Math Standards Document

Algebra II

Final Draft

Hawaii School Districts

Prepared by Marzano and Associates

Algebra 2 Summary

TOPIC / STRAND(S) / STANDARD(S) / NUMBER OF ELEMENTS
Equations and Inequalities / Patterns, Functions, and Algebra / 10 / Level 4.0-1
Level 3.0-1
Level 2.0-2
Linear Equations and Functions / Patterns, Functions, and Algebra / 9 / Level 4.0-2
Level 3.0-4
Level 2.0-4
Linear Systems / Patterns, Functions, and Algebra
Numbers and Operations / 10, 3 / Level 4.0-3
Level 3.0-2
Level 2.0-2
Quadratic Equations and Functions / Measurement
Patterns, Functions, and Algebra / 4, 10 / Level 4.0 -2
Level 3.0-3
Level 2.0-3
Complex Numbers / Numbers and Operations / 1,2,10 / Level 4.0-2
Level 3.0-3
Level 2.0-3
Polynomial Functions / Patterns, Functions, and Algebra / 9 / Level 4.0-3
Level 3.0-1
Level 2.0-1
Rational and Radical Functions / Patterns, Functions, and Algebra / 10 / Level 4.0-2
Level 3.0-2
Level 2.0-2
Exponential and Logarithmic Functions / Numbers and Operations
Patterns, Functions, and Algebra / 2, 9 / Level 4.0-1
Level 3.0-2
Level 2.0-2
Conic Sections / Patterns, Functions, and Algebra / 10 / Level 4.0-3
Level 3.0-2
Level 2.0-2
Sequences and Series / Patterns, Functions, and Algebra / 9, 10 / Level 4.0-2
Level 3.0-2
Level 2.0-2
Probability / Data Analysis, Statistics, and Probability / 14 / Level 4.0-1
Level 3.0-2
Level 2.0-2
Data Analysis and Statistics / Data Analysis, Statistics, and Probability / 12 / Level 4.0 -1
Level 3.0-1
Level 2.0-2
Total of Levels 3.0 / 25
Topic: Equations and Inequalities
Strand: Patterns, Functions, and Algebra
Standard 10: Symbolic Representation: Use symbolic forms to represent, model, and analyze mathematical situations.
Algebra II
Level 4.0 / In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught such as:
·  models and solves real-world problems using equations in one variable and absolute-value equations and inequalities
Level 3.5 / In addition to Level 3.0 performance, in-depth inferences and applications with partial success.
Level 3.0 / While involved with tasks involving equations and inequalities, the student will:
·  (MA.AII.10.1) solve equations and inequalities involving absolute values (apply absolute value properties to solve absolute value equations and inequalities, and represent the solution numerically and graphically)
The student exhibits no major errors or omissions.
Level 2.5 / No major errors or omissions regarding the simpler details and process and partial knowledge of the more complex ideas and processes.
Level 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
·  recognizes or recalls specific terminology such as:
o  equation, linear equation, linear inequality in one variable, solution of a linear inequality in one variable, graph of a linear inequality in one variable, absolute value, compound inequality.
·  performs basic processes such as:
o  solving simple (one- and two-step) equations and inequalities in one variable
o  solving simple (one- and two-step) absolute-value equations and inequalities in one variable
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
Level 1.5 / Partial knowledge of the simpler details and processes but major errors or omissions regarding the more complex ideas and procedures.
Level 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
Level 0.5 / With help, a partial understanding of some of the simpler details and processes but not the more complex ideas and processes.
Level 0.0 / Even with help, no understanding or skill demonstrated.

Sample Tasks for Levels 4.0, 3.0, & 2.0

Level 4.0

·  Given a variety of real-world problems, ask students to write an open sentence that models the problem, solve the open sentence, and answer the question. Translated problems should include equations, inequalities, and absolute-value equations and inequalities.

Level 3.0

·  Ask students to solve multi-step equations in one variable.

·  Ask students to solve multi-step inequalities in one variable.

·  Ask students to solve compound inequalities in one variable.

·  Ask students to solve and graph absolute-value equations in one variable.

·  Ask students to solve and graph absolute-value inequalities in one variable.

·  Ask students to translate between absolute-value equations and inequalities, graphs of solutions, and compound sentences.

Level 2.0

·  Ask students to match terms with their definitions.

·  Ask students to solve simple (one- and two-step) equations and inequalities in one variable.

·  Ask students to solve simple (one- and two-step) absolute-value equations and inequalities in one variable.

