Feel free to use fins if you have any difficulty with the following drills.
Traditional freestyle catch-up has both hands reach each other in front of the swimmer before starting the pull portion of the stroke. Half catch-up is different as the recovery arm stops about half of the way through the stroke (between the ears and entry point) and pauses for a slow three- to four-beat count.
While you are pausing, focus on the arm extended out front—establishing a great catch position with the elbow up and the fingertips down. Pretend you are reaching over a big barrel of water. After your pause, finish your stroke, roll onto your opposite arm and take a breath. Repeat that sequence down the pool.
This drill helps with rolling forward. Push off the wall and take six kicks (count each right foot kick as one) on your side with your bottom arm extended, top arm at against your body, and one goggle lens below the water level and one above.
After six kicks, take three strokes without a breath. Then, roll forward on the third stroke and take six kicks on the other side. Breathe while on your side, but keep your goggles in the same half in/half out position. Repeat this sequence down the pool. If you train in a 50-meter pool try a sequence of 10/7/10.
Kick on your side with your bottom arm extended against your body. Swing the top arm until the hands are directly above the shoulder, which is high and dry. You are essentially forming the letter "L" with your arms. Pause in this position for a slow three to four count. After the pause, roll onto your arm and repeat the sequence on the opposite side.
This is the same drill as the similarly-named one in freestyle, but keep your head in backstroke position. Focus on keeping your head still as you go from kicks to strokes.
Use the above drills to learn the movement of freestyle and backstroke swimming. Learning how to roll before you pull is essential in learning how to swim with leverage versus muscling your way down the pool. Think Movement vs. Muscle!