The Babylonians used a base 60 numbering system that serves as the basis of modern time telling and the degrees in a circle. Modern mathematical systems use a base 10 system for easy counting, but the number of seconds in a minute, as well as minutes in an hour, derives from the Babylonian counting system.
The base 60 system the Babylonians used helped them derive a fairly accurate calendar. It required periodic adjustments, but the Earth's movement is not precisely regular. In fact, even in modern times adjustments are necessary through leap years and periodic changes of a few seconds to the atomic clock that tracks world time.
The Babylonians also developed a table of squares that some elementary math teachers use to help students learn their squares. Using that table, the Babylonians could derive the product of any two integers up to 59. Their formula for these two integers was similar to a*b = [(a + b)^2 - (a - b)^2] / 4. This reduced the number of multiples they had to memorize. Therefore, rather than learning an entire times table, they only had to learn the squares; however, they had to remember the formula.
Another primary difference between Babylonian math and modern math is that the Babylonian system lacked a zero or another symbol signifying the absence of value.