In which stage(s) of non-rem sleep do brain waves become larger and punctuated with occasional sudden bursts of electrical activity? ?

The correct answer is second stage of non-rem sleep.

Explanation:

The NREM of the non-rapid eye movement sleep, also called the quiescent sleep comprises three stages of sleep. In NREM, there is little or no movement of eye witnessed in any of the three stages, which is dissimilar to REM sleep.  

In the second stage of NREM sleep, no movement of eyes is witnessed, and dreaming is very rare. The sleeper can get awaken quite easily. In the stage, the electroencephalogram readings demonstrate sleep spindles, that is, the brief bursts of high-frequency activity of the brain, and K-complexes.