Algebra 2 - 2004
Strand Analysis
Unit: Algebraic Concepts
Mathematics
MTHCORE
Absolute Value
Absolute
Value Problems solve absolute value
problems.
Binomial Expansion
Binomial
Expansion: Finding Terms find an nth
term within a binomial expansion.
Equality/Inequality
Equality/Inequality:
Solution Methods use technology (i.e.,
calculators), matrices, and graphing to solve systems of 2 first degree
equations or inequalities with 2 variables in real world situations.
Equations
Diagrams
with Equations use a diagram to
demonstrate the meaning of a given equation.
Algebra II Equations: Writing write
equations for real-world scenario problems.
Algebra II Equations: Exponential/Log/First Degree solve problems with exponents, first degree equations, and
logarithmic equations in one variable.
Exponents
Exponential
Numbers: Multiply exponential numbers
that have the same base and integer exponents.
Algebra II Exponential Numbers: Divide
exponential numbers that have the same base and whole number exponents.
Algebra II Exponential Equations solve equations
involving exponents.
Algebra II Exponents: Multiple Step Problem determine the solution to a problem requiring multiple operations
involving exponential numbers with the same base.
Algebra II Logarithms/Exponents: Simplifying use
relationships between logarithms and exponents to simplify expressions.
Expressions
Expressions:
Addition/Subtraction use addition or
subtraction in one variable expressions and equations and determine the number
sentence for a written expression.
Algebra II Expressions: Multiplication/Division use
multiplication or division in one variable expressions and equations and
determine the number sentence for a written expression.
Algebra II Expressions: Real World evaluate
expressions (and formulas) when the expressions are presented within the
context of a real-world problem.
Formulas
Fundamental
Theorem of Algebra identify and use the Fundamental Theorem of Algebra.
Inequalities
Inequalities
solve for the value of a variable given
in an inequality and as shown on a graph by manipulating the inequality correctly.
Algebra II Inequalities: Writing write inequalities for real-world scenario problems.
Algebra II Inequality identify smallest exponent
of two different bases required to validate an inequality.
Logarithms
Logarithms:
Simplifying use logarithmic properties
to simplify expressions.
Algebra II Logarithmic Equations solve equations
involving logarithms.
Order of Operations
Order
of Operations: Exponents determine the
correct order of operations for an exponential equation.
Polynomials
Polynomials:
Addition/Subtraction identify and justify each step and rule of adding and subtracting
polynomials.
Algebra II Polynomials: Multiplication translate sentences into numerical equations including monomials
and binomials.
Algebra II Polynomials: Division divide both monomials and polynomials.
Algebra II Polynomials: Synthetic Substitution solve problems with polynomial equations using synthetic substitution.
Algebra II Polynomial Equations: Relationships solve
problems with polynomial equations by applying relationships between synthetic
division, polynomial factoring, and rational root theorems.
Algebra II Polynomials: Factoring/Uses factor
polynomials with complex numbers and state their use within a real life
situation.
Quadratic
Equations/Formula
Quadratic
Equation: Standard Form state a quadratic equation in standard form.
Algebra II Quadratic Formula describe the discriminant, identify the quadratic formula and solve an
equation using the quadratic formula .
Algebra II Quadratic Equations: Graphing solve
quadratic equations with 2 variables by graphing the system on a coordinate plane.
Algebra II Quadratic/Linear Equations: Justifying solve
linear and quadratic equations with 2 variables by graphing and justifying the
solution.
Algebra II Quadratic Formula: Relating Graphs relate
graphs of second degree equations to the quadratic formula.
Algebra II Quadratic Formula: Number Line/Cartesian relate
both number line and Cartesian graphs of second degree equations to the
quadratic formula.
Radicals
Radicals:
Addition/Subtraction combine radical
terms, find the simplest radical form, and approximate square roots.
Algebra II Radicals: Variables solve a radical
equation by substituting for a variable.
