Mater monet ne scintillas tangamus.

Ne introduces a negative command/warning clause after verbs like monet (warns/advises).

So:

• Mater monet = Mother warns
• ne ... tangamus = that we should not touch ... / not to touch ...

A very common pattern in Latin is:

• monere ut ... = to advise/warn someone to do something
• monere ne ... = to advise/warn someone not to do something

So ne here means something like that ... not.

Because after monet with ne, Latin normally uses a subjunctive clause.

• tangimus = we touch (plain statement, indicative)
• tangamus = we may/should touch or, in this context, part of a warning: that we not touch

This is not a normal statement of fact. It is a clause depending on monet, expressing what Mother is warning us not to do.

So the subjunctive is required by the construction.

Tangamus is present subjunctive, first person plural, from tangere (to touch).

Formally it means let us touch in some contexts, but here that is not the meaning. In this sentence, because it follows monet ne, it means:

• that we should not touch
• not to touch
• that we are not to touch

So you should understand the tense mainly as part of the standard subordinate subjunctive construction, not as an independent let us command.

The ending -mus tells you it is first person plural: we.

So:

• tangam = I may touch
• tangas = you may touch
• tangat = he/she/it may touch
• tangamus = we may touch
• tangatis = you all may touch
• tangant = they may touch

In this sentence, the subject we is not separately stated, because Latin often leaves subject pronouns implied in the verb ending.

Latin usually does not need an explicit subject pronoun, because the verb ending already shows the person and number.

Here, tangamus already means we may/should touch.

If Latin added nos, it would usually be for emphasis:

• Mater monet ne scintillas nos tangamus = Mother warns that we should not touch the sparks
  (with extra emphasis on we)

But normally just tangamus is enough.

Because tangere (to touch) takes a direct object, and the direct object goes in the accusative case.

So:

• scintilla = a spark (nominative singular)
• scintillas = sparks (accusative plural, or nominative plural in some contexts)

Here it is accusative plural because it is the thing being touched:

• touch what? → the sparks

The dictionary form is scintilla, scintillae, a first-declension feminine noun, meaning spark.

In this sentence:

• scintillas = sparks (accusative plural)

So the full phrase means not to touch the sparks.

All three can be possible translations of monet, depending on context, because monere has a range of meanings:

• to warn
• to advise
• to remind

In this sentence, because of ne plus subjunctive, warns is especially natural:

• Mother warns us not to touch the sparks

But advises us not to touch the sparks is also possible in some contexts.

Latin often leaves out the person being warned if it is clear from the context or from the subordinate clause.

Here, tangamus already shows that the people involved are we, so the sentence naturally implies:

• Mother warns us not to touch the sparks

Latin could say Mater nos monet ne scintillas tangamus, and that would be perfectly possible. But nos is not necessary.

Yes, it is very close to what grammars often call an indirect command or subordinate jussive-type clause.

A common pattern is:

• verb of ordering/advising/warning + ut or ne
  • subjunctive

Examples:

• imperat ut veniamus = he orders us to come
• monet ne abeamus = he warns us not to go away

So Mater monet ne scintillas tangamus fits that pattern.

Not in the standard classical construction after monet with this meaning.

English says warns us not to touch, using an infinitive. Latin usually prefers:

• monet ne tangamus

rather than a direct infinitive equivalent.

So this is a place where Latin and English structure the sentence differently.

Latin word order is flexible, so this order is only one possible arrangement.

This sentence puts the main idea in a clear sequence:

• Mater = subject
• monet = main verb
• ne scintillas tangamus = what she warns us not to do

Other orders are possible, such as:

• Ne scintillas tangamus mater monet
• Mater ne scintillas tangamus monet

But the given order is straightforward and natural for learners.

Tangere is a third-conjugation verb.

The present subjunctive of third-conjugation verbs uses -a- before the personal endings:

• tangam
• tangas
• tangat
• tangamus
• tangatis
• tangant

So tangamus = stem tang- + subjunctive vowel a + ending -mus.

That is why it is tangamus, not tangemus or tangimus.

Yes, by itself ne tangamus could be an independent hortatory subjunctive meaning let us not touch.

But in this sentence it is not independent, because it depends on monet:

• Mater monet ne scintillas tangamus

So here it means:

• Mother warns us not to touch the sparks

The grammar is similar, but the sentence function is different.