Trashketball (cylinder)
35
skips
skips
65
questions
questions
Act One
Act Two
 Teacher noteHow do you find the diameter of a trashketball? Have your students come up with ideas. Provide scratch paper for them to test those ideas. Make conjectures.
Want to go paperless? I crumpled up 8.5"x11" paper and made it as compact as possible. I took a handful of trashketballs and put them down on a ruler to get a rough mental mean of the diameters. Then I traced the bestfitting circle to measure the bestfitting diameter of each trashketball. I took the mean of these five diameters.
CCSS assessments might provide students with formulas or they might give students choices. Image 7 has many formulas with Pi. Display this for your students and have them figure out if any of them are useful, which one(s) to use, and if you can verify the correct formula via textbook, chart, or internet.
An extension to the task would be to explore the difference onetenth the radius makes in your calculated answer.  Image1  Can Dimensions Estimate
 Image2  Can Dimensions
 Image3  How do you measure a trashketball?
 Image4  Sample Trashketballs
 Image5  Bestfitting circles & diameters
 Image6  Trashketball diameter
 Image7  Formulas with Pi
Act Three
 Teacher noteThis is a great opportunity to talk about the theoretical answer versus the practical answer. Why is there a difference? Does it make sense? Have students explain their reasoning/justification.
What could be done to actually fit all of the theoretical answer trashketballs in the can?  VideoTrashketball  Act 3 (cylinder)
Sequel
 1.
How long does it take to fill the trash can?
 2.
Keep the diameter of the can and trashketballs, how tall would the can need to be to fit 1000 balls?
 3.
Keep the height of the can, how many trashketballs would fit if the canâ€™s diameter were doubled?
show 65 more questions

How many crumpled / uncrumpled pieces of paper would it take to fill up the trash can?














How many trashketballs fit in the can? What is your "field goal" percentage?













































What equation could define the path of a paper ball that lands in the waste paper bin?





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