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#### New Jersey Core Curriculum Content Standards

May 1996

Mathematics Standards And Progress Indicators
Standard 4.11:
All Students Will Develop An Understanding Of Patterns, Relationships, And Functions And Will Use Them To Represent And Explain Real-World Phenomena

Descriptive Statement: Patterns, relationships, and functions constitute a unifying theme of mathematics. From the earliest age, students should be encouraged to investigate the patterns that they find in numbers, shapes, and expressions, and, by doing so, to make mathematical discoveries. They should have opportunities to analyze, extend, and create a variety of patterns and to use pattern-based thinking to understand and represent mathematical and other real-world phenomena. These explorations present unlimited opportunities for problem-solving, making and verifying generalizations, and building mathematical understanding and confidence.

Cumulative Progress Indicators

By the end of Grade 4, students:

 1 Reproduce, extend, create, and describe patterns and sequences using a variety of materials. 2 Use tables, rules, variables, open sentences, and graphs to describe patterns and other relationships. 3 Use concrete and pictorial models to explore the basic concept of a function. 4 Observe and explain how a change in one physical quantity can produce a corresponding change in another. 5 Observe and recognize examples of patterns, relationships, and functions in other disciplines and contexts. 6 Form and verify generalizations based on observations of patterns and relationships.

Building upon knowledge and skills gained in the preceding grades, by the end of Grade 8, students:

 7 Represent and describe mathematical relationships with tables, rules, simple equations, and graphs. 8 Understand and describe the relationships among various representations of patterns and functions. 9 Use patterns, relationships, and functions to model situations and to solve problems in mathematics and in other subject areas. 10 Analyze functional relationships to explain how a change in one quantity results in a change in another. 11 Understand and describe the general behavior of functions. 12 Use patterns, relationships, and linear functions to model situations in mathematics and in other areas. 13 Develop, analyze, and explain arithmetic sequences.

Building upon knowledge and skills gained in the preceding grades, by the end of Grade 12, students:

 14 Analyze and describe how a change in an independent variable can produce a change in a dependent variable. 15 Use polynomial, rational, trigonometric, and exponential functions to model real-world phenomena. 16 Recognize that a variety of phenomena can be modeled by the same type of function. 17 Analyze and explain the general properties and behavior of functions, and use appropriate graphing technologies to represent them. 18 Analyze the effects of changes in parameters on the graphs of functions. 19 Understand the role of functions as a unifying concept in mathematics.

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