I coach a high school rowing team and core strength is very important for rowing, so here is what i do with them. I also use these for my own core routine, and the emphasis is getting a lot accomplished in a short amount of time, so they can get out on the water, and I can get out on my bike!
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Plank - keeping the back straight, toes on the ground and elbows on the ground. This should be held for at least a minute, and gets your abs, obliques and lower back.
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Sit-jacks - start on your back. raise your upper body off the floor, and raise straight legs off the floor. As you raise up your upper body, bend your knees as well so at the end they are close to your body. slowly lower your legs straight again while you lower your upper body, keeping your legs off the floor.
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(this one is at the gym if you have access) hanging leg raises. Go on that stand where you rest on arm rests and lift your legs straight up in front of you. This one is very good and i find it doesn’t strain my back as much as leg raises lying down does.
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Sit ups on an incline bench with weight
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Medicine ball knee-tucks - start in a push-up position with your shins on the medicine ball, then draw your knees into your body, so the ball rolls towards you.
If you move quickly with little rest in between each of these, it takes less than 10 mins. I also do exercises to work my lower back and hips, for a more comprehensive core workout. That is more because I need to due to nagging hip flexor problems.