A Billion Nickels
Problem
Media: A Billion Nickels
Possible Questions (directed by students): Would Andy be able to carry $1000 in nickels? What does $1000 in nickels look like? What does $1,000,000,000 in nickels look like? (Would it fit in this room?)
Implementation
- Show the video clip: A Billion Nickels.
- Ask students what questions they have about the video. Student questions will most likely be similar to the above questions mentioned.
- Have students take guesses to a probable answer. Place guesses on the board or ask them to write them down on their own paper.
- Have students help to develop a limit for guesses (what is too high? what is too low?).
- Distribute resources necessary for problem solving.
- Separate students into small groups (2-5 individuals each) and allow time to determine a possible solution. During this time circulate among the groups to help support understanding, do not allow yourself to "think" for your students (engage them with questions such as "why?" or "how?", regardless of if students are on the right track or not).
- Call together the classroom and ask individuals from each group to explain their findings. Ask deeper questions to gauge their understanding. If groups have a discrepancy ask them to "argue" their point.
- If time allows, extend the task with listed possible extensions.
Extension
- If multiple questions were asked by students, consider going over an additional question or two.
- Consider asking additional questions such as the ones listed above or...
- How heavy would $1000 in nickels be?
- If we stacked $1000 in nickels, how high would they reach? How about 1,000,000,000 nickels?
- If he made a pyramid out of the nickels, how big would the base have to be? (See: Pyramid of Pennies)
Resources and References
Resources
References
Zero Knowledge Proofs - A Billion Nickels