Fair sharing Exploration (warm-up)

who: J1 and J2
when: over a course of weeks (this is a plan, not a historical record)
what material: the objects to be shared

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This post: http://letsplaymath.net/2014/08/13/fractions-15-110-180-1/#more-28158 gave me the inspiration to create an extended plan to explore ideas around fair sharing. The idea got a further boost from our warm-up discussion about breaking swords and cutting cakes last weekend.

In our house, issues of fairness lurk just below the surface of almost every interaction between the children. Actually, that's not accurate, since fairness is often a visible dark cloud hanging over the proceedings.
Part of the idea for this exploration is to harness their strong feelings on this topic to examine:
- fractions (naturally)
- approximations
- competing theories of fairness/equality
- their own intuition and biases around what is fair and why something should (or shouldn't, or doesn't have to be) fairly distributed, including concepts of ownership ("that is mine!"), earned privileges ("he got X because he did Y"), and private valuations ("you like X more than Y, but she likes Y more than X").

The basic idea is to present different types of sharing problems as thought experiments: talk through or play-act the scenarios, do some analysis of different sharing tactics (maybe using manipulatives, diagrams, etc) and later come back to these in live examples.

Examples of different classes of sharing problems I see:
- cakes/pies: things that can easily be cut into small fractions
- sausages, or apples: something that can be cut reasonably accurately into moderate fractions (maybe down to 1/8th)
- ice cream, or soup/rice/etc: something that needs to be weighed or volume measured
- KEX cookies/small candies: something that can, at best, be cut in half, maybe not cut at all.
- ballons/babies/bicycles/scooters: items that are indivisible objects
- balls/group toys: items that increase in value as more people play (up to a point)

some types of questions are:
1) technically, what tactics can be used to divide, what are the pros and cons
2) strategically, how can you get buy-in that your approach to divide is fair?

Let me know if you have any tips or thoughts on how this will all turn out.