Before you begin introducing tonic sol-fa to your children, I would like to recommend The Curwen Method as an excellent, comprehensive website for those new to solfege (like me!). Also, there are several resources available in the Ambleside Online FAQ under "What is solfege?". Lynn Bruce has written a helpful overview that can be found on AO through that FAQ link.
Another useful link before you get started :) One of the best tips from this site is to have beginners sign with both hands (in mirror image). Later, as sol-fa skills develop, the children can switch to using only one hand. Also, as you watch the video, be sure to pay attention to where the instructor is placing her hand. For instance, at her chin or at her chest. The hand signs go higher up the body as the notes go higher up the scale. I didn't think that was clear from the YouTube clip.
Here's a Classics for Kids link that shows illustrated versions of the signs.
"Another feature of the Curwen Method was a well-founded pedagogy. In his Teacher’s Manual (n.d.[c.1876]), Curwen set out the following precepts:
… let the easy come before the difficult.
… introduce the real and concrete before the ideal or abstract.
… teach the elemental before the compound and do one thing at a
… introduce, both for explanation and practice, the common
before the uncommon.
… teach the thing before the sign, and when the thing is
apprehended, attach to it a distinct sign.
… let each step, as far as possible, rise out of that which goes
before, and lead up to that which comes after.
… call in the understanding to assist the skill at every stage."
The above was quoted from this excellent Curwen Method website (don't let the technicalities psych you out!)
The YouTube video below addresses using hand signs with intervals