Electromagnetic induction and its effects
Push the press switch several times. The thin rod gets sucked into the electromagnet and can be suspended there, or you can bounce it up and down. When you push the press switch, the thin rod gets sucked up and wiggles up and down until settling in position just below center. Measure how high you get the thin rod to go, then try with old and brand new batteries.
Also try adjusting the height of the electromagnet.
With the switch pressed and the thin rod suspended in mid-air, hold the magnet near the thin rod. Notice that one side of the magnet repels the thin rod but the other side attracts it.