Is this exercise just about agreement of adjectives?

In Exercitia for Cap xxxvi (exercitium 6) Orberg has an exercise which he introduces as follows:

Exempla:

media Italia = medium (= media pars) Italiae
prima/postrema aestas = initium / inis (=prima/postrema pars) aestatis
summus/infimus mons = summum/infimum (= summa/infima pars) montis…

I don’t really understand this. Is this an exercise to distinguise between adjectival use ‘media Italia’ and the noun + gen ‘medium Italiae’?

By some instinct I did get most of it right – but I’m ont really clear what he’s trying to teach.

The following questions are thus confusing to me (all of the text below is Orberg):

  1. Naxos in medi__ mar__ Aegaeo [= in medio maris Aegaei] sita est.

  2. Hora sexta dicitur ‘meridies’, id est medi__ di__ [= medium diei].

  3. Sol altissimus est hora sexta vel meridie, id est med__ di__ [= medio diei]

The correct answer to these is given by Orberg as follows:

  1. Naxos in medi[o] mar _Aegaeo [= in medio maris Aegaei] sita est.
    \
  2. Hora sexta dicitur ‘meridies’, id est medi[us] di[es] [= medium diei].
    \
  3. Sol altissimus est hora sexta vel meridie, id est med[io] di[e] [= medio diei]


    Let me try to explain my thinking:
    \
  4. Naxos in medio mari Aegaeo [= in medio maris Aegaei] sita est.
    \
  • ‘medio’ = neuter ablative adjective to agree with noun ablative ‘mari’
    \
  • ‘mari’ = ablative of neuter noun ‘mare’.

    \
  1. Hora sexta dicitur ‘meridies’, id est medius dies [= medium diei].
    \
  • ‘medius’ = masculine nominative singular adjective to agree with ‘dies’. It is the middle of the day.

    \
  1. Sol altissimus est hora sexta vel meridie, id est medio die [= medio diei]
    \
  • ‘medio’ = masculine ablative to agree with ‘die’ – to indicate a time when.

    This is just about agreement of adjectives isn’t it..?_

Est // Yes.

…in a place where other languages use a genitive in preference modernly. He’s highlighting the construction.
…cum aliae linguae genetivum casum his diebus praeferunt. Emphasim ad formam dat.

In Execitia Capituli XXXVI Orberg scribit:

  1. Sol altissimus est hora sexta vel meridie, id est medi_ di_ [=medio diei]

Now it seems the answer should be ‘…id est medius dies’ (given the hint he has in square brackets) but he has ‘medio die’…? What am I missing here?

…especially since in the following question (6.) he asks:

Sexta hora noctis est medi_ nox [= medium noctis].

…the correct answer being:

Sexta hora noctis est media nox..

i.e. Nominative Feminine singular - this is what it is..

the strong implication to me is that he is looking for an answer in the nominative to question 5.

Sic non concludit. Is ablativum jam denotavit per hoc: [=medio diei].
No. He has already specified the ablative with [=medio diei].