Jumping exercises are  great way to work on strengthening leg muscles and get a sweat going in a small space. 
SfA subscribers can download a PDF version of the exercise instruction. 

Small jumps and walking on toes to strengthen the calf muscles  
A good way to strengthen calf muscles 

Two-foot jumping activities for training general fitness

A good way to improve a young child's fitness is to create repeated opportunities for short bouts of all-out exercise. Jumping activities are a good way to do this in a small space, and will quickly get the heart racing and increase the breathing rate.Below are some ideas for jumping games that can be graded to make them progressively more difficult.

Pre-school activities: Jumping over obstacles

From the age of about 3 years, typically developing young children learn to jump over an obstacle. This action requires more planning and coordination than a simple forward jump: the child needs to start the jump by standing fairly close to the obstacle, and to jump high and far forward enough to clear it. 

Standing broad jumps between cushions

In this exercise the child does big jumps, taking off from and landing on, a big cushion. The cushion helps to absorb some of the impact of landing from a big jump and gets the child accustomed to the sensations muscle  effort that happen when landing from a jump.