Min søn tager sin madkasse med i skole, medmindre han glemmer den på bordet.

Because Danish uses the reflexive possessive sin/sit/sine when the thing belongs to the subject of the same clause.

Here, the subject is min søn, so sin madkasse means his own lunchbox.

• Min søn tager sin madkasse med = my son takes his own lunchbox with him.
• Min søn tager hans madkasse med would usually suggest he is taking someone else’s lunchbox, or it would sound contrastive.

This is one of the most important differences between Danish and English, because English just says his in both cases.

Because sin/sit/sine must agree with the noun that follows.

Here the noun is madkasse, and that is:

• singular
• common gender (en madkasse)

So the correct form is sin.

The pattern is:

• sin
  • singular common gender noun
• sit
  • singular neuter noun
• sine
  • plural noun

Examples:

• sin bog = his/her own book
• sit hus = his/her own house
• sine sko = his/her own shoes

Tage med is a very common Danish verb combination meaning take along or bring.

In Danish, this kind of verb is often split:

• Han tager sin madkasse med.

So med belongs with tager, even though another word comes in between.

You can think of it like this:

• tage = take
• tage med = take along / bring

In this sentence, English might naturally translate it as either:

• takes his lunchbox to school
• brings his lunchbox to school

Both can fit depending on perspective.

Because i skole is a fixed expression meaning something like to school / at school in the general sense.

Danish often leaves out the article in expressions like this:

• i skole = to school / at school
• i seng = to bed
• på arbejde = at work / to work

So med i skole means along to school.

If you used a definite form, it would usually sound more literal or more specific, such as the physical school building rather than the general institution or activity.

Medmindre means unless.

So:

• ..., medmindre han glemmer den på bordet
  = ..., unless he forgets it on the table

It introduces a subordinate clause, just like unless does in English.

Also, even though it starts with med-, you should learn medmindre as a whole word. In modern Danish, learners should just treat it as the conjunction unless.

Because after a possessive word like min, din, sin, hans, vores, etc., Danish normally uses the indefinite noun form.

So Danish says:

• min søn
• sin madkasse
• hans bil

not:

• min sønnen
• sin madkassen
• hans bilen

The possessive already makes the noun definite in meaning, so Danish does not add the definite ending as well.

Yes, absolutely.

That would also be correct, because in that clause han is the subject, and the lunchbox is still his own, so sin madkasse works perfectly.

The version in your sentence uses den simply to avoid repetition:

• medmindre han glemmer den på bordet

That sounds natural and smooth.

One important point: you cannot use sin by itself here, because sin is a possessive determiner, not an object pronoun. So you can say:

• glemmer sin madkasse
• glemmer den

but not just:

• glemmer sin

Because den and det depend on the grammatical gender of the noun they refer to.

The noun is en madkasse, so it is a common gender noun. That means the pronoun is den.

• en madkasse → den
• et bord → det

So:

• han glemmer den = he forgets it

If the noun had been a neuter noun, you would use det instead.

Because Danish usually puts the definite article at the end of the noun.

So:

• et bord = a table
• bordet = the table

That is why på bordet means on the table.

This is very normal in Danish. A few more examples:

• en bog → bogen
• et hus → huset

Yes. Medmindre introduces a subordinate clause, and Danish subordinate clauses do not use normal main-clause verb-second word order.

In your sentence:

• medmindre han glemmer den på bordet

the order is straightforward:

• medmindre = conjunction
• han = subject
• glemmer = verb
• den = object
• på bordet = adverbial

The difference becomes clearer when a sentence adverb is present:

• main clause: Han tager den ikke med.
• subordinate clause: ..., medmindre han ikke tager den med.

So after words like at, fordi, hvis, medmindre, Danish uses subordinate-clause word order.

Because medmindre introduces a subordinate clause.

In Danish, many writers put a comma before a subordinate clause like that. However, under modern Danish comma rules, this start comma is optional.

So you may see both:

• Min søn tager sin madkasse med i skole, medmindre han glemmer den på bordet.
• Min søn tager sin madkasse med i skole medmindre han glemmer den på bordet.

Both are possible, depending on the writer’s comma style.