**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 ELEMENTSEquations 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 SystemsStrand: 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.

Topic: Quadratic Equations and FunctionsStrand: 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