With the very young (preschool), the key is to be quick to give them short things to do. They are incredibly energetic and the hardest part of teaching them is to keep them interested and busy. I would go through as many of the following concepts and exercises until one third of the way through their lesson time, then go back to the beginning.
I like to approach their lesson as visiting categories of learning: aural training, visualizing keyboard/ keyboard awareness, tactile (finger dexterity/technique), vocalization, rhythm, and notation. Combinations of these categories are inevitable, especially the physical aspect, which the child craves. In the beginning, relationship is of utmost importance: develop mutual trust, appreciation, and optimism.
Some method books have activities for the very young. There are so many methods, and so many different activities, since teaching the very young is challenging. They have less skills and basic understanding then an older child. You can't take much for granted (e.g., ability to distinguish loud and soft on different octaves).
Here are some ideas from the recently post video and my experience:
in Front of Piano - quickly ask to sit with feet in front. Repeating this
frequently is unecessary; if child moves, it is usually because you
aren't keeping them...you guessed it... interested and busy.
Find groups of 2 black keys.
Play together, separately, with index fingers only. Repeat in all octaves.
Copy game: Play same key as me. As many times. Loud, soft, short, long.
I copy you!
Finger Exercise - Discover if child is right/left handed. Teach R and L. Count fingers. Show me 2, 3, etc.
Simon says touch the piano with finger 2, 3, etc. Switch hands.
Play hi and lo keys. Tell me too!
Teach Hot Cross Buns
Student claps, teacher counts 1 - 2, by twos. Switch.
Aural/Visual : Play and ask questions about Loud, soft, short, long.
Watch and Copy game on 2 black keys.
Use previous finger exercise game.
Hot Cross Buns with both hands
Student claps, teacher counts 1 - 2, by twos. Fast, slow. Switch.
Hot Cross Buns
Repeat in all octaves.
Repeat with teacher accompaniment.
Repeat using E, D, C.
Finger Exercises on 2 keys, copy teacher
Find groups of 3 black keys.
Teacher counts 1 - 2, by twos, student improvises. Switch roles.
Introduce posture and hand position.
Learn Hot Cross Buns with 3 Fingers
Mary Had a Little Lamb