Learn Hardcore Spanish (Latin America): Nosotros formamos un club de español en la escuela y organizamos un pequeño torneo de vocabulario cada mes. - We formed a Spanish club at school and organize a small vocabulary tournament every month.

Want to emphasize “we” (not someone else):
Nosotros formamos un club, no ellos. – We formed a club, not them.
Want extra clarity in a long or complicated sentence.

In your example, Nosotros is not grammatically required; it’s just a bit more explicit or emphatic.

How can formamos and organizamos mean both “we form / we organize” (present) and “we formed / we organized” (past)? How do I know which tense it is here?

For regular -ar verbs, the 1st person plural (nosotros) form is the same in the present and the preterite:

Present:
(Nosotros) formamos – we form
(Nosotros) organizamos – we organize
Preterite (simple past):
(Nosotros) formamos – we formed
(Nosotros) organizamos – we organized

So you use context to decide:

Time expressions like ayer, el año pasado, en 2020 → usually past.
Habitual markers like cada mes, todos los días, siempre → usually present or imperfect.

In your sentence, cada mes (“every month”) describes a repeated, ongoing action, so the natural reading is present:
We form a Spanish club at school and (we) organize a small vocabulary tournament every month.

If it were clearly past and habitual, a native speaker would more likely use the imperfect for the second verb:
…y organizábamos un pequeño torneo… – and we used to organize a small tournament…

Why is it un club de español and not un club español?

Spanish often uses de + noun to show the type or focus of something:

un club de español – a Spanish (language) club, i.e., a club about Spanish
una clase de historia – a history class (class about history)
un torneo de ajedrez – a chess tournament

If you say un club español, you’re describing the club itself as Spanish (by nationality/origin), like:

un club español – a club that is from Spain / culturally Spanish
(for example, a Spanish soccer club like Real Madrid)

So:

un club de español = a club for learning/using the Spanish language
un club español = a club that is Spanish (its nationality/identity)

Why is español not capitalized here, even though “Spanish” is capitalized in English?

In Spanish, language names and nationalities are not capitalized, unless they start a sentence:

Hablo español. – I speak Spanish.
Estudio inglés y francés. – I study English and French.
Los estudiantes españoles… – Spanish students…

So:

un club de español – correct
un club de Español – incorrect (unless starting a sentence)

This is just a standard spelling rule in Spanish.

Why do we use un before club and before pequeño torneo? Could we leave out un, like in English “We formed Spanish club”?

Spanish uses the indefinite article (un, una, unos, unas) more consistently than English.

Formamos un club de español… – We formed a Spanish club…
Saying Formamos club de español… sounds unnatural or incomplete in most contexts.

Before pequeño torneo, un is also needed:

…y organizamos un pequeño torneo de vocabulario…

Here, un goes with torneo, and pequeño is just an adjective modifying it. You cannot drop un in standard Spanish:

✓ un pequeño torneo
✗ pequeño torneo (as the whole object in a normal sentence)

So in this sentence, both uses of un are required.

Why is pequeño placed before torneo? Can I say un torneo pequeño de vocabulario instead?

Both word orders are grammatically correct:

un pequeño torneo de vocabulario
un torneo pequeño de vocabulario

The difference is mainly emphasis and style:

pequeño before the noun is more common when it’s a general, descriptive or slightly subjective quality. It can sound more “built‑in” to the idea:
- un pequeño torneo – a little tournament (a modest event, no big deal)
pequeño after the noun can sound a bit more objective or contrastive, like you’re describing the size as a specific feature:
- un torneo pequeño – a tournament that happens to be small (maybe compared to another one)

In everyday speech, both are fine, and the meaning difference is subtle. In your sentence, un pequeño torneo de vocabulario is very natural.

What exactly does torneo mean here? I thought torneo was mostly for sports tournaments.

Torneo does often refer to sports:

un torneo de fútbol – a soccer tournament
un torneo de tenis – a tennis tournament

But it can also be used more broadly for any structured competition with rounds, matches, or a bracket, including academic ones:

un torneo de debate – a debate tournament
un torneo de ajedrez – a chess tournament

In un torneo de vocabulario, it suggests some kind of organized competition involving vocabulary (e.g., teams, rounds, elimination).

For a more general “contest” or “competition” that doesn’t feel like a bracketed tournament, many speakers would say:

un concurso de vocabulario – a vocabulary contest/competition

Both torneo and concurso can work; torneo just emphasizes a more tournament-like structure.

Why is it torneo de vocabulario and not something like torneo de las palabras?

Spanish often uses de + noun to show the field or content of an activity:

torneo de ajedrez – chess tournament
concurso de matemáticas – math contest
competencia de canto – singing competition

Vocabulario is treated like an abstract/mass noun (the whole set of words), so:

torneo de vocabulario – a tournament focused on vocabulary

De las palabras (literally “of the words”) would sound odd here. It doesn’t pattern with how competitions are usually labeled. You’d almost never hear:

✗ torneo de las palabras

You might see something like:

juegos de palabras – word games

But for a competition about vocabulary knowledge, de vocabulario is the natural choice.

Why do we say en la escuela instead of just en escuela? Is the article la necessary?

Yes, in this kind of expression, Spanish normally requires the definite article:

en la escuela – at school
en el trabajo – at work
en la universidad – at the university

Saying en escuela without the article is not natural in standard Spanish.

In Latin America, you might also hear different words for “school” depending on the level:

en la escuela primaria – in elementary school
en el colegio – often “school” (especially middle/high school, depending on country)
en la secundaria / en la prepa – high school (varies by country)

But whichever noun is used, it will still take an article:

en el colegio
en la secundaria

What’s the difference between cada mes and todos los meses? Can I use them interchangeably here?

Cada mes and todos los meses are very close in meaning and can both fit in this sentence:

…organizamos un pequeño torneo de vocabulario cada mes.
…organizamos un pequeño torneo de vocabulario todos los meses.

Nuances:

cada mes – literally “each month”; feels a bit more neutral and concise.
todos los meses – literally “every (all the) months”; can sound slightly more colloquial or emphatic in some contexts, but in practice they’re almost interchangeable.

In everyday speech, both are fine; cada mes might be just a little more compact and formal.

Could I move cada mes to another part of the sentence, like Cada mes organizamos…? Where can I put it?

Yes, Spanish is flexible with time expressions. All of these are acceptable:

Cada mes organizamos un pequeño torneo de vocabulario.
Organizamos un pequeño torneo de vocabulario cada mes.
En la escuela organizamos un pequeño torneo de vocabulario cada mes.

Some notes:

Putting Cada mes at the beginning gives it a bit more emphasis:
Cada mes organizamos… – “Every month, we organize…”
Time expressions like cada mes, todos los días, a veces commonly go:
- at the beginning or
- at the end of the clause.

Just avoid splitting the verb phrase in a strange way, like:

✗ Organizamos cada mes un pequeño torneo – not wrong, but less natural than the other options in many dialects; some speakers still say it, though.

How do I know that club and torneo are masculine, so I need un and pequeño and pequeño torneo, not una, pequeña, etc.?

You mostly have to learn the gender with each noun, but there are hints:

torneo ends in -o, which is usually masculine:
- el torneo, un torneo, pequeño torneo
club is a borrowed word (from English). Most such loanwords ending in a consonant are treated as masculine:
- el club, un club

So:

un club de español (not ✗ una club)
un pequeño torneo (not ✗ una pequeña torneo)

The forms of the article (un) and adjectives (pequeño) must match the noun in gender and number.