Hodie magistra dicit quattuor casus huius lectionis esse nominativum, accusativum, dativum, et ablativum.

Because Latin usually does not use a separate word for that here.

After verbs like dicit (says), Latin very often uses the accusative-and-infinitive construction instead:

• magistra dicit
• quattuor casus ... esse

Literally, that is something like:

• the teacher says
• the four cases ... to be ...

Natural English adds that, but Latin normally does not.

Because this is an indirect statement.

In a direct statement, Latin would say:

• Quattuor casus huius lectionis sunt nominativus, accusativus, dativus, et ablativus.

But after dicit, Latin changes the verb of the reported statement into an infinitive:

• ... quattuor casus huius lectionis esse ...

So:

• direct statement: sunt
• indirect statement after dicit: esse

Here it is plural: four cases.

Why does it look singular? Because casus is a 4th-declension noun, and some of its forms look the same in ordinary spelling.

• nominative singular: casus
• accusative plural: casus
  or, if macrons are written, casūs

In this sentence, it must be plural because:

• it is modified by quattuor (four)
• it is the subject of the infinitive clause after dicit

So even though the spelling looks singular, the meaning and syntax show it is plural.

Because quattuor is normally indeclinable.

That means it keeps the same form no matter what case it would logically belong to.

So Latin uses:

• quattuor puellae
• quattuor libros
• quattuor casus

without changing quattuor itself.

This is different from English learners’ expectations, since many Latin adjectives change form, but some numerals do not.

Huius lectionis is genitive singular, and it means of this lesson.

It depends on casus:

• quattuor casus huius lectionis
• the four cases of this lesson

Breaking it down:

• huius = genitive singular of hic, haec, hoc = of this
• lectionis = genitive singular of lectio = of lesson / lecture / reading

So the genitive phrase tells you which cases: the ones belonging to this lesson.

Because the sentence needs of this, not just this.

• haec lectio = this lesson
• huius lectionis = of this lesson

So huius is the genitive singular form of the demonstrative hic, haec, hoc.

A detail that often surprises learners: huius is the same genitive singular form for masculine, feminine, and neuter.

Because they are functioning inside the indirect statement, and each one is understood with casum:

• (casum) nominativum
• (casum) accusativum
• (casum) dativum
• (casum) ablativum

So the idea is:

• the teacher says the four cases ... to be the nominative case, the accusative case, the dative case, and the ablative case

Since the clause is an indirect statement after dicit, these labels appear in the accusative.

A very helpful comparison:

• direct style: nominativus
• indirect style after dicit ... esse: nominativum

Because each item in the list names one case.

English does the same thing:

• The four cases are the nominative, the accusative, the dative, and the ablative.

Each label is singular, even though the whole list contains four items.

Latin is doing the same thing. You can think of it as an expanded version:

• quattuor casus ... esse casum nominativum, casum accusativum, casum dativum, et casum ablativum

The repeated casum is simply left understood.

Magistra is the subject of dicit.

It is:

• nominative singular
• feminine
• from magistra, -ae

So it means female teacher or mistress / instructress, depending on context. In a classroom sentence like this, teacher is the natural meaning.

If the subject were masculine, you would expect magister instead.

Latin word order is fairly flexible, because the endings show the grammar.

So this sentence could be rearranged in several ways and still mean the same basic thing. For example, Latin can move words around for emphasis.

In the given sentence:

• Hodie comes first to set the time: Today
• magistra comes early because it is the subject
• dicit introduces the indirect statement
• the long reported clause follows after it

So the order is natural and clear, but it is not as rigid as English word order.

A direct version would be:

• Quattuor casus huius lectionis sunt nominativus, accusativus, dativus, et ablativus.

Then, after magistra dicit, Latin changes it into indirect statement:

• Hodie magistra dicit quattuor casus huius lectionis esse nominativum, accusativum, dativum, et ablativum.

This is a very useful transformation to practice, because it helps you see:

• sunt → esse
• subject of the reported clause handled in the accusative construction
• predicate words adjusted to fit the indirect statement

If you can move back and forth between the direct and indirect versions, this kind of sentence becomes much easier to read.