My process of teaching scales is as follows

A pentascale pattern do re mi fa so fa mi re do mi so mi do followed by a block chord.

Next step is to extend to hands separate octave scales using correct fingering (eg 123123454321321)

However, today I've discovered tetrachord position! Never heard of it in my life before.

You use both hands to do a single octave for example in C the LH fingers 5432 would play CDEF then the RH fingers 2345 would play GABC.

Now I'm wondering if I should add this in between my two stages or is it an unnecessary step?

Do you use tetrachord position to teach scales?

Not usually, no, but just now and then, yes.

A couple of the books I use have a tune that uses this pattern to teach key G. So in this case - especially with a child who needs a bit more 'filling in' I might do this.

I have tried lots of different ways of teaching scales and have come to the conclusion that simple is best.

I give students a printed sheet with the letters of the scale typed out in order with the RH fingering above and the LH fingering below. eg:

RH 123123412312345
CDEFGABCDEFGABC
LH 543213214321321

(except that the numbers and letters are correctly aligned of course)

It works for me.

Tetrachords are fine for scales with C major fingering, not so good Bb major etc, or any of the melodic minors.