Children and karate mixed together are one of the toughest shooting environments I've ever been in to try and capture good photos. Both of my children (age 8 and 10) take multiple karate classes each week.
For one thing, the classes are held indoors with dim-as-heck lighting. Second, some karate activities, such as board breaking, require a very fast shutter speed. Third, I am sitting far enough back that I have to use a long focal lens. And finally, it’s kids! Meaning, that they are the most erratic subjects on earth to photograph!
I generally crank up the ISO to at least 4000 on the Fujifilm X-T2 with a minimum shutter speed of 500/sec. I’ve found that it’s better to have more ISO noise than to try and crank up the exposure in Lightroom.
Focusing is another matter. I can't tell you how often I've failed to nail focus.
Although the Fujifilm X-T2 has a great auto-focus (heck, they even have their own dedicated website just for it), I do find that even with the Fuji 50-140mm f/2.8 lens, it just cannot complete the focus quickly enough. But when it does, it looks spectacular though!
Eventually, I discovered that it's just better to throw the camera in manual focus, then pre-focus the area that you expect to get a good shot in, because then at least you can concentrate more on composition.
Also, I tend to expose to the right (as in, the histogram) than usual. I've found that high ISO + recovering shadows in Lightroom = miserable mess.
Some of my photography tips for shooting Kids and Karate:
It's tempting to just shoot the action. Don't. Look for the other moments. See the photo below of the boy and the instructor. It's the best of the bunch and there's zero action in it at all.
If you are shooting board-breaking, they usually do a quick test run-through to get the kicking/punching position. During that time, drop your camera in manual focus mode and pre-focus on the board. Then, you can focus more on composition when you get the shot. If you enlarge the one below of the board, you'll see that this shot would have been very difficult to achieve in auto-focus mode, center-weighted.
Post-processing: running more contrast and clarity sliders in Lightroom help. I also experiment with bleach bypass.
Black and white look wonderful in Karate. Try that also.
Watch your camera! Especially if you are up close and personal to the kicks and punches. Objects are closer they appear in some lenses and you want to avoid getting kicked in the face!
All in all, if you have kids and they are in Karate, by all means, bring a camera and have fun! If you don't have kids, head to a karate studio anyway and talk to the instructors. You may be able to work out some exchange, e.g., a few free shots for their social media pages for the opportunity to shoot a few board-breaking demos.