A therapy ball is invaluable for a young child who needs a lot of intensity but insists on maintaining control of the activity. The child can sit and bounce to his heart's content, with the added bonus of strengthening up the intrinsic musculature around the spine and working the eyes. The correct size allows the child to sit with hips and knees at 90 degree angles. The therapy ball can used for homework, eating dinner, or sitting while watching television or working on the computer. The child can play catch and shoot targets from the ball, as well.
A large therapy ball is great for all kinds of play activities at home. An excellent activity the child can do independently is to drape himself over it and roll back and forth, landing forward onto his hands and then rolling back onto his feet. This develops protective extension responses, which are frequently lacking in low tone children. He can also spin himself around in a circle using his hands and feet on the floor. Another great game to promote strengthening and vision is to hold the child by the legs while he lays across the ball, have him walk forward on his hands to pick things up and toss them at targets, then walk back. You can use foam alphabet letters and spell words, or use Handwriting Without Tears wooden pieces and build letters.
Games that require the child to use his body with his head in different positions are very challenging and alerting. I have children bend over and shoot at targets through their legs, sing "Head Shoulders Knees and Toes", and play Twister.
I have a long tube made out of stretchy fabric, purchased at a fabric store, that the children love to crawl through. Drape it over sofa cushions for an obstacle course. Put stuffed animals inside, and have the child rescue them, or have him push a therapy ball through. Two adults can also pick the child up and swing him back and forth while he's inside.
An indoor tunnel is a great workout, especially for a child who did not crawl. I toss toys inside for the child to rescue, or pieces of a puzzle which he can then put together. You can gently roll the child back in forth inside, or have him roll himself across the room.
Roll the child up in a blanket like a burrito, and then unroll him by holding onto the end and unfurling him. If he enjoys deep pressure, bury him in sofa cushions while he lies on his belly and then roll the therapy ball on top of him. This is very calming.
Piggy back rides are as therapeutic as they are fun. This is a great way to improve endurance, strengthen up the child's flexor muscles, and to work on head righting, which is often weak or absent in children with poor balance. While the child is clinging to your back, put on some music and do a dance, dipping and leaning from side to side. Shake your hips and spin around in a circle. The child should be able to wrap his arms and legs strongly around you and hold on to you without assistance. If he can't, that's something to work on.
If he is not righting his head and is falling off when you lean over, dance in front of a full length mirror so he can use his reflection to keep his head in midline. Or another adult can provide a visual target by holding something interesting for the child to look at on the opposite side. {When you lean to the left, the target is moved to the right, and vice versa.}
Old fashioned calisthenics are great for building strength and endurance, and for turning restless, antsy, oppositional children into exhausted, compliant ones. {I refer to this tactic as fatiguing them into submission.} Running and marching in place to music, deep knee bends, jumping jacks, push ups, planks, and sit ups are all great. If there is room, military style frog crawling under and around an obstacle course of chairs set up around the room is fun and a very good way to improve brain functioning.
Wrestling is a great, high intensity indoor activity. Let the child pin you, but make him work for it. Keep it as low to the ground as possible. Or I will get on my hands and knees and challenge my friend to do the same and try to knock me over by pushing me steadily or slamming into me with his booty. This is an excellent activity for a child who constantly squirms around in his chair or doesn't like to wear underwear.
Booty walk: Sit on the floor with your legs straight out in front of you and your arms across your chest. Walk yourself across the room, keeping your bottom on the floor and your legs straight in front of you, by leaning slightly and using the muscles in your behind. Race the child across the floor, or start on opposite ends of the room and meet in the middle, then booty-walk backwards. {Jane Fonda did this in her exercise videos.}
A pair of foam bats can be used for indoor fencing or for sparring. {The ones in the link are flimsy, and don't last long. You could probably get a pretty good custom made pair at the local foam or futon shop.}
The child can practice somersaults, go crab walking, and do wheelbarrow walking with you.
A roller racer is a great way for the child to improve trunk rotation and upper body strength.
Set up a water filled basin with a magnetic fishing game, {easily purchased at the 99 cent store} and have the child lie on his belly with his head over the edge of a bed or coffee table and fish from that position.
Install a chin up bar, and have him get in the habit of hanging and doing chin-ups whenever he walks by.
Many more great ideas here.
To learn more about how movement affects learning and development, I recommend this book.
{And I surrender to the inevitable: there is always the Wii.}