Getting down to 'cases'  (with Ath. 2b)

You've already dealt with the so-called nominative and accusative--the endings for subject and object of the verb.

The other 2 cases (not counting direct address=vocative) convey the basic relations "of" or 'belonging to' (possession, etc); and "to/for" (=indirect object).

You've already met the genitive with preposition ἐκ, as in ἐκ τοῦ οἴκου, 'out of the house.'

But the genitive all by itself conveys the idea "of":

τοῦ οἴκου  means "of the house."  

So 'the man of the house' is ὁ ἄνθρωπος τοῦ οἴκου.

Translate these examples--all genitive with -ου --using "of" or equivalent.

τοῦ καλοῦ ἀγροῦ                                     τοῦ χαλεποῦ πόνου

τοῦ μικροῦ δένδρου                                 τοῦ μακροῦ οἴκου

τοῦ ἰσχυροῦ ἀνθρώπου                          τοῦ καλοῦ δεσπότου  

Now translate into Greek (all genitive case using forms above)

of the beautiful house                                   of the small field   

of the hard master                               of the strong tree  

The same phrases could be found with ἐκ;

out of the beautiful house          out of the small field

ἐκ τοῦ καλοῦ οἴκου                        ἐκ τοῦ μικροῦ ἀγροῦ

Now for the case called 'dative' (from Latin for 'give'):

Again, you've already met this case in the phrases

ἐν τῷ οἴκῳ = 'in the house,',  ἐν τῷ ἀγρῷ ='in the field', etc.

This case by itself conveys the relation "to" or "for"

as the indirect object with 'give', 'bring', 'provide' etc.

 --You give something to (or for) somebody in the dative case.

So for example,

The master brings food for the slave:

ὁ δεσπότης φέρει σῖτον τῷ δούλῳ.

The field provides much work for the farmer:

ὁ ἀγρὸς πολὺν πόνον παρέχει τῷ αὐτούργῳ.

 Practice with the following phrases --all dative with - ῳ --

to the beautiful tree                             for the long house

for the small man                                          to the strong slave