Summer school, tutoring, homework...It is all helpful, and a beneficial contribution toward keeping kids sharp for the Fall. However, I think it is important to promote play and movement more often and possibly include it in our tutoring if we can.
Teaching math to an elementary student? Try using sound and rhythm as a warm up or intro into patterns. Go outside, sit down and face your student. Begin with a rap on your lap, a clap, and finish with another rap on your lap. Then progress with a rap on your lap, a clap and another rap and another clap. You have anchored a two beat rhythm. Perhaps follow up with collecting twigs or rocks in the yard that mirror your rhythm pattern (e.g. a short twig and a long twig in 3 repetitions). Practice any pattern you want that you feel is appropriate for the age of your student. This bridges concept to concrete.
Working on multiplication? Try creating hopscotch multiplication with sidewalk chalk.
How about students learning word families such as the sounds "ar" or "oa?" You can create a spin on musical chairs by spreading out words with a variety of sounds on the ground intermittently. Display the sound such "oa," for example, turn on the music, and let the kids dance around attempting to find the correct word to match the sound displayed and hopefully they will be present and be the first that gets to stand on those words when the music stops. Join in the fun!