Background Information for Teachers
If the mathematics of three dimensions feels less certain to you than that of two dimensions, you are not alone! These professional resources support the teaching of solid geometry in both the areas of shape and measurement. They include two workshop sessions that review the material, while allowing for hands-on experimentation; a book chapter that gives the underpinnings and relevance of the whole study of solids; and a set of activities addressed to teachers for their classrooms. We hope you will enjoy revisiting and reinforcing your knowledge of this practical, and sometimes beautiful, topic of geometry.
Through these activities, developed for teachers, you can explore three-dimensional figures by building and manipulating the Platonic solids, exploring their properties and some of the geometric relationships between them. Other investigations focus on nets and cross-sections of solids. This is one session in the free online course Learning Math: Geometry.
This online workshop for teachers begins with an examination of the relationships between area and perimeter but goes on to the proportional relationship between surface area and volume and some of its applications. For instance, you will construct boxes and use graphs as you try to find the dimensions of the rectangular prism that holds the maximum volume. Video segments of teachers working on this activity lead to further discussion in this session from Learning Math: Measurement.
"Shape is a vital, growing, and fascinating theme in mathematics with deep ties to classical geometry but goes far beyond in content, meaning, and method," writes the author of "Shape," a chapter in On the Shoulders of Giants: New Approaches to Numeracy (National Academies Press, 1990). The chapter focuses on the significance of shape as a concept, its place in mathematical history, the tools used to study it, and its connections to art and other fields. Throughout, the language is accessible, and the author continually highlights the relevance of the topic to the school curriculum. Excellent professional background reading! On the Shoulders of Giants is available free online. MSP full record
These are behind-the-scenes lesson ideas for teachers. George W. Hart, polyhedral master, gives ideas and instructions on how to construct polyhedral models from paper, soda straws, wood, and the Zometool kit. Although Hart does not give step-by-step directions here, he does make his ideas clear and shows a picture of each model. Part of Hart’s Virtual Polyhedra: The Encyclopedia of Polyhedra.
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Copyright
September 2006 — The Ohio State University. This material is based upon work
supported by the National Science Foundation under Grant No. 0424671. Any
opinions, findings, and conclusions or recommendations expressed in this
material are those of the author(s) and do not necessarily reflect the views of
the National Science Foundation.
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