The key to achieving the fine texture of this refreshing flavored ice is to periodically stir and mash it as it freezes, a process that makes for a fun boredom-buster on a long afternoon. When it's done, spoon the ice into paper cups or, for a fancy presentation, into reamed lemon halves.
Wash the fruit. Show your child how to grate the peel of 2 of the lemons, then combine the lemon zest, water, and sugar in a medium saucepan.
Bring the liquid to a simmer and continue simmering it, stirring occasionally, until the sugar has dissolved (about 3 minutes). Remove the pan from the heat and let the mixture cool. Pour the cooled liquid through a mesh strainer into a medium mixing bowl. Discard the zest left in the strainer.
Cut the lemons into halves and, with a lemon reamer or citrus juicer, juice enough of them to make 2/3 cup of strained lemon juice. (If you plan to serve the ice in the reamed halves, store them in the refrigerator until you're ready to use them.)
Stir the juice into the sugar water. Then pour the mixture into a large, shallow nonaluminum baking dish. Place the baking dish in your freezer. (Note: if the liquid is still warm, first refrigerate it for 1 hour so you don't defrost your freezer!)
When the mixture starts to freeze around the edge, stir and mash it with a fork to break up the ice. Repeat this periodically until the ice is firm (about 3 to 5 hours). Makes 8 to 10 servings.