Stream cipher example for an introductory cryptography course
The shrinking generator (open to divide and conquer) or self-shrinking generators are possibilities.

If you use a nonlinear combination generator with 3 relatively prime length primitive LFSRs and a nonlinear boolean function $f(x_1,x_2,x_3)$ you can also illustrate the tradeoff between nonlinearity and the degree of the function (Xiao-Massey lemma) as well as have some room for divide and conquer. You can spend 10 minutes on Geffe and show how its weaknesses can be ameliorated with this generator.

It also enables you to explicitly compute the nonlinearity via $f(L_1, L_2, L_3)$ over the integers.