Perhaps you find yourself self-pressured to know the particular nakshatra of a planetary placement, given only the degree and sign. I know I do.
Here is an easy way to remember the changes. It all has to do with the inherent trinal nature of the four elements in the chart. Since nakshatra lords also have a trinal quality, we can borrow the structure of the elements in signs to extrapolate to nakshatras.
Fire signs (Aries, Leo, Sagittarius) start off the zodiac and represent a complete set of nine nakshatras, one for each of the nine graha.
As they are the start, the degree at which the nakshatra sequence begins is zero.
Earth signs (Taurus, Virgo, Capricorn) come next and you just have to memorize that their starting point is at 10 degrees.
Air (Gemini, Libra, and Aquarius) come next and represent a step down by one pada (a quarter of a nakshatra) to 6 degrees and 40 minutes.
Water (Cancer, Scorpio, and Pisces) come next and represent one pada down, so 3 degrees and 20 minutes.
If you want to consider it again, water to fire represents one pada down, and so we are back at the start of the cycle, to zero degrees. You can even extend the theory one more back to the earth element as being -3 degrees and 20 minutes which is another way of remembering it is equivalent to 10 degrees (since each nakshatra is 13 degrees and 20 minutes).
It is important to note that each element has a different degree at which a new nakshatra starts, that this is repeated 3 times, and that they step down by 3 degrees and 20 minutes with each one.
Ultimately this mnemonic references the repetition of 27 as the number of nakshatras and 108 as representing this magic number of nakshatras happening four times. The four elements represent this repetition of four.
As a further help, each pada of a nakshatra also maps onto a whole sign in the navamsha. Thus the nakshatra cycle of 27, each of which has 4 padas, walks us through the navamsha 9 times. Surely, this has meta-meaning given the beautiful quality and unique mathematics of 3 (the number of Jupiter) repeated in 9, 12, 27, and 108.
Feel free to ask any clarifying questions.