11-4.1.1
Students will analyze and
make inferences from a
set of data with no more
than two variables, and
will analyze situations for
the use and misuse of
data representations.
DOK - 3
MA-11-4.1.2
Students will construct
data displays for data
with no more than two
variables.
DOK - 2
Table, scatter plot, best
fit line, correlation,
modeling, cubic
regression, quartic
regression
Analyze different graphs of the same data to
understand how scale affects interpretation.
Table, scatter plot
Represent data using tables or graphs
 Years of education/salary
 Indy 500/winning speed
 Altitude/precipitation
 Price/sales
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
Key Vocabulary
Activities
and
Assessments
Mean, median, mode,
range, standard
deviation, distribution
Gaussian normal
distribution, bell curve
Correlation, causation
Review mean, median, and mode.
MA-11-4.1.3a
Students will represent
real-world data using
matrices and will use matrix
addition, subtraction,
multiplication (with matrices
no larger than 2x2), and
scalar multiplication to
solve real-world problems.
Characteristics of
Data Sets
 How do you compare
data distributions
using measures of
center and measures of
spread?
MA-11-4.2.1
Students will describe
and compare data
distributions and make
inferences from the
data based on the
shapes of graphs,
measures of center
(mean, median, mode)
and measures of spread
(range, standard
deviation).
DOK – 2
MA-11-4.2.1a
Discuss how to determine which central tendency is
most appropriate.
Measuring spread using range & standard deviation.
Essential Questions
toward
Course Objectives
 How do you use data
and curve of best fit to
make and defend
predictions?
Kentucky
Core Content
Version 4.1
Students will know the
characteristics of the
Gaussian normal
distribution (bell-shaped
curve).
MA-1-4.2.2 DOK 3
Students will:
 Identify an
appropriate curve
of best fit (linear,
quadratic,
exponential) for a
set of twovariable data.
 Determine a line
of best fit
equation for a set
of linear twovariable data: and
 Apply line of best
fit equations to
make predictions
within and
beyond a given
set of data.
MA-11-4.2.2a ADP
Students will recognize
when arguments based on
data confuse correlation
and causation.
Key Vocabulary
Activities
and
Assessments
Table, scatter plot, best
fit line, correlation,
modeling, linear
regression
 First, by hand, graph data using a scatter plot and dertermine
Correlation, causation
line of best fit. Then, using the same data, graph and
determine line of best fit on a graphing calculator to make
comparisons.
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
Key Vocabulary
Activities
and
Assessments
Experiments and
Samples
 How do you
understand the use and
misuse of statistics
which leads to
inaccurate inferences?
MA-11-4.3.1
Students will recognize
inappropriate strategies
for data gathering (e.g.,
non-random sampling,
polling only a specific
group of people, using
limited or extremely
small sample sizes, bias
issues) and explain why
these strategies can lead
to inaccurate
inferences.
DOK – 2
MA-11-4.3.1a
Students will design simple
experiments or
investigations to collect
data to answer questions of
interest.
MA-11-4.3.1b
Students will explain the
differences between
randomized experiments and
observational studies.
Class discussion: What factors need to be considered
when gathering data?
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
Key Vocabulary
Activities
and
Assessments
Probability
 What is the difference
between theoretical
and experimental
probability?
 Interpret the results of
probability. Draw
conclusions and make
predictions based on
those results.
MA-11-4.4.1 DOK 3
Students will:
 Determine
theoretical and
experimental
(from given data)
probabilities;
 Make predictions
and draw
inferences from
probabilities;
 Compare
theoretical and
experimental
probabilities; and
 Determine
probabilities
involving
replacement and
non-replacement.
MA-11-4.4.1a Supporting
Students will recognize or
identify differences
between combinations and
permutations and use them
to count discrete quantities.
Law of large numbers
Probability, theoretical
probability,
experimental
probability,
permutation,
combination,
replacement, nonreplacement, compound
event, independent
event, dependent event,
discrete quantity
Combination,
permutation, discrete
quantity
Probability, fraction,
decimal, percentage,
circle graph
Use coins, number cubes, or cards to set up
experiments.
Compare theoretical and experimental probabilities.
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
Key Vocabulary
Activities
and
Assessments
MA-11-4.4.1b Supporting
Students will represent
probabilities in multiple
ways, such as fractions,
decimals, percentages and
geometric area models.
MA-11-4.4.1c ADP
Students will explain how
the law of large numbers
can be applied in simple
examples.
Patterns, Relations,
and Functions
 How do you use
formulas, tables and
graphs to represent
equations of
functions?
MA-11-5.1.1
Students will identify
and apply multiple
representations (tables,
graphs, equations) of
functions (linear,
quadratic, absolute
value, exponential) to
solve real-world or
mathematical
problems. DOK 2
Table, graph, equation,
quadratic
Applications
1. Making tables, graphing, and interpreting the
slope and intercepts rising from real world
quantities.
 Fahrenheit/Celsius
 Distance/time
 Ocean depth/pressure
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
Key Vocabulary
MA-11-5.1.1a
Students will identify,
relate, and apply
representations (graphs,
equations, tables) of a
piecewise function (such as
long distance telephone
rates) from mathematical or
real world information.
MA-11-5.1.1b
Students will demonstrate
how equations and graphs
are models of the
relationship between two
real world quantities (e.g.,
the relationship between
degrees Celsius and
degrees Fahrenheit)
MA-11-5.1.1c
Students will recognize and
solve problems that can be
modeled using an
exponential function, such
as compound interest
problems.
MA-11-5.1.2 DOK 2
Students will:
Relation, function,
domain, range,
quadratic, slope, x-
Activities
and
Assessments
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1

