How to pass your thumb correctly on piano using only 3 fingers?

Passing the thumb under the hand makes it possible to run the keyboard and to begin the study of the scales.

To pass the thumb, fold it under the hand, loosely; then as soon as the note is played, restore the position of the hand, facing the keyboard, in line with the forearm. During this moment, the wrist is slightly raised (simple accompanying gesture).

In drill 1 and 2, the hand returns to its position facing the keyboard on the doted half.

Then Work on the drills with the finger 2341.

In drill 3 and 4 the hand returns to its position facing the keyboard on the 3rd finger.

Then work on the drills with the finger 1432.

The hand returns to its position facing the keyboard on the 4th finger.

This exercise is taken for the book Ma Première Année De Piano.