Gym with lights:
Set the camera to Tv (Shutter Priority AE, see page 110 of your manual) Mode: Shutter speed 1/125 or 1/250 at ISO 800 (page 92) for a gym with lights. ISO and shutter speed can be increased in steps, if, for example, you are trying to freeze the motion of the ball or a hockey puck. You will also need to manually set the White balance (page 137) under artificial lights to get rid of the orange tint.
In addition try shooting some continuous shots, say bursts of 3 shots to catch the action in steps (page 104).
Kids playing violin not on a stage:
This one is a little harder and may require shooting in manual mode, because, depending on the angle, the lights from the stage will give a false setting. If you are shooting at audience level without the stage in the frame Tv (Shutter Priority AE) is good for this. Shutter speed 1/125 or 1/250 at ISO 1600 - 3200. If the surrounding stage lighting is in the frame, set the mode to M (manual) and use the same ISO & shutter speeds and set the aperture (lens opening) to the largest available (smallest f#) on the lens. Depending on the type of lights, the white balance may need adjustment.
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