another "wish I had a video" moment, for its instructional value. This wasn't a light bulb going on, but oh, perhaps a dimmer switch being eased forward to provide some more light.
I had a student working on "The Ruler Game." (not the fraction game... but that's a good google, too... more on that later!) She had no trouble with wholes and halves, and not too much trouble with fourths, a.k.a. quarters.
I had noted that the game never uses fractions that could be reduced. The student has to find 3 1/4 on a ruler; never 3 2/8. INtuitively I like this because this is what you're going to be expected to do. However, I wondered about the "missing piece."
Well, with a sample size of one I'm not going to dash out and draw conclusions, but when we got to the eighths, serious thinking had to happen... and it included talking through the other representations of the fractions. 2/8 was the same as 1/4. 4/8 was the same as one half. I suggested the strategy of finding 5/8 by starting at 4/8 and working forward and this was successful.
More importantly, I got to watch "constructivism" in progress. Information was organized; ideas were explored; questions were asked. There were/are some conceptual issues still - the "1/16 is always the same distance" isn't really solid (but "it's the smallest step" is sinking in and I'm pretty sure that it will register, probably overnight and tomorrow it'll be obvious :-)).
CHeck out that fraction game :-) Oh, it's also pretty darned good for impulse control and mouse maneuvering skills.
Now, the setting up those notorious "Lou drives away at 40 mph. Jenny realizes he forgot his notebook and drives after him at 60 mph. In how many hours does she catch up?" problems... welp, even that isn't too insane.