I don't know what background you have given the kids or what level, but here's something we do in a non-majors freshman level biology course that could easily be adjusted. First, to get them thinking about trees and relationships, give them a simple family genealogy (use only 1 parent for simplicity). I use my family tree going back to my grandmother. With cousins, aunts, and siblings, they begin to understand how to interpret family trees. You can substitute the family names with organism names to make it a basic phylogenetic tree.
We teach tree construction simply. We give students a list of six species (fake birds) with DNA sequences that are only 20 nucleotides long. Students have to calculate the number of base pair differences between each pair of sequences which, in our case, range from 2-10 nucleotides.
They then use the pairwise differences to construct their tree, with the understanding that fewer nucleotide differences between organisms means they are more closely related.
You can do this type of activity over a couple of days (depending on time). Then, you can begin to show them trees that become gradually more complex. Because the kids will have constructed a tree and now how it is constructed, they will have a much easier time interpreting larger trees.