Mathematics: Algebra

• Standard 1: Problem Solving
• Standard 2: Communication
• Standard 3: Reasoning
• Standard 4: Connections
• Standard 5: Estimation & Computation
• Standard 6: Numeration & Number Theory
• Standard 7: Geometry
• Standard 8: Measurement
• Standard 9: Statistics
• Standard 10: Probability
• Standard 12: Patterns, Relations, Functions
• Introduction to Mathematics
• Table of Contents - All Standards

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Content Standard: Algebra

Students will apply algebraic reasoning to explore the structure of mathematics.

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Fourth Grade Performance Standards: Algebra

By the end of grade Four, students will:

Use letters, boxes, or other symbols to stand for any number, measured quantity, or object in simple situations (e.g., N + 0 = N is true for any number)

Use the vocabulary, symbols, and notation of algebra accurately (e.g., correct use of the symbol "="; effective use of the associative property of multiplication)

Work with simple linear patterns and relationships in a variety of ways, including

• recognizing and extending number patterns
• describing them verbally
• representing them with pictures, tables, charts, graphs
• recognizing that different models can represent the same pattern or relationship
• using them to describe real-world phenomena

Recognize variability in simple functional relationships by describing how a change in one quantity can produce a change in another (e.g., number of bicycles and the total number of wheels)

Use simple equations and inequalities in a variety of ways, including

• using them to represent problem situations
• solving them by different methods (e.g., use of manipulatives, guess and check strategies, recall of number facts)
• recording and describing solution strategies

Recognize and use generalized properties and relationships of arithmetic (e.g., commutativity of addition, inverse relationship of multiplication and division)

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Eighth Grade Performance Standards: Algebra

By the end of grade Eight, students will:

Work with algebraic expressions in a variety of ways, including

• using appropriate symbolism, including exponents and variables
• evaluating expressions through numerical substitution
• generating equivalent expressions
• adding and subtracting expressions

Work with linear and nonlinear patterns and relationships in a variety of ways, including

• representing them with tables, with graphs, and with algebraic expressions, equations, and inequalities
• describing and interpreting their graphical representations (e.g., slope, rate of change, intercepts)
• using them as models of real-world phenomena
• describing a real-world phenomenon that a given graph might represent

Recognize, describe, and analyze functional relationships by generalizing a rule that characterizes the pattern of change among variables. These functional relationships include exponential growth and decay (e.g., cell division, depreciation)

Use linear equations and inequalities in a variety of ways, including

• writing them to represent problem situations and to express generalizations
• solving them by different methods (e.g., informally, graphically, with formal properties, with technology)
• writing and evaluating formulas (including solving for a specified variable)
• using them to record and describe solution strategies

Recognize and use generalized properties and relations, including

• additive and multiplicative property of equations and inequalities
• commutativity and associativity of addition and multiplication
• distributive property
• inverses and identities for addition and multiplication
• transitive property

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Grade Level Performance Standards: Grade Six: Algebra

The student will:

Write mathematical equations to describe situations involving equalities and inequalities.

Solve linear equations given replacement sets for one variable.

List a series of possible values for two variables in linear equations.

Combine numbers and operations in various ways to arrive at given solutions.

Plot and describe points on coordinate grids.

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Grade Level Performance Standards: Grade Seven: Algebra

The student will:

Determine the possible values of variables in equations.

Graph and identify ordered pairs on coordinate grids.

Write algebraic expressions using one or two variables to model real situations.

Develop equations from known values in function tables.

Use graphs to find solutions to equations.

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Grade Level Performance Standards: Grade Eight: Algebra

The student will:

Solve linear equations when given replacement sets for one variable.

Graph linear functions on coordinate planes.

Develop formal methods for solving linear equations and inequalities after experimenting with informal methods.

Use concrete, numeric and graph methods to describe algebraic relationships.

Use graphing utilities to generate relationships between two expressions.

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Twelfth Grade Performance Standards: Algebra

By the end of grade Twelve, students will:

Analyze and generalize patterns of change (e.g., direct and inverse variation) and numerical sequences, and then represent them with algebraic expressions and equations

Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways, including

• recognizing that a variety of mathematical and real-world phenomena can be modeled by the same type of function
• translating different forms of representing them (e.g., tables, graphs, functional notation, formulas)
• describing the relationships among variable quantities in a problem
• using appropriate technology to interpret properties of their graphical representations (e.g., intercepts, slopes, rates of change, changes in rates of change, maximum, minimum)

Solve linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities

• numerically
• graphically, including use of appropriate technology
• symbolically, including use of the quadratic formula

Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations, and inequalities

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