Magic Mirror Book and Magic Mirror Tricks show incomplete illustrations--sometimes halves of objects, especially in the tricks book, hence the link to symmetry--that children can complete by holding a small mirror up next to the picture. The books, though out-of-print, can be found very cheaply.
symmetry lesson, I drew a light pencil line down the center of a piece of paper and asked my son to make a pattern block pattern on one side of the line only. He traced the blocks to make a new symmetry puzzle which he then completed by finishing the design on the other side of the line. He quickly discovered it was easier to trace blocks if he used the magnetic blocks on our new cookie sheet math board so the pieces didn't move.
I then asked him to make a riddle to give a hint as to the picture he'd made. He wrote one about a lion, the second about a hyena.
It would be fun to further extend the lesson by making his own Magic Mirror book. Sounds like a good summer project!