A natural progression in your reading activities with your children is that after you read them to a passage from the story; have them paraphrase the story back to you. This will help you to understand what level of listening ability and understanding they are at, as well has help them to begin building their vocabulary as they work to find new words they can use with their description of the story they are giving back to you.
Good reading activities don’t always have to occur at the house, or just before bedtime. While you’re running errands around town or on vacation, perhaps have the kids begin to collect words from signs, or spell objects they see. Encourage them to learn different ways to describe objects see. Instead something big, it may by huge, or enormous... or even of gargantuan proportion! Have you child arrange the words they have collected into silly sentences or phrases. Even something as simple as collecting letters from signs, license plates, and such to work their way through the alphabet is a good kindergarten age reading activity.
Not in the car, or travel around much? Use every day items around the house to do the same thing. Labels, there are plenty of labels around the house. Actually put labels on everyday items around the house so your child can associate the spelling, and reading with a tangible item. Then, after a while, take the labels off the items and help your child read and re-label the house.
Once you get your creative juices flowing, you’ll come up with many more reading activities. The key is to make reading activities an every day part of their life. Make an effort to spend an hour a day reading more with an hour less of television. T.V. is an extremely passive thought processing activity. While reading and using one’s imagination is a source of growth and a great foundation from which to build.