The brain is so complex that much of its function still isn't understood. The basic parts of the brain and what they control however are understood --- at least to a certain degree. You can show children how their motor controls function based off the brain with a simple, free experiment. Have kids all wink, walk in a line and write down a sentence at the same time. Tell them to take note of and record which eye they blinked with, which foot they started with and which hand they wrote with. The dominant hemisphere of their brain will generally be the one opposite to their answers.
Gravity can be a tricky concept for children. Most experience it every day without realizing it or consciously thinking about it. Once kids realize gravity is a force, it can still be counterintuitive in some respects. The common thinking is that heavier objects will fall faster; however, a simple and free classroom activity can show otherwise. Have each child take objects from their desk, hold them from an equal height and drop them. Either have them record the time it takes or closely observe the scenario. The objects will hit at the same time regardless of weight if done correctly.
If you're looking to test kids' investigative skills, then a scavenger hunt can be just the ticket. Hide several objects, which can be anything from created objects to common classroom objects. Create hint sheets for the students. Allow the students to use their cognitive skills to find the various objects. Although this can be done in the classroom, it generally works better over a larger area, such as a playground.
Social skills in kindergarten can arguably be as important as any other skill kids learn. There are several free activities that teachers can play in a classroom that encourage social interaction and teamwork. Create a designated confined area outside and divide kids up into teams of two. Give each team a blindfold and foam ball. One person on the team wears the blindfold and is responsible for throwing the ball at the other team's players. The non-blindfolded teammate is responsible for giving instructions, ranging from where to throw the ball to where to pick up loose balls. This player can give his teammate verbal instructions, as well as guide him by his arm.