Mathematics: Patterns, Relations, Functions

• 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 11: Algebra
• Introduction to Mathematics
• Table of Contents - All Standards

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Content Standard: Patterns, Relations, Functions

Students will recognize and use the concepts of patterns, relations and functions to describe, analyze, predict and model a variety of situations.

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Fourth Grade Performance Standards: Patterns, Relations, Functions

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: Patterns, Relations, Functions

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: Patterns, Relations, Functions

The student will:

Complete patterns in a variety of numeric and geometric sequences.

Find formulas to express the patterns illustrated in input/output tables.

Identify patterns in exponential and proportional relationships.

Use patterns, relations and functions to predict solutions to problems; generalize the results.

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Grade Level Performance Standards: Grade Seven: Patterns, Relations, Functions

The student will:

Extend geometric and arithmetic sequences.

Write rules or formulas for determining sequences of numbers or patterns.

Arrange numbers in grids, tables or charts to illustrate given rules.

Make, test and use generalizations about given information in problem situations.

Solve problems by reading and interpreting function tables.

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Grade Level Performance Standards: Grade Eight: Patterns, Relations, Functions

The student will:

Describe the advantages/disadvantages of using tables of data, graphs and expressions to describe functions.

Use observed patterns in gathered data to generalize to other situations.

Complete patterns in function tables for complex expressions.

Write mathematical rules in narrative and symbolic forms.

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Twelfth Grade Performance Standards: Patterns, Relations, Functions

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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