I don't know how everyone else does it but in my case:
1). You remember to take cash and if you forget, you always have your cards on you and an atm is usually no more than a few minutes away. You can also increasingly pay for these sorts of things via mobile phone.
2). The school sends their bank account details along with the trip information and I setup a same day wire transer online.
Or the school wants the kids to send in a fee to cover some trip they are going on? How do you do it without a check?