there's not much controvosy about Carbon dating - but this isn't very accurate - and depends on a fairly subtle effect that living organisms tend to favour using higher Carbon isotopes - and that the readioactive decay of these can determine when the organism was actually alive.
C-14 dating depends on half-life and isolation from new carbon, along with estimates (getting darned good, with Antarctic ice core data) of atmospheric carbon distribution in the past. Due to the half-life calculations, obviously the farther back you go, the greater the 'error' bar gets. For archaeologists, the figures start becoming useless for actually dating history at about 5,000 years; results can be used to put events/materials in chronological order but not pegged to specific calendar periods. By 10,000 years, they're guessing at the century.
For biologists, though, dealing with materials generally having a much higher carbon content, the method is useful back to 50,000 years. Even that number is being pushed back as greater precision in measurement is achieved; good estimates can reach back to 60,000 B.P.
For dates beyond that, there's potassium-argon, rubidium-strontium, the two uranium pathways (lead, and IIRC thorium), and certainly others I don't know anything about. I don't recall the time scales those apply to.
The other evidence that has been accumalated overwhelmingly points to around a 4 billion year age for the world, There is nothing to support any other age - not 6000 years nor just a few hundred thousand years nor a few hundred million years.
The Canadian Shield dates to ~2.5 billion years, using a variety of methods. I read a while back that the Greenland portion of that formation may date to ~2.8+ billion. Just as trivia, that formation of rock is close to being round, except for Hudson's Bay sitting in the middle (the round shapes of the Bay and its sides suggest a calved comet strike, but no evidence has been found to support an impact hypothesis).
Nor is the Canadian the oldest; I forget which is, but surface rocks elsewhere have been dated to ~3.2+ billion years, using radiometric and crystal deformation (and other) methods.
Just allowing for the erosion rates on those formations, the continents themselves are at least ~3.8 billion years old.
WRT the oinkers who think the earth is only tent thousand or less years old.... I was once talking with one, who was explaining how God had put dinosaur bones into the rocks, and stacked all the layers, and on and on. I interrupted about the tenth time he said "God did....", and said, "You mean the Devil." The expression on his face was priceless -- shock, confusion, outrage. "The devil is the Father of Lies, and you're telling me someone stacked up a whole pile of lies for us. That's the Devil." I didn't go quite so far as to say he was actually worshiping Satan, or to pat him on the head; I just offered him a cold drink and went off to swim for a bit.
He actually came back later and asked how those things got there if the earth was only ten thousand years old. I just asked, "Who told you that?" "Our pastor." "Where'd he get it?" "The Bible." I shook my head and said, "No, he didn't. I've read the whole thing in Hebrew and Aramaic and Greek, and there's no such thing in there." Then I took him through the grammar of Genesis 1 and showed him that for what the text says, the earth could be a hundred billion years old -- so he wanted to know how we could know, and I took him to places in the Bible where, to paraphrase, God tells us to study and think; in other words, use science.
I think I left behind a troubled and hopefully more educated guy (and his gf, who thought me skinny-dipping was awesome, and tried to get him to join me).
In fact in this case - any religiouslly inspired idea to "Teach the Controversy" is totally spurious - there isn't any scientific controvosy about the age of the Earth - it is what it is - not what anyone wants it to be - in the same way the world isn't flat - no mater how much some people might think this is (or want this to be) the case.
The only controversy I'd teach would be a unit called "How stupid do you think people are?", followed by "Why would God lie to us?" Or maybe reverse them.