Delta RV Algebra II
Revised-2009
Read, write and compare
numbers
A
Students will:
compare and order
rational and irrational
numbers, including
finding their
approximate locations
on a number line.
Extended Thinking
Math: Algebra II (Grades 10-12)
Strand: Numbers and Operations
GLE 1: Understand numbers, ways of representing numbers, relationships among numbers and number systems
MA 1: Addition, subtraction, multiplication an division; other number sense, including numeration and estimation; and the application of these operations and concepts in the workplace and other situations
MA 5: Mathematical systems (including real numbers, integers, fractions), geometry, and number theory (including primes, factors, multiples)
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
Assessment
GLE
Objective
Standards
Skills
Activities/Resources
MA 5
3.3
Students will be given sets of
numbers. They will identify the
number as rational or irrational
and order and compare these
numbers by finding an
approximate location on the
number line.
Given a set of
number, the students
will identify each
number as either
rational or irrational.
They will then find an
approximate location
on the number line,
hence comparing and
ordering the numbers.
Students will solve word problems
involving real life situation.
Examples of the situations include
distance, rate and time, mixture
problems, and cost problems.
Real numbers are used to solve the
problem and in the solution.
The students will be
given word problems
involving real life
situations involving
distance, rate and
time, mixtures, and
cost functions. Real
numbers will be used
to solve the problem
and in the solution.
use real number to
solve problems.
MA 1
3.4
Skill/Concept
Represent and use rational
numbers
B
1
Math: Algebra II (Grades 10-12)
Strand: Numbers and Operations
GLE 1: Understand numbers, ways of representing numbers, relationships among numbers and number systems
MA 1: Addition, subtraction, multiplication an division; other number sense, including numeration and estimation; and the application of these operations and concepts in the workplace and other situations
MA 5: Mathematical systems (including read numbers, integers, fractions), geometry, and number theory (including primes, factors, multiples)
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
Assessment
GLE
Objective
Standards
Skills
Activities/Resources
Students will:
use a variety of
representations to
demonstrate an
understanding of very
large and very small
numbers.
Students will convert very large
and very small numbers from
standard notation to scientific
notation and vice versa and will
simplify expressions involving
multiplication and division.
MA 5
3.6
Skill/Concept
Compose and decompose numbers
C
use vectors and
matrices as systems
and compare their
properties to the realnumber system.
2
Given very large and
very small numbers
in standard and
scientific notation
students will convert
these numbers to the
alternate form and
will simplify
expressions involving
multiplication and
division.
Math: Algebra II (Grades 10-12)
Strand: Numbers and Operations
GLE 2: Understand numbers, ways of representing numbers, relationships among numbers and number systems
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
MA 5: Mathematical systems (including real numbers, integers, fractions), geometry, and number theory (including primes, factors, multiples)
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
Assessment
GLE
Objective
Standards
Skills
Activities/Resources
Students will:
describe the effects of
operations, such as
multiplication,
division, and
computing powers and
roots on the magnitude
of quantities.
MA 4
3.4
Recall
Describe effects of
operations
B
4.1
apply PROPERTIES OF
EXPONENTS (including order
of operations) to simplify
expressions.
MA 4
apply PROPERTIES OF
EXPONENTS to simplify
expressions or solve equations.
1.6
apply PROPERTIES OF
LOGARITHMS to simplify
expressions or solve equations.
MA 5
Skill/Concept
Apply properties of operations
C
1.10
apply PROPERTIES OF
FUNCTIONS to simplify
expressions or solve equations.
3
Given a variety of algebraic
expressions or equations, apply the
properties of exponents to simplify
completely using a calculator to
approximate values of various
roots.
Given an algebraic
expression or
equation, students
will simplify
completely or solve.
Math: Algebra II (Grades 10-12)
Strand: Numbers and Operations
GLE 2: Understand meanings of operations and how they relate to one another
MA 1: Addition, subtraction, multiplication an division; other number sense, including numeration and estimation; and the application of these operations and concepts in the workplace and other situations
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
MA 5: Mathematical systems (including read numbers, integers, fractions), geometry, and number theory (including primes, factors, multiples)
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
Assessment
GLE
Objective
Standards
Skills
Activities/Resources
Students will:
apply operations to real
numbers, using mental
computation or paperand-pencil calculations
for simple cases and
technology for more
complicated cases.
MA 1
MA 4
MA 5
Use order of operations when
simplifying algebraic expressions.
