Why is November the 11th Month, but means Nine?

I was wondering why November is the 11th month of the year, but is derived from the Latin word Novem which means 9. Same can be said about December, which is the 12th month, but is derived from the Latin, Decem, being 10.
When I found the answer it was obvious, but, as I went to the trouble of looking it up, I will share the obvious.
Originated from the Roman calendar, which had 10 months. This calendar was invented by Romulus, in about 753BC. This was not a lunar calendar and had 304 days. There were 61 winter days that did not fall into this calendar. So November was the 9th and December the 10th month.
In 713BC Pompilius revised the calendar to make up for the lost days and squeezed in January and February, (the missing winter months). November and December moved forwards, to make place for the new ones.
Now the calendar had 12 months.
During this time June and July were known as Quintilis and Sextilis, which were later named July and August, after the Caesars.
All calendar names from Latin.
Maybe this will pop up in Trivial Pursuit, then we will all know.