This lecture is best introduced with the Computing the $S^{2}$ Operator for the Spin-$\frac{1}{2}$ System activity.

The $S_{x}$, $S_{y}$, and $S_{z}$ operators for the spin-1 system can then be written on the board. From here, have a third of the room calculate $S_{x}^{2}$, a third calculate $S_{y}^{2}$, and the final third calculate $S_{z}^{2}$. Gather answers from each side and write the answers under the non-squared operators.

Finally, add all of the squared operators for the spin-1 system to find $S^{2}$. It can be shown that $S^{2}$ for the spin-1 system is $2\hbar^{2}$ multiplied by the identity matrix.

When $2\hbar^{2}$ is compared to the expression $l(l+1)\hbar^{2}$, we can find that $l=1$, indicating that the system is a spin-1 system as we knew before.