Algebra II Radical Expressions: Represent/Solve use
manipulatives, pictures, and technology (i.e., calculators) to solve operations
with radical expressions.
Systems
of Equations
Systems
of Equations: Determinants solve systems
of equations by applying determinants.
Theorems
Proving
Theorems use mathematical structures
such as field properties to prove elementary theorems.
Strand Analysis
Unit: Calculus and Pre-Calculus
Mathematics
Algebra 2 - 2004
MTHCORE
Strands Courses The Learner
will be able to...
Complex
Numbers
Complex
Numbers: Compare with Real determine properties of
real and complex numbers and examine their similarities and differences.
Algebra II Complex Numbers: Basic Operations use
pictures, technology (i.e., calculators), and principles of algebra to perform
basic operations on complex numbers.
Algebra II Complex Numbers: Operations/Vectors use
vectors to perform basic operations on complex numbers.
Algebra II Complex Numbers: Applying Absolute Value use
vector, geometric, and algebraic representations to apply absolute value to
complex numbers.
Algebra II Complex Numbers: Equations/Inequalities solve
equations and inequalities that have complex numbers for coefficients.
Algebra II Complex Numbers: Compare Subsets recognize
and compare subsets of complex numbers.
Conic
Sections
Conic
Sections identify the graph of a conic
section (circle, parabola, ellipse, hyperbola) and use
it to solve a problem.
Limits
°Limiting
Processes explore the following limiting
processes by analyzing them graphically: series, sequences, targets, and areas
under curves.
Matrices
Matrices:
Basic Operations solve problems where
performing basic operations on matrices is required.
Algebra II Matrices: Operations/Real Numbers complete
operations on matrices, exponents, and logarithmic expressions with real
numbers.
Algebra II Matrices: Systems of Equations solve
problems involving systems of equations using the properties of matrices.
Problem
Solving
Problem
Solving: Graphs of Maxima/Minima find a
maxima and minima of a graph and use it to solve a problem.
Strand Analysis
Unit: Data Interpretation
Mathematics
Algebra 2 - 2004
MTHCORE
Strands Courses The Learner
will be able to...
Analyzing/Evaluating
Graphical Forms
*Mathematical
Information: Communication select the appropriate
means to communicate mathematical information (i.e. create charts or graphs to represent
demographic data).
Strand Analysis
Unit: Functions
Mathematics
Algebra 2 - 2004
MTHCORE
Strands Courses The Learner
will be able to...
Exponential/Logarithmic
Functions
Non-Linear
Functions: Represent model real life
processes with logarithmic, exponential, and other non-linear functions.
Algebra II Exponential/Logarithmic Functions: Graph graph both exponential and logarithmic functions.
Functions/Relations
Functions:
Properties describe both the behavior
and properties of functions.
Graphing
Functions
Graphing:
Analyze/Parameter Changes analyze graphs
of functions to determine the effects of parameter changes.
Inverses
Inverses:
Graphing use a Cartesian plane to graph
both a function and its inverse.
Operations
Operations:
Sums/Products/Compositions represent
graphically and symbolically the sums, products, and compositions of functions.
Representations
of Functions
Representations:
Various Problems recognize how a
function can be a model for a variety of problems.
Algebra II Representations understand and
transfer functions represented in tables, symbols, and graphs.
Strand Analysis
Unit: Measurement
Mathematics
Algebra 2 - 2004
MTHCORE
Strands Courses The Learner
will be able to...
Accuracy
*Application:
Tolerance/Precision understand tolerance, precision, and their application (i.e. explain
how the error in computing the area of a rectangle depends on the errors in
measuring its length and width).
Strand Analysis
Unit: Number Theory
Mathematics
Algebra 2 - 2004
MTHCORE
Strands Courses The Learner
will be able to...
Logarithms
Relationships:
Log/Exponents/Radicals recognize and use
relationships between both real number xponents and
radical symbols and logarithmic and exponential expressions.