Topic: Linear Equations and Functions
Strand: Patterns, Functions, and Algebra
Standard 9: Patterns and Functional Relationships: Understand various types of patterns and functional relationships.
Algebra II
Level 4.0 / In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught such as:
·  graphs piecewise, step, and absolute-value functions
·  models and solves real-world problems using piecewise, step, and absolute-value functions
Level 3.5 / In addition to Level 3.0 performance, in-depth inferences and applications with partial success.
Level 3.0 / While engaged in tasks involving patterns and functional relationships, the student will:
·  (MA.AII.9.4) use the appropriate terminology and notation to define functions and their properties (e.g., domain, range, function composition, inverses, zeros) (define a variety of functions using the correct terminology and notation)
·  (MA.AII.9.6) describe the relationship among relations and functions (provide an example of a function and an example of a relation that is not a function and explain the difference; explain whether or not a given relation is a function)
·  (MA.AII.9.7) determine the domain and range of a relation given a graph or a set of points (use a graph (or other representation, including graphing technology) of a relation to identify the domain and range)
·  (MA.AII.9.3) use the properties of many types of functions (polynomial, step, absolute value, exponential, and logarithmic) to identify the function’s graph (recognize the kind of function that a graph represents by analyzing the graph’s features; use the properties of a certain type of function to graph the function)
The student exhibits no major errors or omissions.
Level 2.5 / No major errors or omissions regarding the simpler details and process and partial knowledge of the more complex ideas and processes.
Level 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
·  recognizes or recalls specific terminology such as:
o  domain, range, function, relation, function composition, inverses, zeros, linear function
·  performs basic processes such as:
o  recognizing or recalling examples of appropriate terminology and notation to define functions and their properties (domain, range, function composition, inverses, zeros)
o  determining if a relation is a function based on a graph, ordered pair, or table
o  recognizing or recalling examples of the domain and range of a relation given a graph or set of points
o  recognizing or recalling examples of various types of functions
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
Level 1.5 / Partial knowledge of the simpler details and processes but major errors or omissions regarding the more complex ideas and procedures.
Level 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
Level 0.5 / With help, a partial understanding of some of the simpler details and processes but not the more complex ideas and processes.
Level 0.0 / Even with help, no understanding or skill demonstrated.

Sample Tasks for Levels 4.0, 3.0, & 2.0

Level 4.0

·  Ask students to graph a variety of functions (i.e., piecewise, step, and absolute-value).

·  Given a variety of real-world problems, ask students to write a function that models the problem, solve, and answer the question. Translated problems should include piecewise, step, and absolute-value functions.

Level 3.0

·  Ask students to define a variety of functions using the correct terminology and notation.

·  Ask students to provide an example of a function and justify their choice.

·  Ask students to provide an example of a relation that is not a function and justify their choice.

·  Given the graph or set of ordered pairs of a relation, ask students to determine the domain and range.

·  Given a variety of functions, ask students to name the type of function and justify your choice.

Level 2.0

·  Ask students to match terms and their definitions.

·  Given a graph, a set of ordered pairs, or a table, ask students to determine whether the relation is a function or not.

·  Ask students to match the graph of a relation or set of ordered pairs with its domain and range.

·  Given a graph of a variety of functions, ask students to name the type of functions.

Topic: Linear Systems
Strand: Patterns, Functions, and Algebra
Standard 10: Symbolic Representations: Use symbolic forms to represent, model, and analyze mathematical situations.
Strand: Numbers and Operations
Standard 3: Computational Strategies: Use computational tools and strategies fluently and, when appropriate, use estimation.
Algebra II
Level 4.0 / In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught such as:
·  solves systems of linear equations in four or more variables using a variety of strategies (e.g., Cramer’s rule, Gaussian elimination, Gauss-Jordan, technology, matrices)
·  uses linear models in four or more variables to solve real-world problems
·  uses linear programming to solve real-world problems
Level 3.5 / In addition to Level 3.0 performance, in-depth inferences and applications with partial success.
Level 3.0 / While engaged in tasks involving symbolic representations, the student will:
·  (MA.AII.10.2) solve systems of linear equations and inequalities in two or three variables using a variety of strategies (e.g., substitution, graphing, matrices, technology)
While involved in tasks related to computational fluency, the student will:
·  (MA.AII.3.1) use matrix operations (multiplication and inverse) to solve problems (solve problems involving systems of equations by representing the information in a matrix, and perform the appropriate operation on the matrices to solve the problem)
The student exhibits no major errors or omissions.
Level 2.5 / No major errors or omissions regarding the simpler details and process and partial knowledge of the more complex ideas and processes.
Level 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
·  recognizes or recalls specific terminology such as:
o  system of linear equations, substitution method, linear combinations method, system of linear inequalities, graph of a system of linear inequalities, matrix, dimensions of a matrix, row matrix, column matrix, square matrix, zero matrix, equal matrices, scalar, identity matrix, inverse matrix, matrix multiplication, matrix of variables, coefficient matrix, matrix of constants, determinant, Cramer’s rule.
·  performs basic processes such as:
o  describing a method to solve a system of linear equations
o  using simple matrix operations to solve problems (add, subtract, scalar multiplication, matrix multiplication)
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
Level 1.5 / Partial knowledge of the simpler details and processes but major errors or omissions regarding the more complex ideas and procedures.
Level 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
Level 0.5 / With help, a partial understanding of some of the simpler details and processes but not the more complex ideas and processes.
Level 0.0 / Even with help, no understanding or skill demonstrated.

