Besides explaining how we are looking for a nonce, I find it both difficult as well as elucidating to explain how whomever mined a block is rewarded.

The main point of block-chain is decentralization. It is thus important to emphasize that there isn't a central authority that rewards the mining of a block, but instead that the miner includes his reward in the block. It is also important (though less relevant) that the challenge of mining a block is a mathematical result of the last block. It too arises without a central authority.

Moving to even less relevant and yet interesting thing is that not all miners need be mining the same block. This is already the case for the 'reward' they are mining, but miners are free to exclude a transaction from their mining attempts. This then begets the matter of fees as a secondary incentive for mining besides the block reward.