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davidcycleback1800s scraps (generic name for small die cuts of everything from puppies to angels to flowers to these ball players) were sold as sheets, with the individual scraps intended to be punched out, or otherwise removed. So originally being connected in sheet, or connected to each other, form was the norm.
Scraps were invented in Germany and were originally made to decorate cakes. By the late 1800s, they were typically pasted into albums as a hobby.