Roots/Radicals
Square
Roots calculate squares and square
roots.
Scientific
Notation
Scientific
Notation in Context: Large use
scientific notation to express ten digit numbers in the context of a science
scenario.
Algebra II Scientific Notation in Context use
scientific notation to express large and small numbers in the context of real
science situations.
Algebra II Scientific Notation: Story Problems solve
story problems where the information is given in scientific notation.
Strand Analysis
Unit: Numeration
Mathematics
Algebra 2 - 2004
MTHCORE
Strands Courses The Learner
will be able to...
Ordinal
Numbers
Terms
in a Sequence: Ordinality determine
what position a given term holds within a given sequence.
Patterns
Pattern:
Finding Solutions find pattern to
determine solution.
Patterns:
Number
Pattern:
Exponents recognize and extend a number
pattern involving exponents.
Patterns:
Represent
Pattern:
Represent Algebraically represent patterns algebraically that are found on graphs.
Rounding
*Rounding:
Accumulation/Errors understand that
error accumulates in a computation when there is rounding at intermediate steps.
Sequences/Series
Sequence:
Arithmetic/Geometric identify and use arithmetic and geometric sequences to solve
real world problems.
Algebra II Sequence: Defining recursively define
sequences.
Variations
Inverse
and Direct Variation identify correct
formulas and when to use them, describe the differences between inverse and
direct variation, and find and explain the constant of variation.
Strand Analysis
Unit: Perspective/Role in Society
Mathematics
Algebra 2 - 2004
MTHCORE
Strands Courses The Learner
will be able to...
Applications
*Mathematical
Models understand the nature and use of
mathematical models (i.e. set up spreadsheets to model financial or statistical
problems).
Strand Analysis
Unit: Probability/Statistics
Mathematics
Algebra 2 - 2004
MTHCORE
Strands Courses The Learner
will be able to...
Binomial
Probabilities
Probability:
Binomials/Pascal's Triangle solve probability problems
and expand binomials by using the binomial theorem and Pascal's Triangle.
Combinations
Combinations
determine the number of combinations
that can be made by putting a limited number of items into a limited number of
spaces.
Independent/Dependent/Mutually
Exclusive
Independent/Dependent
Events find the probability of both
dependent and independent events.
Permutations
Permutations
determine the number of possible
outcomes for a limited number of choices or with a limited number to choose from.
Probability
*Probability:
Basic Concepts understand and apply the
basic concepts of probability.
Algebra II Probability identify
the probability of a given situation.
Strand Analysis
Unit: Real Numbers and the Coordinate Plane
Mathematics
Algebra 2 - 2004
MTHCORE
Strands Courses The Learner
will be able to...
Coordinate
Geometry
Coordinate
Plane: Analyzing Points analyze points
on a coordinate plane.
Graphing
Graphing:
Relating/Algebraic Equations graph
linear equalities and relate the graph to the algebraic solution without
computers and calculators.
Algebra II Graphing: 2nd Degree Equations/Identify recognize the graph of a second degree equation.
Real
Numbers
Real
Numbers: Components recognize components
of the real number system.
Sets/Subsets
Subsets:
Relationships understand the real number
system by examining relationships between its subsets.
Strand Analysis
Unit: Technology
Mathematics
Algebra 2 - 2004
MTHCORE
Strands Courses The Learner
will be able to...
Algebra
Algebra:
Systems in 2 or 3 Variables use
technology (i.e., calculators) to solve systems of equations with 2 or 3
variables (both linear and quadratic).
Algebra II Algebra: System of Equation/Determinants use technology to evaluate determinants and solve systems of
equations.
Patterns
Patterns:
Represent/Generalize use manipulatives
and technology (i.e., calculators) to explore number patterns in order to
generalize about operations and numbers.
Technology
as a Tool
*Technology:
Purpose/Capabilities understand the
purpose and capabilities of appropriate technology (i.e. use graphing
calculators to fit curves to data and use computers for manufacturing process control).