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My study group cannot come to a consensus on the elements of a battery in a single intent jurisdiction. We all agree that, with regards to dual intent, the actor must intend both the contact and the harmful/offensive consequences. In a single intent jurisdiction, however, must the actor appreciate the potential harmful/offensive nature of his contact? We all agree that he must either intend the contact or have knowledge to substantial certainty that a contact will result, but must he be aware that the potential contact can be harmful or offensive? For example, what if Brian Dailey played games with his friends where they pulled chairs out from under people and nobody ever got hurt or was offended.

Our torts class didn't cover the distinction, but after looking it up, we only covered single intent.

All you need is intent to contact. Look at the kid-kicking-the-sick-kid's-leg case for reasoning.