I wouldn't be surprised if there aren't always cases that meet the narrow 3 symptom criteria from one tested positive child because children are often asymptomatic or differently symptomatic.
We don't know numbers because they're not testing asymptomatic / differently symptomatic contacts as a general rule.
We do know, when tested (e.g. at Eton) large numbers of asymptomatic positives among children show up.
We know asymptomatic spread is a problem with covid.
WE know viral load is a problem with severity of disease for covid.
WE know indoor, crowded environments with no masks for long periods are the most dangerous for transmission.
This means schools, as they are, especially if not isolating whole classes who've been in contact with known positive, are unsafe environments for teachers (and probably, some children too).