Word Construction, Roller Blades, Helping, Ratio, and Headed North?

Yeesh, the last two days have been full!
Lily made a new friend yesterday, and today decided to roller blade with them (and the entire run of kids on our street), as well as Russ and I around the neighborhood.  She has learned how to have mama on her blades while Lils enjoys a very fast trike ride, and has become quite proficient at riding her two wheel bicycle that is now attached to mine.  We ordered a Trailgator, which is like a tow arm that puts her little bike in line behind my big one.  She really seems to enjoy it.
(Pictures coming)
A few days ago, we took the training wheels off her bike and she and I went around a bit.  She doesn’t like the wobbly feeling much, and on a bike so small, it’s very hard (even for her comparable size) to gain enough momentum to feel the sense of balance occur.  The wheels are just too small and disproportionate with the frame of the bike and its occupant for the laws to easily apply.  I expect it won’t matter much, however, as she’ll be in the next size by next spring and we can work on it then.
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She’s now building/working out words right and left. If she sees a word on the tv, a sign, or book/paper/mail/whatever, and is so inclined, she works through it until she figures it out.  Most of the time, my assistance is not only unnecessary, but made well known it is unwanted.
This week, she has started building real words, at random and unsolicited by either of us.  Previously, she’d throw together a bunch of letters, sound through them, and hope she came up with a word (or make a new one).  Now, however, she’s got a solid enough foundation both in phonics and the concept of order, combination, and vowels that she works out the word in her head and then makes it with her letters. She builds letter by letter most of the time.
She has perfected the art of writing her name, and now is showing interest in trying to write other words.  We installed a handwriting app on her tablet so she can play with letters, characters, and continue her fine motor development.  Of course, she has paper and writing utensil as well, but we try to use as many different mediums as possible.  The other day, she wrote in the sand, and the next time we fog up the bathroom mirror, I will try to remember to encourage her to draw and write in the fog, instead of just feverishly clearing it away with her palms as she does.
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Last night, we went for a something-on-wheels ride and I answered a question of Russ’s as to which direction we should initially go.  Lily was listening.  My response was “north”? Lily responded, “Ok, Colton (the neighbor boy accompanying us, who will be 5 next month) that’s this way.  And off she went, northbound.
Neither of us had a clue she had any directional orientation comprehension.  Though, actually, I have heard her fill in the missing city when Russ stated once that we were headed east.  She indicated that we must be going to Alamosa or Grandma’s then.  We were going to La Veta, but one must pass through Alamosa first, and La Veta is 1/4 the way to Grandma’s.  She knows the hospital and the stores are in Alamosa, and if we turn west out of our neighborhood, or deviate n/s off the main road that takes us to Alamosa, (given that she has been told of our intended destination being Alamosa) she’ll tell us we’re headed in the wrong direction.
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Russ put his blades on last night for the first time in years and Lily helped him skate.  She went on her trike, which has a Papa handle and the two of them went cruising around the neighborhood.  She knew she was assisting him significantly, and I swear it propelled her forward a good few years for the duration.  I think we saw a glimpse of her compassion matured last night.
He crashed once, and she responded as if she’d personally failed him.  Which she hadn’t.  The pavement had turned to sand and Russ didn’t see it in time, it was well after sunset that we were out.  It took both of us explaining the physics of the fall to her a couple of times before she decided the best thing to do was remain available to Papa with her trike, and steer him home, straight and safe.
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Umizoomi had a short on tv last night with Milli using her pigtails (normally for measuring length) as scale arms.  Then Geo and Bot placed buckets filled with water on either end.  Milli explained that the heavier bucket, the one with more water in this case (for this demonstration, both buckets were comprised of the exact same material and mass) would go down.  Bugz watched intently.  I suspect we will have a large scale reconstruction underway today.
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Oh, how to explain ratio to the littlest minds… Lily has demonstrated her comprehension of the concept indirectly on more than a few occasions.  She reasons through the concept of ratio, but has no clue that she is doing something in a broader sense, that has been given a title no less.  I’d like to encourage this particular development, but am having a bit of a time coming up with scenarios and situations in which she has to reason through and either determine ratio or just think within the concept.
Ratio can be determined in just about anything, which is the problem.  I’m looking for some ideas on how to get her to naturally work though a more complex computation of ratio, based on something she wants/needs requiring it.  – This might be very simple to some to come up with such scripted opportunities, and so I welcome suggestions.
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I have seen profound social development in the last two days.  Where, just a few months ago, she struggled immensely to assert herself with the older kids (except Savannah), and where just a few weeks ago, she struggled immensely with being included/excluded, she now seems to be able to roll with the flow.  She stands up for herself, but she is learning when to just blend.  She asserts, and sometimes needs me, but generally she will have a tolerant attitude that is responsive and fun instead of singular and stressed.
Case in point, on Saturday, she and I decided to make water balloons; we invited a couple of the kids to join our competition (two 9 year old girls, and a 4 year old boy).  They readily joined in, except the 4 year old who adamantly did not wish to get wet.  The girls are unbelievably gentle with Lily, but a couple stray balloons got her good.
In the immediate moments after each balloon burst, I watched Bugz sort through her responses to being suddenly drenched by the opponent. The first couple of times, I saw fear, injustice, confusion, annoyance, helplessness.  But she quickly adapted, and the fear became surprise/startle, the injustice turned into a desire to return the favor, confusion disappeared as she popped a few on herself unintentionally (and then intentionally), the annoyance faded somewhat into fun and anticipation, and the helplessness disappeared (right about the same time she landed one smack in the middle of MY back).
She went after (with ammo) all of the kids equally, including the 11 year old neighbor boy who joined in the festivities.  She was also fair game by her own decision, while the 4 year old remained “off limits”.  Though, I over heard her telling him that since she was only three, either she could get him or he was littler than she.  He doesn’t want to be called smaller than her – they are physically the same size, mind you.  She knows this is a weak spot with him and she used it to get him to play with the group.  And while I’m not certain I want to encourage such manipulation, it is intriguing that she’s already developed the ability to use it.
She communicated to him her reasoning in a very direct and matter of fact manner, such that I didn’t sense any malice or intent to harm.  She may or may not be able to understand the complexity of others’ feelings at that level yet.  I believe she experiences the dynamics of the full spectrum of her own emotions, but it’s not clear to what extent her empathy has developed where hidden/layered emotional responses of others are concerned.  Judging from the boy’s response, however, he felt the hit of the lack of respect.  I have a feeling it’s something he’s accustomed to (most unfortunately), and so I will begin to work with Lily on this. Ideally, I’d like to see her sensitivity and empathy develop specifically with this particular boy because I think they both would benefit greatly from it, especially if we live here long enough.  They’re close enough in age and categorical interests that a solid and lasting friendship could develop.