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When an animal or plant dies and is buried under the ground with the right conditions for thousands or even millions of years, it turns to stone. Later when we dig them back up, we call them a fossil. When something has been turned into a fossil it is fossilised.
People have found fossils of all sized creatures, from tiny sea snails, to frogs, right up to enormous dinosaurs. Most of the creatures that people find as fossils are extinct - you can no longer see a living animal of that kind.
The fossil in the picture is a trilobite.
Gills are what creatures that live in water use to breathe. Fish gills are easy to see, between their head and their side fins. Other creatures have less obvious gills, that look like fine, tufty growths.
A grille is a metal grate used as a decorative and protective covering, especially for a car or a fireplace.
Hills are small mountains, and have a much gentler slope than mountains do.
You kill something when you stop it from being alive. When a person kills another person on purpose, it is called murder.
Killing might also mean stopping something from happening, for example "lack of money killed his plans to go to Europe".