Es mejor que guardemos silencio cuando la profesora habla.

Because es mejor que normally triggers the subjunctive in Spanish.

• guardamos = indicative, used for facts or neutral statements
• guardemos = present subjunctive, used here because the sentence expresses a recommendation or value judgment

So:

• Es mejor que guardemos silencio = It’s better that we keep quiet

This is a very common pattern:

• Es importante que estudies
• Es bueno que descanséis
• Es mejor que esperemos

Spanish often uses the subjunctive after expressions that show:

• advice
• importance
• preference
• emotion
• doubt
• necessity

Es mejor que... is an expression of recommendation/judgment, not a simple statement of fact, so the subjunctive is expected.

Compare:

• Creo que habla mucho → indicative, because it is presented as a statement
• Es mejor que hable menos → subjunctive, because it expresses what would be preferable

Guardemos is the first person plural present subjunctive of guardar.

That means we keep / we should keep in this kind of sentence.

Formation:

• infinitive: guardar
• present indicative nosotros: guardamos
• present subjunctive nosotros: guardemos

For -ar verbs, the subjunctive uses -e- endings:

• yo guarde
• tú guardes
• él/ella guarde
• nosotros/nosotras guardemos
• vosotros/vosotras guardéis
• ellos/ellas guarden

Guardar silencio is a very natural Spanish expression meaning to keep silent or to remain quiet.

It is an example of a common Spanish structure: verb + noun rather than a single verb. English can do this too:

• keep calm
• pay attention
• make noise

Similar Spanish expressions include:

• hacer caso = to pay attention / to obey
• tener razón = to be right
• dar miedo = to be scary

You may also hear:

• callarse = to be quiet / to shut up
• estar en silencio = to be in silence

But in this sentence, guardar silencio sounds formal and natural.

Because guardar silencio works as a fixed expression. In Spanish, certain noun phrases used idiomatically do not need an article.

So:

• guardar silencio = standard and natural
• guardar el silencio = possible only in a more specific or unusual context, not the normal phrase here

It is similar to other article-less expressions:

• tener paciencia
• hacer daño
• dar clase

It can mean either, depending on context.

In this sentence, the most natural idea is often whenever the teacher is speaking or when the teacher speaks in general.

Because habla is in the present indicative, it usually refers to:

• a habitual situation
• a general truth
• something that really happens

So the sentence can be understood as a general classroom rule.

If it referred to a future event, Spanish often uses the subjunctive after cuando:

• Cuando la profesora hable, guardemos silencio or more naturally
• Cuando la profesora hable, guardaremos silencio

Because here cuando refers to something habitual or real, not a future/unknown event.

• cuando + indicative → when/whenever something actually happens or happens regularly
• cuando + subjunctive → when referring to a future or not-yet-realized event

So:

• cuando la profesora habla = whenever the teacher speaks / when the teacher is speaking
• cuando la profesora hable = when the teacher speaks next time / when she speaks in the future

That distinction is very important in Spanish.

Yes. That is also correct, and it means almost the same thing.

Difference:

• Es mejor que guardemos silencio... = more personal, explicitly includes we
• Es mejor guardar silencio... = more general, more like it’s better to keep quiet

So both are natural:

• Es mejor que guardemos silencio cuando la profesora habla
• Es mejor guardar silencio cuando la profesora habla

The first one sounds a bit more like a recommendation aimed at a group including the speaker.

In Spanish, it is very common to use the definite article with professions or roles when talking about a specific person in a general identifying way.

So:

• la profesora = the teacher

You usually need the article here because it refers to a known person.

Compare:

• La profesora habla = The teacher is speaking / speaks
• María es profesora = María is a teacher

After ser to give someone’s profession, the article is often omitted unless the noun is modified:

• Es profesora
• Es una profesora excelente

Yes.

• profesora = female teacher
• profesor = male teacher

Spanish nouns often show gender in this way. Since the sentence says la profesora, we know the teacher is female.

Spanish often leaves out subject pronouns because the verb ending already shows who is doing the action.

• guardemos already means we keep / we should keep

So nosotros is understood automatically.

You could say:

• Es mejor que nosotros guardemos silencio

But that would usually add emphasis, and in most contexts it is unnecessary.

No. In standard Spanish, h is silent.

So habla is pronounced roughly like abla.

This is true for most words with h:

• hola
• hacer
• hablar
• ahora

A learner might expect the h to sound like English, but it does not.

It has two main parts:

1. Es mejor que guardemos silencio

   • main clause + que
     • subordinate clause in the subjunctive

2. cuando la profesora habla

   • time clause introduced by cuando

So the structure is:

• Es mejor que + subjunctive
• plus
• cuando + indicative for a habitual/real situation

This is a very useful pattern to learn because you can reuse it easily:

• Es mejor que salgamos temprano cuando hace calor
• Es importante que escuchemos cuando el profesor explica
• Es bueno que descanséis cuando estáis cansados

Yes, completely natural.

It is grammatical and appropriate in European Spanish. Depending on tone and context, people in Spain might also say:

• Es mejor que estemos en silencio cuando habla la profesora
• Es mejor guardar silencio cuando habla la profesora
• Hay que guardar silencio cuando habla la profesora

All are natural, but your original sentence is perfectly good Spanish.