Encouraging Mathematical Thinking


 Abstract
 Introduction

 Discourse
 Interventions
 Decisions

 Cylinder Problem
 Lesson Reflections
 Student Predictions

 Project Reflections
 Conclusion

 References
 Acknowledgments
 Teacher Resources



Authors'
Biographies

Table of Contents


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Incorporating the Geometer's Sketchpad



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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