Het dagritme verandert met de groepsgrootte.

Dagritme is a het-word in Dutch, so it takes het.

A useful pattern is that many neuter nouns and many nouns with the diminutive ending -je take het, but for a word like dagritme, you mostly just have to learn the article with the noun.

So:

• het dagritme
• not de dagritme

Dutch very often forms compound nouns by joining words together into a single word.

Here:

• dag = day
• ritme = rhythm

Together:

• dagritme = day rhythm / daily rhythm

This is much more common in Dutch than in English, where English often prefers separate words.

The infinitive is veranderen = to change.

In the present tense, the third-person singular form takes -t:

• ik verander
• jij verandert
• hij/zij/het verandert

The subject here is het dagritme, which is singular, so the correct form is verandert.

Here it is used intransitively, meaning the subject changes by itself:

• Het dagritme verandert. = The daily rhythm changes.

Dutch veranderen can also be used transitively in some contexts, but in this sentence it simply means to change, not to change something.

Here met means something like with in the sense of in relation to or depending on.

So verandert met de groepsgrootte means:

• changes with the group size
• changes as the group size changes

It does not mean physical accompaniment, like together with.

Groepsgrootte is also a compound noun:

• groep = group
• grootte = size

In Dutch compounds, the last part usually determines the grammatical gender and article. Since grootte is a de-word, the full compound is also a de-word:

• de grootte
• de groepsgrootte

That -s- is a linking element often found in Dutch compound nouns.

So:

• groep
  • grootte becomes
• groepsgrootte

This linking -s- does not usually have a separate meaning by itself. It just helps form the compound in the way Dutch normally does.

You will see this in many Dutch words, and unfortunately it is not always fully predictable, so learners often need to learn compounds individually.

Yes. The sentence can be reordered for emphasis.

Standard order:

• Het dagritme verandert met de groepsgrootte.

You could also say:

• Met de groepsgrootte verandert het dagritme.

That version puts more emphasis on met de groepsgrootte. In Dutch main clauses, the finite verb still stays in the second position, so after moving met de groepsgrootte to the front, verandert must come immediately after it.

A rough guide:

• dagritme → something like DAKH-rit-muh
• groepsgrootte → something like khroops-KHRO-tuh

A few pronunciation points:

• g in standard Dutch is usually a harsh throat sound, not like the English g in go
• ij is not in this sentence, so that is one less difficulty here
• ritme has a reduced final -e, like uh
• Dutch compounds usually keep the main stress near the beginning of the compound

You can absolutely reuse the pattern. This is a very useful structure:

• Het/De [subject] verandert met de [factor].

Examples:

• De sfeer verandert met het seizoen.
• De prijs verandert met de vraag.
• Het gedrag verandert met de leeftijd.

So the sentence is a good model for expressing that something changes depending on another variable.