No matter HOW you discard a piece of unclaimed work, my advice is as long as you NEVER let the children see you getting rid of it. Wait until they've gone.

Imagine a child sitting there not having the courage to speak up in a group to claim a piece of work, and you turn away and place it in the waste bin or recycling bin! They would be so SAD! :weepy:

I would suggest holding onto unclaimed work for a set period of time, maybe a week, and by the time you have moved onto a new topic, they would probably have forgotten about it, and it's given them time to come to you and ask, so you can then dispose of it.