Use mental math or paper-andpencil calculations for simple
cases and a calculator or more
complicated cases.
Given an algebraic
expression, the
student will use order
of operations to
simplify using mental
math, paper-andpencil calculations, a
graphing calculator.
Add, subtract, and multiply
matrices using both mental or
paper-and-pencil calculations and
the matrix features on a graph
calculator. Add, subtract, multiply
and divide complex numbers.
The student will solve
problems involving
addition, subtraction, or
multiplication of matrices
using mental math, paperand pencil calculations,
and the matrix features on
a graphing calculator.
The student will find the
inverse of a matrix using
the graphing calculator.
The student will add,
subtract, multiply and
divide complex numbers.
1.4
Skill/Concept
Apply operations on real and complex numbers
D
3.4
apply operations to
matrices and complex
numbers, using mental
computation or paperand-pencil calculations
for simple cases and
technology for more
complicated cases.
4
Math: Algebra II (Grades 10-12)
Strand: Numbers and Operations
GLE 3: Compute fluently and make reasonable estimates
MA 5: Mathematical systems (including read numbers, integers, fractions), geometry, and number theory (including primes, factors, multiples)
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
Assessment
GLE
Objective
Standards
Skills
Activities/Resources
C
Students will:
apply all operations on
real numbers.
MA 5
1.10
Skill/Concept
Compute problems
3.3
5
Math: Algebra II (Grades 10-12)
Strand: Numbers and Operations
GLE 3: Compute fluently and make reasonable estimates
MA 1: Addition, subtraction, multiplication and division; other number sense, including numeration and estimation; and the application of these operations and concepts in the workplace and other situations
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
Assessment
GLE
Objective
Standards
Skills
Activities/Resources
Students will:
judge the
reasonableness of
numerical
computations and their
results.
MA 1
Extended Thinking
Estimate and justify
solutions
D
3.8
E
MA 1
MA 4
3.3
Skill/Concept
Use proportional reasoning
solve problems
involving proportions.
6
Given a variety of equations,
students will identify proportions
and solve them using the cross
multiplication technique. They
will also identify situations in
which extraneous solutions are
possible and check when
necessary.
Students will solve
proportions and check
their solutions.
Math: Algebra II (Grades 10-12)
Strand: Algebraic Relationships
GLE 1: Understand patterns, relations and functions
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
GLE
Objective
Standards
Skills
Activities/Resources
Students will:
generalize patterns
using EXPLICITLY
and RECURSIVELY
defined functions.
MA 4
Strategic Thinking
Create and analyze
patterns
B
1.6
3.5
compare and contrast
various forms of
REPRESENTATIONS
of patterns.
MA 4
1.6
Strategic Thinking
Classify objects and representations
C
7
Given an arithmetic sequence,
students will be able to extend the
sequence and write an explicit and
recursive formula for the
sequence.
Assessment
Students will extend,
write explicit, and
write recursive
formulas for
arithmetic sequences.
Math: Algebra II (Grades 10-12)
Strand: Algebraic Relationships
GLE 1: Understand patterns, relations and functions
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
GLE
Objective
Standards
Skills
Activities/Resources
Students will:
understand and compare the
properties of LINEAR and
EXPONENTIAL functions
(including intercepts).
MA 4
understand and compare the
properties of LINEAR,
EXPONENTIAL and
QUADRATIC functions
(include domain and range).
3.6
1.6
Strategic Thinking
Identify and compare functions
D
Assessment
understand and compare the
properties of LINEAR,
QFFUADRATIC,
EXPONENTIAL,
LOGARITHMIC and
RATIONAL functions
(include asymptotes).
understand and compare the
properties of
EXPONENTIAL,
POLYNOMIAL,
RATIONAL, and
LOGARITHMIC functions
(include asymptotes).
8
Completely analyze a linear,
exponential, quadratic,
logarithmic, and rational function.
The process should include
intercepts, domain, range, and
asymptotes where appropriate.
Use this information, along with
test points and transformations, to
graph the function.
Given the equation of
a linear, exponential,
quadratic, logarithmic
and rational function
the student will
analyze completely
by finding intercepts,
domain, range and
asymptotes where
appropriate. They
will use this
information along
with transformations
to graph the function.
Math: Algebra II (Grades 10-12)
Strand: Algebraic Relationships
GLE 1: Understand patterns, relations and functions
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
GLE
Objective
Standards
Skills
Activities/Resources
Students will:
describe the effects of
PARAMETER CHANGES
on LINEAR FUNCTIONS.
