Let's get down to the practical end of things. I'll assume that you're using a film camera. For digital, all bets are off, as it were.
You say that you're photographing moving children. This means that all your attention is [or should be] devoted to focussing and framing. All you can do is set your shutter speed so that blur from motion will not be objectionable and then set the aperture to provide the correct exposure for the available light and film speed [ASA].
You can decrease the sharpness of the background by getting closer to the subject. This will mean that you focus the lens to a shorter distance. It will automatically result in more blur to the background.
Finally, if the combination of shutter speed and lens opening results in an f stop more than two numbers above the wide-open stop of your lens, consider going to a slower ASA film [eg, from ASA 400 to ASA 200 or 100]. This will force you to open the lens and this, in turn, will help to blur the background.
Sounds like a lot of stuff to think about right now, but with time, this sort of mental computation should become second nature. The trick with a camera is to learn it so thoroughly that you don't have to stop to think everything through. A camera is a tool, after all -- like a painter's brush or a novelist's typewriter. When you pick up a hammer to hit a nail, you don't stop to consider how to grip the handle.