On some of the homework related to spherical harmonics, I saw several students struggling with the fact that $$\vert Y_1^1\vert^2+\vert Y_1^{-1}\vert^2\neq\vert Y_1^1+ Y_1^{-1}\vert^2$$ This activity may be one place to address when one wants the square of the sum (probability density for a linear combination) and when one wants the sum of squares (probability for measuring a degenerate state)