Exploring Circular Objects

This lesson uses WebImage, a Web-based customized version of ImageJ, to investigate the relationship between the circumference and diameter of a circle. Images of circular objects are provided, and, by measuring diameter and circumference, students are able to obtain an approximate value of Pi. They also explore the history behind Pi and how to find its value.

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Relevant standard(s)

NSES Standard: Science as Inquiry, Grades 5-8, Content Standard A
• USE APPROPRIATE TOOLS AND TECHNIQUES TO GATHER, ANALYZE, AND INTERPRET DATA: The use of tools and techniques, including mathematics, will be guided by the question asked and the investigations students design. The use of computers for the collection, summary, and display of evidence is part of this standard. Students should be able to access, gather, store, retrieve, and organize data, using hardware and software designed for these purposes.

NSES Standard: Science and Technology in Society, Grades 5-8, Content Standard E
• Science and technology are reciprocal. Science helps drive technology, as it addresses questions that demand more sophisticated instruments and provides principles for better instrumentation and technique. Technology is essential to science, because it provides instruments and techniques that enable observations of objects and phenomena that are otherwise unobservable due to factors such as quantity, distance, location, size, and speed. Technology also provides tools for investigations, inquiry, and analysis.

NSES Standard: Science in Personal and Social Perspective, Grades 5-8, Content Standard F
• Societal challenges often inspire questions for scientific research, and social priorities often influence research priorities through the availability of funding for research.

NSES Standard: History and Nature of Science, Grades 5-8, Content Standard G
• Many individuals have contributed to the traditions of science. Studying some of these individuals provides further understanding of scientific inquiry, science as a human endeavor, the nature of science, and the relationships between science and society.

NCTM Standard: Geometry, Grades 6-8
Instructional programs should enable students to use visualization, spatial reasoning, and geometric modeling to solve problems:
• understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;

NCTM Standard: Measurement, Grades 6-8
Instructional programs should enable students to
(a) understand measurable attributes of objects and the units, systems, and processes of measurement:
• understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume, and
(b) apply appropriate techniques, tools, and formulas to determine measurements:
• develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

NETS Standard: Grades 6-8
• Use content-specific tools, software, and simulations (e.g., environmental probes, graphing calculators, exploratory environments, Web tools) to support learning and research.