It started with trying to compare sweets of different sizes. If a big cookie is a sweet, how many skittles make a sweet? How many little cookies? How many rolos? So Lily got into counting: perhaps twelve skittles are a sweet, so she'd count them out. She was very motivated, since she (a) wants as much candy as possible and (b) is very into following rules exactly.

Then we got into sweet combinations. Perhaps Lily would want skittles and ice cream. I would get a half-sized portion of ice cream, and I'd have her figure out how many skittles were half a sweet. One way we'd do this would be to divide them into two equal piles and pick one. We noticed that sometimes you can't make equal piles, because there's one left over, in which case she would generally want to give the extra one to her sister. She got pretty comfortable with the idea of half a sweet.

Currently we're doing a lot on a quarter basis. She doesn't totally have the concept, but understands it well enough for "I've had half my sweet; can I have a quarter sweet worth of chocolate chips?" Or if she's had three of something where four make a sweet she can usually tell me she still has one coming. Today she asked for half a sweet's worth of nutella on waffles for breakfast, and then when they weren't chocolatey enough asked me to bring it up to three-quarters.

One driver here has been uncertainty about what the rest of the day will hold, and wanting to reserve portions of a sweet. If she had a full sweet's worth of nutella on her waffle, and then in the afternoon some tasty option came along, she would be sad not to be able to have any. By eating only partial sweets she keeps her options open. [1]

From a perspective of keeping our kids from having too much sugar this seems like a lot of complexity, but I think it's good complexity. Lily's more motivated here than with anything else except maybe tablet time [2] and that's translated into her starting to learn how to think fractionally. One thing I'd like to get into next is how thirds and halves interact as sixths, but I'm waiting for a natural opportunity, like one where she's had a third of a sweet and then later had half a sweet.

[1] Another possibility is that I might not be great at estimating fractions, and "50% A, 50% B" could potentially end up being more than both "100% A" and "100% B".

[2] We don't do anything fractional here. The kids get unlimited audio-only tablet time (story tapes) and no regular video/game time. On long car trips and airplane rides they get unlimited video/game time, and we sometimes will use videos on the tablet as a special treat when we need to keep them occupied and quiet (we're both in meetings, or hosting a meetup).