Carbon dating has a certain margin of error, usually depending on the age and material of the sample used.
Beyond that timespan, the amount of the original C formed by irradiation of nitrogen by neutrons from the spontaneous fission of uranium, present in trace quantities almost everywhere.
For these samples, other dating methods must be used.
Until this century, relative dating was the only technique for identifying the age of a truly ancient object.
By examining the object's relation to layers of deposits in the area, and by comparing the object to others found at the site, archaeologists can estimate when the object arrived at the site.
Here is an easy-to understand analogy for your students: relative age dating is like saying that your grandfather is older than you.