Not sure why I thought of this but it just popped in my head. When running water for a bath do you wait until it is full to get in (or your kids) or do you (or your kids) get in while the water is running?
I always put the kids in the tub while the water is running and then keep an eye on it to make sure it isn't too hot or cold. Same for myself.. I like to run the water until it is partway full and then get in while water is still running.