Mater dicit magistram mox adfuturam esse.

Because after verbs of saying, thinking, knowing, and perceiving, Latin often uses an accusative-and-infinitive construction instead of a full subordinate clause.

So instead of saying something literally like Mother says that the teacher..., Latin says:

• Mater dicit
• magistram ... esse

Here, magistram is the subject of the infinitive esse, and in this construction that subject goes into the accusative.

So:

• magistra = the teacher, as a normal subject
• magistram = the teacher, as the subject of the infinitive after dicit

Adfuturam esse is the future infinitive of adsum, meaning to be present, to be here, or to arrive / be coming depending on context.

Latin needs the future infinitive here because the action is future relative to the main verb dicit.

So the sentence means:

• Mother says
• the teacher will be here / will soon arrive

That future idea is shown by:

• adfuturam = future active participle, feminine accusative singular
• esse = infinitive of to be

Together they mean to be going to be present / to be about to be here / more naturally, will be here.

Adfuturam agrees with magistram.

Both are:

• feminine
• singular
• accusative

That is because adfuturam is a participle modifying the subject of the infinitive, and that subject is magistram.

So Latin is literally saying something like:

• Mother says [the teacher], about to be present, to be

That sounds strange in English, but it is the normal way Latin forms the future infinitive active.

It is made from two parts:

1. adfuturam

   • the future active participle of adsum
   • from the principal part adfutūrus, -a, -um

2. esse

   • the present infinitive of sum

This is how Latin forms the future active infinitive:

• future participle + esse

Examples:

• venturum esse = to be going to come / will come
• facturum esse = to be going to do / will do
• adfuturam esse = to be going to be present / will be here

Mox means soon.

It modifies the idea of adfuturam esse, so it tells us when the teacher will be present.

So:

• magistram mox adfuturam esse = that the teacher will soon be here

Its position is flexible. Latin word order is freer than English word order, so mox can be placed where it sounds natural or emphatic.

Because after dicit, Latin often prefers the indirect statement construction, not a finite clause introduced by that.

English says:

• Mother says that the teacher will soon be here.

Latin usually says:

• Mater dicit magistram mox adfuturam esse.

That is the standard way to report a statement indirectly.

A finite clause like Mater dicit: "Magistra mox aderit." would be direct speech:

• Mother says: "The teacher will soon be here."

So the sentence you have is indirect statement, not direct quotation.

The subject of the main verb is Mater.

So:

• Mater = subject of dicit
• dicit = main verb, says
• magistram = subject of the infinitive esse, but in the accusative because of indirect statement

This is an important distinction:

• main clause subject: Mater
• subject inside the indirect statement: magistram

Because the two verbs refer to different times:

• dicit = what the mother is doing now: she says
• adfuturam esse = what the teacher will do later: she will be here

The future is expressed inside the indirect statement by the future infinitive, not by changing dicit itself.

So the timeline is:

• now: Mother says
• later: the teacher will soon be here

It comes from adsum, adesse, adfui, which means to be present, to be here, or sometimes to arrive / come to be present.

It is a compound of:

• ad- = to, toward
• sum = I am

Its future participle is adfutūrus, adfutūra, adfutūrum.

So in your sentence:

• adfuturam = feminine accusative singular of that participle

Because it is built from sum, its forms can look unfamiliar at first.

It is a normal and natural Latin word order.

A helpful way to see the structure is:

• Mater — subject
• dicit — main verb
• magistram mox adfuturam esse — indirect statement

Inside the indirect statement:

• magistram = subject of the infinitive
• mox = adverb
• adfuturam esse = future infinitive

Latin does not need to keep the same rigid word order as English, because the endings show the grammatical roles. So the sentence could be rearranged in other ways without changing the basic meaning, though emphasis might shift.

A good clue is this pattern:

• a verb of saying/thinking/perceiving, such as dicit
• followed by an accusative noun
• followed by an infinitive

That usually signals accusative + infinitive, the standard Latin indirect statement.

Here the pattern is very clear:

• dicit = says
• magistram = accusative
• adfuturam esse = infinitive phrase

So when you see that combination, you should think:

• says that...
• not simply says the teacher...

That recognition becomes one of the most useful reading skills in Latin.