This is the Order that includes daisies and asters, as well as bellflowers.
Though this is the second-largest family of flowering plants, it is easy enough to tell when you've found a member: asters and their relatives have very many narrow petals, usually forming a ring around a disc of tiny true flowers in the center. Sunflowers, daisies, and dandelions are in this family.
Please click through to the Asteraceae page
Please click through to the Asteraceae page
I'm including lobelias and their relatives here - some systems have them in a separate family, lobeliaceae.