Encouraging Mathematical Thinking


 Abstract
 Introduction

 Discourse
 Interventions
 Decisions

 Cylinder Problem
  - Elementary
  - Middle School
  - High School
  - Calculus
 Lesson Reflections
 Student Predictions

 Project Reflections
 Conclusion

 References
 Acknowledgments
 Teacher Resources



Authors'
Biographies

Table of Contents


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Family Math Activity



Directions:

Fold the 11" side of an 8.5" by 11" sheet of paper in half and cut the paper along the fold into two pieces, each measuring 5.5" by 8.5". Tape the two pieces together to form a rectangle 5.5" by 17". Repeat the process with another 8.5" by 11" sheet of paper. You should now have two rectangles, each 5.5" by 17".

Now roll these two rectangles into two different cylinders - one taller and narrower (17" high) and another shorter and stouter (5.5" high). Label the tall one E (17" high) and the short one F (5.5" high).

Do you think the two cylinders will hold the same amount? Or will one hold more than the other? If you think that one will hold more, which one will it be?

Record your predictions, with an explanation.

Place cylinder F on a cookie sheet with cylinder E inside it. Fill cylinder E. Slowly lift cylinder E so that the filler material falls into cylinder F.

  1. Was your prediction correct?

  2. Do the two cylinders hold the same amount?

  3. Explain why or why not.

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