Different literature padding for Merkle-Damgard
The customary (and secure) padding is the one you have been taught: at the end of the message add a single 1 bit, then just enough (possibly none) 0 bit(s) to reach the end of a block less the size devoted to the length (64-bit before the 512-bit limit for MD5, SHA-1, and SHA-256; 128-bit before the 1024-bit limit for SHA-512); then add the length (little-endian for MD5, big-endian for SHA-x).

The padding that you describe based on Hans Delf and Helmut Knebl is equally secure, but often uses one more block than the other.