I run with my four year old, and have for some time (though not since he was three). We treat it fairly seriously.
He has three options for using running time with me.
- Constant run - usually at about a 12 minute mile pace for up to a mile or mile and a half
- Constant jog - usually at about a 18 minute mile pace for up to two miles
Races is most commonly his choice. These are basically short distance sprints to particular mileposts - such as a car, or the stop sign/end of street - where he sprints with an appropriate head start and then I run full sprint speed after him. We do a few in a row usually (say a block or two, so maybe 1/8 mile to 1/4 mile), then walk some, then do some more. We can usually keep that up for between one and two miles.
I time the head start so that he can win about half of them, and adjust it on days where he's doing well - telling him so (that he's doing well so I'm adjusting it down). That can become a point of pride for him.
Now that it's warmer, we can do this along with a park visit. One mile or so of running, then go to the park, where I can run on the track while he plays (within sight and hearing) to get a better workout.
My three year old we don't do this with, because he's much slower; partly from physical nature (he's shorter and stockier legs) and partly undoubtedly from age. We do races sometimes, though, just not while I'm trying to exercise.
Finally - I would recommend finding children's races around you. This weekend for example, I'm doing a 5k that has a Junior Dash alongside; after the 5k is over, kids 2-5 can do a 200m-400m race depending on age, with parents or solo. It's a great way to get your child(ren) into running!