Quick side note: This tip may not be easy to apply on day trips such as the zoo, museums, etc. But there may be times where your child/children interact with a specific toy/animal/exhibit long enough for you to work the composition.
It's not about machine gunning your way to a moment--taking 30 or 40 shots at once, hoping to get just one that's decent. Once you're in position, observe your children and the action taking place. Try to anticipate when someone might laugh or smile or do something interesting. Be ready and then get the shot. It takes discipline not to click the shutter 50 times hoping for that moment. Try to trust yourself and you will begin to develop greater discipline and intuition (anticipate moments). Here is a series of seemingly similar shots. I found a composition of my son playing in his room which I liked. I wanted to capture his interactions with the toy. Here is a sample of what I chose to shoot and the type of moments I was looking for. They were taken over a period of around 10 minutes (1ds2, 35L, iso 3200, 1/60, f/2.2)
I enjoy these shots for different reasons, in part because there's a subtle range of expressions and action and they're all genuinely Isaac.
Here's a second, shorter series of my older son just messing around while watching tv (1ds2, 35L, iso 1600, 1/80, f/2.8).
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