Essentially the problem with your lens is that the f-stop only goes from probably f4-f5.9 at its furthermost zoom range, so this is not a "fast" lens (does not let a lot of light in). But this range is pretty typical for consumer type shit. Unless you want to spend tons of money.
That lens needs a lot of light to enter it to make a good picture far away at a fast shutter speed. This is why when pros take pictures of football shit on the sidelines, you usually see some big ass lens that's like 8in dia and a ft long. And they also cost
$6000. Its all about light and how much light a lens captures. that $6000 lens has an f-stop of 2.0 at 200mm, which is insane amount of light let in at the furthermost zoom. this is why its so damned expensive.
So what can you do? Well if your camera has some settings like shutter priority mode or fully manual, I would suggest to up the shutter rate, 1/4000 of a second can be fast enough for racecars. 1/250 is fast enough for a jogger.
Its all about balancing the light you let in (f-stop) and shutter (shutter speed) as fast as it can go. If you're struggling to get enough light in, try cranking up the ISO. ISO is a setting that harkens back to film speeds, remember those? 100 speed film for bright sunny days, 400 for cloudy or evening shots, 800 for interior without flash? So the higher the ISO setting the more sensitive to light the film was. But the problem with bigger ISO is that it introduces a lot of graininess and artifacts to the pictures. I would recommend no more than ISO 400, maybe 800 or so. So if your at your highest workable ISO and your widest f/stop, the shutter speed will be as fast as it can go with the given situation.
Also you can try a technique called panning. This involves moving the camera in tandem with the object that you are trying to capture in order to achieve a sharp image. Imagine trying to photograph a moving car. The photographer, with camera in hand, remains stationary. The car will zoom past the camera and will come out as a blur. If, however, the photographer tracks with the car, turning to follow it as it moves down the street, then there is a far greater chance of capturing a sharp image with the car in focus. So try to focus on your son or the play unfolding and follow him with a smooth panning motion and snap away.