Curriculum Documents by Quarter - Mathematics - Algebra II

Learning Objectives

Students should be able to judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities.

Students should develop fluency in operations with real numbers using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.

Students should be able to judge the reasonableness of numerical computations and their results.

Students should understand the meaning of equivalent forms of expressions, equations, inequalities, and relations.

Students should be able to judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.

Students should be able to draw reasonable conclusions about a situation being modeled.

Students should be able to organize and consolidate their mathematical thinking through communication. 

Students should be able to interpret representations of functions of two variables.

Students should understand the meaning of equivalent forms of expressions, equations, inequalities, and relations.

Students should be able to identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships.

Students should be able to draw reasonable conclusions about a situation being modeled.

Students should be able to organize and consolidate their mathematical thinking through communication. 

Students should be able to communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

Students should be able to understand how mathematical ideas interconnect and build on one another to produce a coherent whole.  

What are different ways of representing, organizing, and relating numbers to mathematical operations?

How do we understand and represent patterns, relationships, and change?

What are the characteristics, properties, and applications of multi-dimensional shapes?

How do we collect, organize, display, and analyze data?

Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?

How can mathematical thinking be effectively communicated to different audiences?

How are mathematical concepts related to one another, other disciplines, and to the real world?

• Graph and solve systems of linear equations in two and three variables.
• Graph and solve systems of linear inequalities.
• Solve linear programming problems.
• Add, subtract, and multiply matrices, multiply matrices by scalar, and solve matrix equations.
• Find inverse matrices, and use them to solve linear equations.
• Graph quadratic equations and inequalities.
• Solve quadratic equations and inequalities by factoring, by finding square roots, and by completing the square.
• Use these concepts to solve real life problems.

 Students should be able to judge the effects of such operations as multiplication, division, and
computing powers and roots on the magnitudes of quantities.

Students should understand relations and functions and select, convert flexibly among, and use various representations for them.

Students should be able to interpret representations of functions of two variables.

Students should write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using
technology in all cases.

Students should use symbolic algebra to represent and explain  mathematical relationships.

Students should be able to use the language of mathematics to express mathematical ideas
precisely. 

Students should be able to understand how mathematical ideas interconnect and build on
one another to produce a coherent whole.

• What are different ways of representing, organizing, and relating numbers to mathematical operations?
• How do we understand and represent patterns, relationships, and change?
• What are the characteristics, properties, and applications of multi-dimensional shapes? 
• How do we collect, organize, display, and analyze data? 
• Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?
• How can mathematical thinking be effectively communicated to different audiences? 
• How are mathematical concepts related to one another, other disciplines, and to the real world?

Vocabulary

Learning Objectives

Graph and solve quadratic equations
and inequalities by factoring, by finding
square roots, by completing the square, and by using the quadratic formula.

Solve quadratic equations with complex solutions and perform operations with complex numbers.

Use completing the square to write
quadratic functions in various forms.

Find the rational zeros of both real and
complex functions.

Analyze graphs of real functions.

Evaluate nth roots of real numbers using both radical notation and rational
exponent notation.

Use properties of rational exponents to
solve equations.

Find inverses of both linear and
nonlinear functions.

Graph and solve equations that contain
radicals or rational exponents.

Use these concepts to solve real life
problems.

 Students should be able to judge the effects of such operations as multiplication, division, and
computing powers and roots on the magnitudes of quantities.

Students should develop fluency in operations with real numbers

using mental computation or paper-and-pencil calculations for simple cases and technology for
more-complicated cases.

Students should be able to judge the reasonableness of numerical computations and their results.

Students should be able to judge the meaning, utility, and reasonableness of the results of
symbol manipulations, including those carried out by technology.

Students should be able to organize and consolidate their mathematical thinking through
communication.

• What are different ways of representing, organizing, and relating numbers to mathematical operations?
• How do we understand and represent patterns, relationships, and change?
• What are the characteristics, properties, and applications of multi-dimensional shapes? 
• How do we collect, organize, display, and analyze data? 
• Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?
• How can mathematical thinking be effectively communicated to different audiences? 
• How are mathematical concepts related to one another, other disciplines, and to the real world?

 Vocabulary