I remember these being a much-loved staple of primary school in the 1980s: while the teachers had their lunch, a dinner lady or two would keep us busy while we sat on the classroom floor. Some of the games were:
Statues: who could sit still the longest.
O' Grady says (instead of Simon Says). It was their cunning way of exercising us: I found the arm-work so tiring I used to get myself "out" as soon as I could. A usual trick was "stand up if you're still in the game... O' Grady says." The well-behaved children were sometimes picked to be O' Grady.
Guess who was speaking in a funny voice (the child guessing was blindfolded so there was no cheating).
Noughts and crosses: boys would be noughts, girls would be crosses. We had to answer questions (spelling, times tables) to be able to place a nought or cross.
What classroom games do you remember?