Hoc consilium discipulis prodest, quia desidiam minuit et perseverantiam auget.

Because consilium is a neuter singular noun, and the demonstrative hic, haec, hoc has to agree with it in gender, number, and case.

• hoc = nominative singular neuter
• consilium = nominative singular neuter

So hoc consilium means this plan or this advice.

If the noun were masculine, you would expect hic instead.

Hoc consilium is in the nominative singular, which is the case normally used for the subject of a sentence.

We know it is the subject because:

• prodest is third person singular
• consilium is singular
• the meaning fits: this plan benefits the students

So hoc consilium is the thing doing the action of prodest.

Because prodesse regularly takes the dative of the person or thing benefited.

So:

• discipulis = to the students or for the students
• hoc consilium discipulis prodest = this plan is beneficial to the students

This is a very common Latin pattern:

• alicui prodesse = to benefit someone

A native English speaker often wants an accusative here, but Latin uses the dative instead.

Prodest is the third person singular present active indicative of prosum, prodesse, profui.

It means:

• is useful
• is beneficial
• benefits

It is an irregular compound built from pro- plus sum / esse.

So:

• prodest = it benefits or it is of use

That is why the construction is a little different from a more ordinary verb.

Because its subject, hoc consilium, is singular.

Latin verbs agree with their subjects in person and number. Since consilium is one plan, the verb must also be singular:

• consilium ... prodest = the plan benefits
• if it were plural, you would expect prosunt

Quia means because and introduces a clause giving the reason.

So the structure is:

• main clause: Hoc consilium discipulis prodest
• reason clause: quia desidiam minuit et perseverantiam auget

In other words: the plan benefits the students because it reduces laziness and increases perseverance.

They are in the accusative because they are the direct objects of the verbs:

• desidiam minuit = it reduces laziness
• perseverantiam auget = it increases perseverance

Both minuere and augere are transitive verbs, so they take direct objects in the accusative.

The subject is still hoc consilium, even though Latin does not repeat it.

So the sentence is understood as:

• hoc consilium ... minuit
• hoc consilium ... auget

Latin often leaves out a repeated subject when it is already clear from the context. English usually repeats it, but Latin does not need to.

They are both present active indicative, third person singular.

So they mean:

• minuit = it reduces
• auget = it increases

The present tense here states a general truth or a present effect: this plan benefits students because it reduces one thing and increases another.

Because Latin does not normally need an expressed subject pronoun when the verb ending already shows the person and number.

• minuit already means he/she/it reduces
• auget already means he/she/it increases

Since hoc consilium has already been named, Latin simply continues with the verbs.

Consilium can mean several related things, including:

• plan
• strategy
• advice
• policy
• decision

In this sentence, the best English choice depends on context. If the sentence is about a method or approach used in teaching, plan or strategy is probably the most natural. If it is about guidance given to students, advice could also fit.

So a learner should not assume that one Latin noun always matches one exact English word.

Latin word order is much more flexible than English word order because Latin uses case endings to show grammatical function.

English relies heavily on position:

• subject + verb + object

Latin can move words around more freely because forms such as discipulis, desidiam, and perseverantiam already show what they are doing in the sentence.

This order:

• Hoc consilium discipulis prodest, quia desidiam minuit et perseverantiam auget

is perfectly natural. A different order could also be grammatical, though it might change emphasis.

Yes. Both are abstract nouns:

• desidia = laziness, idleness
• perseverantia = perseverance, persistence

In Latin, abstract nouns are often used in the singular when speaking generally, just as in English:

• laziness
• perseverance

So the sentence is not talking about one single act of laziness and one single act of perseverance, but about those qualities in general.

Yes, several are easy cognates:

• consilium is related in meaning to English counsel
• discipulis comes from discipulus, related to disciple
• desidia is related to desidious only very indirectly, but not a common transparent cognate for most learners
• perseverantia is clearly related to perseverance
• auget comes from augere, related to augment

Noticing cognates can help vocabulary, but it is still important to learn each Latin word in its own usage.