Unschooling, Math, and Motivation

I had a fabulous idea for a math problem for chana.  Well, actually, it started as something I was starting to figure out and decided it would be great to fob off onto chana.  I noticed I was running low on face wash.  I have two brands.  One is 6oz and one is 16oz.  I like them both equally.  I wondered which one to replenish.  I thought it would be great for chana to do that.  Real live math.  So practical. 

All she has to do is go online, find the prices for each one, and she'll slowly and eventually realize that since they are different sizes, the cheaper one might be smaller so it's not necessarily the better deal.  Then she'll have to do some math.  She probably won't do it efficiently, but she'll be able to do it at her pace, and it will provide her with a deep understanding of unit price, much better than anything I could teach her from a book.

So I went downstairs and told her I would like help figuring out my shampoo.  She was in the middle of animating her latest movie.  She has subscribers who are waiting for the next installment.  Without taking her eyes off the screen, she told me she's not interested.

I am absolutely positive that as soon as she has her own, limited amount of money, and she has objects that she would like to buy, she will figure out how to get the most item for the cheapest unit price.  I tried to nudge her towards it, but since she doesn't need it now or find it useful, she is not interested.

I could urge her to work through the steps with me.  It would take about a half an hour, she'd be longing to go back to animation, she'd be annoyed that I'm disturbing her creativity, and she may or may not understand it.  Let's even say that she will understand it, since we are doing one-on-one work and i ought to be able to figure out a way.  But she won't be emotionally connected to it, she won't care, she might or might not remember it when it does eventually become relevant to her.

On the other hand, if I wait until she encounters it herself, and she has the idea that these types of questions are answerable with a little thought and calculation, and she knows i'm available for guidance if she gets stuck, then as soon as she needs it, she'll figure it out extremely quickly.  She'll be motivated and efficient.
***
The other day, chana was trying to figure out how many pages she had left to the book.  She wanted to calculate how many pages she had to do per day in order to finish it in a week.

I wanted so badly to show her how to look at the page numbers and subtract.  I tried to show it to her.  She was counting page by page.  She got irked that I butted in.  I've been thinking about that.  If I let her do it at her pace, using the method that she is figuring out, then she'll have a much deeper understanding of the process and it will be much more real and useful to her, then if I impose my way of doing the calculation.