(Lecture: 10 minutes)
An explicit derivation of the Galilean transformation between (Newtonian) inertial frames is probably not helpful, although it is worth presenting the simple derivation that, since two such frames differ by a constant velocity, all accelerations are the same in either frame.
This lecture works well as a continuation of the wrap-up to the Inertial Frames SWBQ. The key point is that Newton's laws (as usually formulated) are only valid in inertial frames. The next step will be to find a formulation which holds in rotating frames; whether the result should be referred to as “Newton's laws” is a separate, and largely philosophical, question.