I can't imagine that happens very often at all. Do you have data?
The one child I heard of dying while playing drowned; and there's traffic. Not a problem on most school grounds.
No data about deaths, I'm sorry. I already reported of an accident I remember personally though: my mother was a primary school teacher, in the early 1960s a child from her class happened to fall and beat his head against a low wall during recreation time, being knocked unconscious and then hospitalized (luckily he suffered no permanent damage). The children were being attended by the staff (including my mother), nonetheless she had a lot of troubles, being investigated for 'lesioni colpose' before being finally acquitted without trial. I'm not sure what's the exact legal term in English for 'lesioni colpose', I guess 'injuries due to negligence', which basically means your actions indirectly caused harm and is the lower level of culpability in Italy, the same case as someone driving along a road, respecting all the driving regulations, and then suddendly a pedestrian crosses in front of him and is hit. Had the children been unattended it would have been 'lesioni dolose', the next level of culpability (gross negligence, maybe?): this is the same as someone driving under the influence and hitting a pedestrian as above, a big difference.
I'm sure deaths of children while playing at school are pretty rare, luckily, but one just need to fall from a stair while chasing his classmates to kill himself.
Edit: I just remembered this case
https://milano.corriere.it/notizie/...lo-d6354fd4-8f2a-11ec-af55-d575edc6dd9d.shtml
"Milan, Leonardo, 5 years old, died falling from a staircase: the teacher has been acquitted on appeal, 1st degree sentence overturned.
Drama at school.
On October 18, 2019 at 9:30 am the child was allowed to go to the bathroom. Probably "intrigued by chattering voices he heard" from children of another class he climbed onto a revolving, wheeled chair which had been left in the corridor, he leaned from the handrail losing his balance and fell to his death from a height of about 13.5 meters in the school of Via Goffredo in Bussero [a small Italian town]."
The janitor was sentenced to two years jailtime and she was surely held responsible for at least a hefty part of the damages, possibly together with the school (civil liabilities are set in a different, subsequent trial in Italy. Yeah, it's silly). The teacher had been sentenced to one year before being acquitted on appeal (and, even if acquitted, she had to pay her lawyer fees, for two trials).
Notice the child
was technically unattended when the accident happened: he was going alone to the bathroom. The janitor took an objectively small risk by not following him, how many children kill themselves going to the bathroom, after all? It probably was a 10 meters walk along the corridor. But she paid dearly for that and the poor Leonardo payed dearly too for her mistake. Leaving 250(!) children to play alone on wide premises for a substantial amount of time in the 'most expensive private school' of the capital city, well, borders on crazyness. That said, it's not impossible, just very improbable.