 How do you determine
if a relation is a
function and evaluate
the function?
 How do you determine
the following
characteristics of a
function:
 Slope of a linear
function
 How slope shows
rate of change
 Intercepts of a linear
function
 Maximum/minimum
of a quadratic
function
 Domain and range




Determine if a
relation is a
function;
Determine the
domain and range
of a function (linear
and quadratic);
Determine the slope
and the intercepts of
a linear function;
Determine the
maximum,
minimum, and
intercepts of
quadratic function;
and
Evaluate a function
written in function
notation for a
specified rational
number.
MA-11-5.1.2a Supporting
Students will find the
domain and range for
absolute value functions.
MA-11-5.1.2b Supporting
Students will apply and use
Key Vocabulary
intercept, y-intercept,
maximum, minimum,
evaluate, function
notation
Activities
and
Assessments
Present vocabulary
Relate vocab to a graphical representation
Evaluate functions
Graph functions
 Slope intercept
 Tables
 x- & y- intercepts
Determine parallel & perpendicular lines using
slope.
Essential Questions
toward
Course Objectives
 How do changes in
parameters affect
graphs of a function?
Kentucky
Core Content
Version 4.1
direct and indirect variation
to solve real world and
mathematical problems.
MA-11-5.1.3
Students will identify the
changes and explain how
changes in parameters
affect graphs of functions
(linear, quadratic,
absolute value,
exponential) (e.g.,
compare y=x2, y=2x2,
y=(x-4)2, and y=x2+3).
DOK - 2
Key Vocabulary
Parameters, function,
linear, quadratic,
absolute value,
exponential, vertical
shift, horizontal shift,
stretch, shrink
Variables,
Expressions, and
Operations
 How do evaluate
polynomial and
rational expressions?
MA-11-5.2.1 DOK 1
Students will apply order of
operations, real numbers,
properties (identity, inverse,
commutative, associative,
distributive, closure), and
rules of exponents (integer)
to simplify algebraic
expressions.
MA-11-5.2.1a ADP
Order of operations,
identity property,
inverse property,
commutative property,
associative property,
distributive property,
closure property,
exponents, integer,
expression
Activities
and
Assessments
Identify a function from an equation or shape
Graph parent functions
Discovery lessons
 Horizontal & vertical shifts
 Reflections
 Vertical stretch & shrink
Essential Questions
toward
Course Objectives
 How do you simplify and
factor polynomial
expressions?
 How do you simplify
rational expressions?
Kentucky
Core Content
Version 4.1
Students will evaluate
polynomial and rational
expressions and expressions
containing radicals and
absolute values at specified
values of their variables.
MA-11-5.2.2 DOK 2
Students will:
 Add, subtract, and
multiply polynomial
expressions;
 Factor polynomial
expressions using the
greatest common
monomial factor; and
 Factor quadratic
polynomials of the
form ax2 + bx + c,
when a = 1, and b
and c are integers.
MA-11-5.2.2a Supporting
Students will factor quadratic
polynomials, such a perfect
square trinomials and
quadratic polynomials of the
for ax2 + bx + c when a ≠ 1
and b and c are integers.
MA-11-5.2.3 DOK 1
Students will add, subtract,
Key Vocabulary
Activities
and
Assessments
Polynomial, factor,
monomial, greatest
common factor
Factoring polynomials to solve geometric figures.
Rational expression,
monomial,
Recognizing rational expressions
 Finding common denominators
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
multiply, and divide simple
rational expressions with
monomial first-degree
denominators and integer
numerators (e.g.,
Key Vocabulary
denominator, first
degree denominators,
numerator
Activities
and
Assessments

Performing basic operations & simplifying
3 + 4 ; 9 - -7 ;
3 • -4;
5x 3y 2a 4b -5x 7y
5  9 ), and will express
2c
-11d
the results in simplified
form.
Equations and
Inequalities
 How do you model
and solve singlevariable equations and
inequalities?
MA-11-5.3.1
Students will model or
solve first degree, single
variable equations and
inequalities, including
absolute value, in realworld situations, and will
graph the solutions on a
number line.
DOK - 2
MA-11-5.3.1a
Equation, inequality,
first degree, absolute
value, number line
Multivariable equation
Review solving equations & inequalities
Introduce absolute value as the distance from zero on the
number line.
Solving absolute value equations and checking for
extraneous solutions.
Solving absolute value inequalities and use to find
allowable ranges in measurements.
Essential Questions
toward
Course Objectives
 How do you model
and solve two-variable
equations and
inequalities?
 How will students
model and graph
systems of linear
equations?
Kentucky
Core Content
Version 4.1
Students will solve for a
specified variable in a
multivariable equation.
MA-11-5.3.2
Students will model or
solve first degree, twovariable equations and
inequalities in realworld problems, and
will graph the solutions
on a coordinate plane.
DOK - 2
MA-11-5.3.3
Students will model and
graph systems of linear
equations (two equations
in two variables) and
apply the system to solve
and interpret real-world
problems.
DOK - 3
MA-11-5.3.3a
Students will write, graph,
and solve systems of linear
inequalities (two
inequalities in two
variables) based on real
world or mathematical
situations and interpret the
Key Vocabulary
Activities
and
Assessments
First degree equation,
first degree inequalities,
coordinate plane
Review graphing linear equations.
System, linear
equations
Write & solve equations that represent real world
situations.
Use test points to determine shading for the related
inequalities.
Applications
 Comparing prices
 Income vs. expenses
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
Key Vocabulary
Activities
and
Assessments
solution.
 How do you solve real
world problems
involving quadratic
equations?
MA-11-5.3.4
Students will solve
quadratic equations from
real world or
mathematical situations.
DOK - 2
Quadratic equations
Applications
 Accelerated motion
 Minimizing costs
 Maximizing profit