MA 4
describe the effects of
PARAMETER CHANGES
on QUADRATIC and
EXPONENTIAL functions.
4.1
1.6
Recall
Describe the effects of parameter changes
E
describe the effects of
parameter changes on
LOGARITHMIC and
EXPONENTIAL functions.
describe the effects of
parameter changes on
POLYNOMIAL functions.
9
Assessment
Math: Algebra II (Grades 10-12)
Strand: Algebraic Relationships
GLE 2: Represent and analyze mathematical situations and structures using algebraic symbols
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
GLE
Objective
Standards
Skills
Activities/Resources
Students will:
describe and use
algebraic manipulations,
including factoring and
rules of integer
exponents.
MA 4
3.1
4.1
describe and use
algebraic manipulations,
including INVERSE of
functions,
COMPOSITION of
functions and rules of
exponents.
Skill/Concept
Describe and use mathematical manipulations
B
describe and use
algebraic manipulations,
including INVERSE of
functions,
COMPOSITION of
functions.
10
Assessment
Math: Algebra II (Grades 10-12)
Strand: Algebraic Relationships
GLE 2: Represent and analyze mathematical situations and structures using algebraic symbols
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
GLE
Objective
Standards
Skills
Activities/Resources
C
Students will:
use and solve
equivalent forms of
equations and
inequalities (linear).
MA 4
1.6
use and solve
equivalent forms of
equations and
inequalities (piece-wise
and quadratic).
Skill/Concept
Utilize equivalent forms
3.4
use and solve
equivalent forms of
equations and
inequalities
(exponential,
logarithmic and
rational).
11
Assessment
Math: Algebra II (Grades 10-12)
Strand: Algebraic Relationships
GLE 2: Represent and analyze mathematical situations and structures using algebraic symbols
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
GLE
Objective
Standards
Skills
Activities/Resources
Students will:
use and solve systems
of linear equations with
two variables.
MA 4
1.6
use and solve systems
of linear equations or
inequalities with two
variables.
Skill/Concept
Utilize systems
D
use and solve systems
of linear and quadratic
equations or
inequalities with two
variables.
use and solve systems
of equations or
equalities.
12
Students will use a variety of
techniques including elimination,
substitution, graphing, matrix
equations, inverse matrices and
augmented matrices to solve
systems of equations. The
graphing calculator will be
incorporated into the matrix
techniques. Systems of
inequalities will be solved by
graphing with pencil and paper.
Assessment
Students will
determine and apply
the most appropriate
method for solving a
system of equations
or inequalities.
Math: Algebra II (Grades 10-12)
Strand: Algebraic Relationships
GLE 3: Use mathematical models to represent and understand quantitative relationships
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
GLE
Objective
Standards
Skills
Activities/Resources
Students will:
identify quantitative
relationships and
determine the type(s)
of functions that might
model the situation to
solve the problem.
MA 4
1.6
3.6
Recall
Strategic Thinking
Use mathematical models
A
13
Assessment
Students will
determine if a linear,
quadratic,
exponential, or some
other model would
best fit a given
situation.
Math: Algebra II (Grades 10-12)
Strand: Algebraic Relationships
GLE 4: Analyze change in various contexts
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
GLE
Objective
Standards
Skills
Activities/Resources
A
Students will:
analyze linear
functions by
investigating rates of
change and intercepts.
MA 4
Assessment
Students will explore the graphs of Students will graph
lines by using slope-intercept form linear equations using
slope-intercept form
to graph them.
of a line.
1.6
Strategic Thinking
Analyze change
4.1
analyze quadratic
functions by
investigating rates of
change, intercepts and
zeros.
analyze exponential
and logarithmic
functions by
investigating rates of
change, intercepts and
asymptotes.
14
Given a quadratic function of the
form f(x)=ax²+bx+c, students will
determine the role of a, b and c;
find the vertex, zeros and
intercepts; determine the steepness
of the graph with the use of a table
of values.
Given a quadratic
function, students
will determine the
direction of opening,
vertex, equation of
the axis of symmetry,
intercepts, and graph.
Given exponential and logarithmic
functions, students will graph the
functions by hand; determine
domain and range; and find
equations of asymptotes.
Students will graph
exponential and
logarithmic functions
by hand; state domain
and range; and find
equations of
asymptotes.
