One lesson that I have used to good effect is to give students a list of animals, vegetables, and minerals (meaning multiple kinds of things) and ask them to prepare a grouping. I ask them to know why they put them together.
For example,If cow and cat were on the list, would you put them together? If you did, would it be because they were both animals? Or would it be because they were both three-letter words? Or would it be because they both began with the letter c?
After the students have time to group them, I ask them to share with a few other students their groupings. Usually most are similar, though they are rarely all identical.
Then, afterwards, I might show them a list where cow and cat are NOT on the same list.
Perhaps cow is on the list of animals to eat and cat is on the list of pets. Or cow is on a list of herbivores and cat is on the list of carnivores.
Or cow and cat are on the same list but for none of the earlier reasons.
For one list, they might be together because they are both farm animals. For another list they might be together because they sleep in the house with the family. For another list they might be together because they are both pets.
Showing the students a radically different grouping and then asking them to try to figure out what those things might have in common gets their heads going in new directions and, when done in a group, they can brainstorm without feeling a personal risk.
After they’ve come up with some reasons why these groupings might exist, ask them how the world would be different based on the new groupings. It’s enlightening–for everyone.