If you are learning German, you can create and memorize a quick reference of German grammar.
When you look at the first letter of a German article der, die, das, den, dem, or des, it is not a unique identifier: d-, d-, d-, d-, d-, or d-.
When you look at the second letter, only two are unique identifiers: -e-, -i-, -a-, -e-, -e-, or -e-.
When you look at the third letter, still, not all of them are unique identifiers: -r, -e, -s, -n, -m, or -s.
Associate each article with a unique, numeric identifier:
You now have a quick reference that is small enough to keep in your head as 1232 4232 5154 6161, which resembles a credit card number. You could also think of these rows as pin numbers for virtual credit cards. During an exam, you can quickly jot down your dummie credit card or pin numbers.
Q: What is plural die in dative?
A: 4, and because 4 = den, den.
Q: What is das in genitive?
A: 6, and because 6 = des, des.
Q: What is die in accusative?
A: 2, and because 2 = die, die.
Note that this becomes lightening fast with a little bit of practice.
To create a quick reference of the adjective endings (either -e or -en), draw a shape around where the adjective endings are -e. Anything outside of that shape takes an -en ending. See the copper-colored line in the following image:
der schöne Hund
die schönen Frauen
auf der schmutzigen Straße
To create a quick reference of the indefinite article endings (a and an), put a circle around the ones that are ein. Each of these circles look like a zero, and because ein does not take an ending, it seems fitting to think of it as a zero.
The remaining endings behave normally. Therefore, there is no need to learn them separately.
auf einer Straße
Tattoo artist rei.ink and I collaborated on this German grammar tattoo where these concepts are present in a grid of cobblestone.