Math: Algebra II (Grades 10-12)
Strand: Algebraic Relationships
GLE 2: Analyze change in various contexts
MA 2: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
GLE
Objective
Standards
Skills
Activities/Resources
Students will:
solve problems related
to two-dimensional
objects by finding the
distance on a Cartesian
plane.
make conjectures and
solve problems
involving twodimensional objects
represented with
Cartesian coordinates.
MA 2
3.2
MA2
Skill/Concept
Use coordinate systems
A
3.6
4.1
15
Assessment
Students will use the distance
formula to find the distance
between two points as well as find
the lengths of sides of twodimensional objects as graphed in
the Cartesian plane.
Given twodimensional objects
graphed in the
Cartesian plane,
students will use the
distance formula to
find the lengths of the
sides of the object.
Students will find the area of a
triangle with vertices as ordered
pairs using the determinant of a
matrix.
Given the coordinates
of the vertices of a
triangle, students will
find its area using
determinants.
Math: Algebra II (Grades 10-12)
Strand: Geometric and Spatial Relationships
GLE 3: Apply transformations and use symmetry to analyze mathematical situations
MA 4: Patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
GLE
Objective
Standards
Skills
Activities/Resources
B
Students will:
translate and reflect
linear FUNCTIONS.
Assessment
MA 4
perform simple
transformations and
their compositions on
linear, quadratic,
logarithmic and
exponential
FUNCTIONS.
Skill/Concept
Use transformations on functions
3.1
16
Students will explore
transformations on linear,
quadratic, logarithmic and
exponential functions on the
graphing calculator. Then they
will graph them by hand using
pencil and paper.
Students will describe
and graph the
transformations of
linear, quadratic,
logarithmic and
exponential functions
without using a
graphing calculator.
Math: Algebra II (Grades 10-12)
Strand: Data and Probability
GLE 1: Formulate questions that can be addressed with data and collect, organize and display relevant data to answer them
MA 6: Discrete mathematics (such as graph theory, counting techniques, matrices)
Measurable Learner
Process
Integrated
DOK
Instructional Strategies/Student
GLE
Objective
Standards
Skills
Activities/Resources
C
Students will:
select, create and use
appropriate graphical
representation of data.
MA 6
Given a set of linear data, students
will draw a scatter plot, write a
prediction equation, and evaluate
the equation to determine a
missing value. This activity is a
graphing calculator activity.
1.8
Skill/Concept
Extended Thinking
Represent and interpret data
3.6
17
Assessment
Given a set of linear
data, students will use
a graphing calculator
to draw a scatter plot,
figure the prediction
equation and evaluate
the equation to
determine a missing
value.
Math: Algebra II (Grades 10-12)
Strand: Data and Probability
GLE 2: Select and use appropriate statistical method to analyze data
MA 3: Data analysis, probability and statistics
Measurable Learner
Process
Integrated
GLE
Objective
Standards
Skills
Students will:
given a scatter plot,
determine an equation
for A LINE OF BEST
FIT.
MA 3
1.6
Strategic Thinking
Represent data algebraically
C
DOK
given a scatter plot,
determine a type of
function which models
the data.
18
Instructional Strategies/Student
Activities/Resources
Assessment
Using a graphing calculator and
set of linear data, the students will
determine the line of best fit.
Students will write
the equation of the
line of best fit for a
set of linear data
using a graphing
calculator.
Using a graphing calculator or a
pregraphed scatter plot, students
will determine which function type
models the data best.
Students will use a
graphing calculator or
pregraphed scatter
plot to state which
function type best
“fits” the data.
Math: Algebra II (Grades 10-12)
Strand: Data and Probability
GLE 3: Develop and evaluate inferences and predictions that are based on data
MA 3: Data analysis, probability and statistics
Measurable Learner
Process
Integrated
DOK
GLE
Objective
Standards
Skills
Students will:
make CONJECTURES
about possible
relationships between
two characteristics of a
sample on the basis of
scatter plots of the data
and approximate lines
of best fit.
MA 3
3.5
Extended Thinking
Develop and evaluate inferences
A
19
Instructional Strategies/Student
Activities/Resources
Assessment
Looking at the scatter plot of a set
of data, make a conjecture as to
whether positive or negative linear
correlation is present. If so, use a
graphing calculator to approximate
the line of best fit.
Using a given scatter
plot, the student will
conjecture if positive
or negative linear
correlation applies to
the sample. If so, the
student will use a
graphing calculator to
approximate the line
of best fit.