March 11, 2013
How many paper balls will fit in the can?
- 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 best-fitting circle to measure the best-fitting 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 one-tenth 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 - Best-fitting circles & diameters
- Image6 - Trashketball diameter
- Image7 - Formulas with Pi
- 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)
How long does it take to fill the trash can?
Keep the diameter of the can and trashketballs, how tall would the can need to be to fit 1000 balls?
Keep the height of the can, how many trashketballs would fit if the canâ€™s diameter were doubled?