An algorithm activity I often do is have the class (group activity) develop an algorithm to back a a car out of a garage. My students are all 11th or 12th graders who are either drivers themselves or have observed their parents drive a great deal.
I tell them to provide detail, but not ridiculously so. For example, "Put on clothes" or "Put on Shoes" may be important but are not relevant to our discussion.
We have to decide what assumptions are necessary. One is - Automatic or Standard transmission. Most of the time this is not discussed until it is time to start the car.
What I like about this example is that the algorithm designed will give you the opportunity to show that there are many steps which do not have to be done in a certain order, but may have to be performed sometime before some other step. It also provides the opportunity to have some types of steps that are decisions and some that are loops.