The rule of thumb without IS is 1.6x the focal length for a minimum shutter speed on a crop body. It's just a rule of thumb though. Some people have surgeons hands and still subjects and can pull off slower shutters. But the shakier your hands, and the more your subject is moving, the more speed you need. This really starts to come more naturally with lots of experience.
Also, subjects that are moving laterally require a much faster shutter to stop motion, whereas subjects moving towards you dont require quite so fast a shutter.
It will be very helpful to see some of your images and the corresponding exif data. People should be able to help you a lot with those two things.