El profesor quiere que dejemos más margen en cada hoja para poder corregirla mejor.

Because Spanish normally uses querer que + subjunctive when one person wants someone else to do something.

Here, el profesor quiere is the teacher’s wish, and dejemos is what he wants us to do.

• El profesor quiere que dejemos... = the teacher wants us to leave...
• If the subject stayed the same, Spanish would usually use an infinitive instead:
  • El profesor quiere corregirla = the teacher wants to correct it

So que is needed because there is a change of subject.

Because after querer que, Spanish uses the subjunctive, not the indicative.

• dejemos = present subjunctive
• dejamos = present indicative

In this sentence, the teacher is expressing a wish or request, so Spanish uses the subjunctive:

• quiere que dejemos

If you said quiere que dejamos, it would be ungrammatical.

Dejemos is the first-person plural present subjunctive of dejar.

So it means that we leave.

Breakdown:

• infinitive: dejar
• present subjunctive:
  • yo deje
  • tú dejes
  • él/ella deje
  • nosotros/nosotras dejemos
  • vosotros/vosotras dejéis
  • ellos/ellas dejen

Because dejemos means we leave, while dejéis means you all leave.

So this sentence suggests that the speaker is included in the group being asked to leave more margin.

• quiere que dejemos = he wants us to leave...
• quiere que dejéis = he wants you all to leave...
  This would be very common in Spain if the teacher were speaking directly to a group.

So the choice depends on who is included.

Margen here means margin or blank space at the side of the page.

Más margen means more margin / more space.

There is no article because Spanish often leaves it out after words like más, menos, mucho, etc. when speaking generally about an amount.

• más margen = more margin
• más tiempo = more time
• menos ruido = less noise

So más margen is completely normal.

Because hoja means sheet of paper, and en is the natural preposition for something written or left on a sheet/page.

• en cada hoja = on each sheet

Also, cada is followed by a singular noun:

• cada hoja
• not cada hojas

Depending on context, hoja may sound more like sheet, while página would be more like page. Here hoja suggests the physical sheet of paper.

Here para expresses purpose.

It means something like:

• so that
• in order to

So the idea is:

• leave more margin on each sheet in order to correct it better

This is a very common use of para + infinitive in Spanish.

Yes, both alternatives are possible, but they are slightly different in feel.

• para poder corregirla mejor = so as to be able to correct it better
• para corregirla mejor = to correct it better
• para que pueda corregirla mejor = so that he/she can correct it better

What poder adds is the idea of being able to do it more easily or effectively.

And para que pueda... makes the subject more explicit. In this sentence, that can be helpful because the person doing the correcting is most naturally the teacher.

So:

• para poder corregirla mejor sounds natural
• para que pueda corregirla mejor is a slightly more explicit alternative

It refers to cada hoja.

That is why it is:

• la and not lo, because hoja is feminine
• singular, because cada hoja is singular

So the structure is basically:

• corregir la hoja → corregirla

It does not refer to margen, because margen is masculine, so that would be lo.

Because object pronouns in Spanish can attach to an infinitive.

So:

• corregirla = to correct it

That is very normal after verbs like poder, querer, deber, etc.

In fact, with poder + infinitive, you often have two possible positions:

• para poder corregirla mejor
• para poderla corregir mejor

Both are grammatical, but corregirla attached to the infinitive is often the more natural choice here.

What you cannot do is place it like English:

• la corregir ❌

The most natural interpretation is that the teacher is the one doing the correcting.

So the idea is:

• the teacher wants us to leave more margin
• so that he/she can correct each sheet more easily

That is why some speakers might even prefer:

• El profesor quiere que dejemos más margen en cada hoja para que pueda corregirla mejor.

This version makes the teacher’s role clearer.

If you wanted to say that we are the ones who will be able to correct it better, Spanish would normally make that explicit:

• ...para que podamos corregirla mejor

Here corregir means something like:

• to mark
• to correct
• to go over and fix mistakes

In a school context, it often means that a teacher is checking written work and marking errors.

So in this sentence, it is not just abstractly to correct; it is specifically the kind of correction a teacher does on a student’s work.