Abstract  Introduction  Discourse  Interventions  Decisions  Cylinder Problem  Lesson Reflections  Student Predictions  Project Reflections  Conclusion  References  Acknowledgments  Teacher Resources Authors' Biographies Table of Contents About the Project VIDEO CLIPS: Internet access via modem may mean very long download times for video clips. If you are not on a fast line, you may want to read this paper without viewing the clips. share your thoughts, ideas, questions, and experiences; read what others have to say. Enter your e-mail to be notified of discussion on this videopaper: Privacy Policy		If you have access to The Geometer's Sketchpad software, the following sketches can be used to illustrate the shape of the paper and the resulting shapes of the graphs of surface area and volume. If you don't have access to GSP, you can still download the graphs and view them using the demo version of the software. Demo versions for both Windows and Mac are available from Key Curriculum Press. Paper with Constant Area This sketch shows a draggable piece of paper with a constant area (93.5 in2). It then graphs the height of the paper versus the volume and the length of the paper versus the volume. Either graph can be shown separately. Click on the graph to download the sketch. Paper with Constant Perimeter This sketch shows a draggable piece of paper with a constant perimeter (39 in). It then graphs the width of the paper versus both surface area and volume. Click on the graph to download the sketch.

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