One of the best ways to strengthen your core and make your back stronger is to use a Swiss Ball. Once you have mastered some of the easy Swiss ball exercises, try some of these moderate level Swiss ball exercises.
You are going to start off with a basic crunch. Roll your body forward until your hips come slightly off the ball and your lower back is touching the ball. Try not to strain your neck while doing these exercises. Roll back slowly and controlled, and roll back up. Just start out with 5-10 and work your way up. Now roll down to where your shoulders are on the ball into a tabletop position. Squat down bending your knees and come back up into the tabletop position. This is working your hamstring muscles. Try to keep the ball as still as possible. If the ball is moving around a lot, you are probably not ready for these exercises yet.
Next, you are going to come off the ball, and kneel down propping your elbows on the ball. This is like a prayer position. Tuck your bottom in so you are in a straight line. If that is easy, then you can push up onto your toes into a plank position. Start off with 5-10 seconds and work your way up. Now you are going to do a walk out or roll out. Put the ball close to you on your knees. Roll onto the ball and continue rolling through and walking your body out with your hands. Just try rolling out to your knees first, and then you can make your way to your toes.