There are many great activities that can be used as whole class starters, Math's Table activities, enrichment and the Chinese NIM Type games fit nicely into this area.
Students once they have mastered the strategy want to then challenge others including teachers and parents.
When working with teachers and Students I regularly had a "Nim" type activity up my sleeve, and would finish the period with it. On my next school visit I would be accosted by students "trying to beat me" Some did but often they would because I might suggest that we play it in reverse-as a way of seeing if they could adapt their thinking/strategy. I really enjoyed leaving the students(and teachers) the challenge and interacting with them on a return visit.
At NO stage would I would give the rule/strategy, but would play the game and acknowledge those students who appeared to have a winning strategy.
This activity, adapted from Family Math's Balloon Ride can be introduced to quite young students but do not force them to look for strategies, but to just play and see their excitement.
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