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ORC Resource Number #107
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Bottles and Divers: Rates of Change
Best Practice
PROFESSIONAL COMMENTARY

This lesson has an introductory activity that uses bottles of various shapes to help students understand rate of change. The lesson then develops the concept of the average rate of change between two points on a curve. Finally, it examines instantaneous rate of change: The rate of change function is used to estimate the rate of change at a particular point. This function is used along with the calculator to make computing the rate of change fast and easy for students. The development of this function helps students understand what is meant by instantaneous rate of change and lays a firm foundation for the study of the derivative in calculus. In addition to the lesson plan, the site includes ideas for assessment, teacher discussion, extensions of the lesson, additional resources, and a discussion of the mathematical content. The user should first locate the lesson and then access the appropriate video clips illustrating lesson procedures. (author/pk).

TECHNOLOGY INTEGRATION
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OHIO STANDARDS
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Mathematics Academic Content Standards
Patterns, Functions and Algebra Standard
Mathematical Processes Standard
NATIONAL STANDARDS
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Principles and Standards for School Mathematics
Algebra Standard
Connections Standard
RESOURCE TYPE
Instructional Resource
PRACTICE LEVEL
Best Practice
STANDARDS ALIGNMENT
Grades 11–12
TOPICS
Mathematics --
Algebra;
Nonlinear functions;
Linear functions;
Calculus, precalculus;
Connections, applications;
Technology;
FOUND IN
KEYWORDS
graphing calculator;
rate of change;
slope;
scatterplot
Publisher: Public Broadcasting Service