Bubblesort is a good way to show it to children.
You can show it on the blackboard. Then assign each child a number, shuffle them, and then let them move around, and do the comparison.
If many children, you can make smaller groups, and finish with a merge sort (lowest number of the 3-4 rows steps forward).
Another simple one is making a maze. Then ask them how to get thru, given that you have breadcrumbs at your disposal. The algorithm might be turn right at every opportunity. Backtrack if cul-de-sac, and turn left, then stick to turn right. You need to make some special case, like a loop in the labyrinth (So you will get back to your breadcrumbs). Development is figuring out how to describe it in a way a computer will understand. It does only what it is told.
These are two examples of different difficulties. But gives a view into development. And the maze is a bit game like.