### DOE Archives

#### New Jersey Core Curriculum Content Standards

May 1996

Mathematics Standards And Progress Indicators
Standard 4.15:
All Students Will Develop An Understanding Of The Conceptual Building Blocks Of Calculus And Will Use Them To Model And Analyze Natural Phenomena

Descriptive Statement: The conceptual building blocks of calculus are important for everyone to understand. How quantities such as world population change, how fast they change, and what will happen if they keep changing at the same rate are questions that can be discussed by elementary school students. Another important topic for all mathematics students is the concept of infinity - what happens as numbers get larger and larger and what happens as patterns are continued indefinitely. Early explorations in these areas can broaden students' interest in and understanding of an important area of applied mathematics.

Cumulative Progress Indicators

By the end of Grade 4, students:

 1 Investigate and describe patterns that continue indefinitely. 2 Investigate and describe how certain quantities change over time. 3 Experiment with approximating length, area, and volume, using informal measurement instruments.

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

 4 Recognize and express the difference between linear and exponential growth. 5 Develop an understanding of infinite sequences that arise in natural situations. 6 Investigate, represent, and use non-terminating decimals. 7 Represent, analyze, and predict relations between quantities, especially quantities changing over time. 8 Approximate quantities with increasing degrees of accuracy. 9 Understand and use the concept of significant digits. 10 Develop informal ways of approximating the surface area and volume of familiar objects, and discuss whether the approximations make sense. 11 Express mathematically and explain the impact of the change of an object's linear dimensions on its surface area and volume.

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

 12 Develop and use models based on sequences and series. 13 Develop and apply procedures for finding the sum of finite arithmetic series and of finite and infinite geometric series. 14 Develop an informal notion of limit. 15 Use linear, quadratic, trigonometric, and exponential models to explain growth and change in the natural world. 16 Recognize fundamental mathematical models (such as polynomial, exponential, and trigonometric functions) and apply basic translations, reflections, and dilations to their graphs. 17 Develop and explain the concept of the slope of a curve and use that concept to discuss the information contained in graphs. 18 Develop an understanding of the concept of continuity of a function. 19 Understand and apply approximation techniques to situations involving initial portions of infinite decimals and measurement.

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