Sample Tasks for Levels 4.0, 3.0, & 2.0

Level 4.0

·  Ask students to solve a system of linear equations in three or more variables using Cramer’s Rule and Gaussian elimination (other methods may include Gauss-Jordan, matrices, and technology).

·  Ask students to model a real-world problem with a system of linear equations or inequalities, solve, and answer the question.

·  Ask students to use linear programming to model and solve a real-world problem.

Level 3.0

·  Ask students to solve a system of linear equations in two variables using graphing, substitution, linear combinations, and the inverse of the matrix of coefficients.

·  Ask students to solve a system of linear inequalities in two variables using graphing.

·  Ask students to solve a system of linear equations in three variables using a variety of techniques (substitution, linear combinations, inverse of the matrix of coefficients, technology).

·  Ask students to find the determinant of a 3x3 matrix using a variety of techniques (properties, technology).

Level 2.0

·  Ask students to match terms with their definitions.

·  Ask students to calculate using simple matrix operations (add, subtract, scalar multiplication, matrix multiplication).

·  Ask students to find the determinant of a 2x2 matrix.

·  Ask students to describe a method to solve a system of linear equations.

Strand: Patterns, Functions, and Algebra
Standard 10: Symbolic Representation: Use symbolic forms to represent, model, and analyze mathematical situations.
Strand: Measurement
Standard 4: Fluency with Measurement: Understand attributes, units, and systems of units in measurement and develop and use techniques, tools, and formulas for measuring.
Algebra II
Level 4.0 / In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught such as:
·  factors polynomials with four or more terms
·  solves and graphs factorable polynomial inequalities
Level 3.5 / In addition to Level 3.0 performance, in-depth inferences and applications with partial success.
Level 3.0 / While engaged in tasks involving numeric and algebraic representations, the student will:
·  (MA.AII.10.4) factor polynomials representing perfect squares, the difference in squares, perfect square trinomials, the sum and difference of cubes, and general trinomials (select and use an appropriate strategy to factor a polynomial completely)
·  (MA.AII.10.5) apply quadratic equations to real-world situations (represent an applicable situation with a quadratic equation, and show/explain how to solve the equation)
While engaged in tasks involving measurement formulas, the student will:
·  (MA.AII.4.1) use advanced formulas or functions to solve problems dealing with determining a measurement based on another derived or given measure (evaluate a formula to solve for a specific measure, e.g., determine at what times an arrow shot into the air will reach its maximum height if the height is determined by the function: )
The student exhibits no major errors or omissions.
Level 2.5 / No major errors or omissions regarding the simpler details and process and partial knowledge of the more complex ideas and processes.
Level 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
·  recognizes or recalls specific terminology such as:
o  binomial, trinomial, factoring, monomial, zero product property, completing the square, discriminant
·  performs basic processes such as:
o  recognizing or recalling examples of polynomials representing perfect squares, the difference in squares, perfect square trinomials, the sum and difference of cubes, and general trinomials
o  recognizing or recalling examples of quadratic equations in real-world situations
o  recognizing or recalling examples of formulas being used to solve real-world problems
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
Level 1.5 / Partial knowledge of the simpler details and processes but major errors or omissions regarding the more complex ideas and procedures.
Level 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
Level 0.5 / With help, a partial understanding of some of the simpler details and processes but not the more complex ideas and processes.
Level 0.0 / Even with help, no understanding or skill demonstrated.

Sample Tasks for Levels 4.0, 3.0, & 2.0