gleichaltrig
same age
Describes people, or more rarely things, that are the same age or come from the same period.
Mein Sohn spielt am liebsten mit gleichaltrigen Kindern.
My son prefers playing with children his own age.

same age
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same age
Describes people, or more rarely things, that are the same age or come from the same period.
Mein Sohn spielt am liebsten mit gleichaltrigen Kindern.
My son prefers playing with children his own age.

The word is made up of 'gleich' (same) and a form of the noun 'das Alter' (age). So it literally means 'of the same age'.
Meine Schwester und ihre beste Freundin sind gleichaltrig.
My sister and her best friend are the same age.
When you want to compare a person directly, you use the preposition 'mit' (with). The structure is: Person A ist gleichaltrig mit Person B.
Der neue Mitarbeiter ist mit meinem Bruder gleichaltrig.
The new employee is the same age as my brother.
The word can also be used as a noun to refer to a person of the same age: 'der/die Gleichaltrige' (person of the same age). In the plural, people often say 'den Gleichaltrigen' to mean one's peer group.
Er verbringt seine Freizeit am liebsten mit Gleichaltrigen.
He prefers spending his free time with people his own age.
simultaneously / at the same time
'gleichzeitig' and 'gleichaltrig' both have to do with sameness, but they mean different things. 'gleichzeitig' describes two things happening at the same time. 'gleichaltrig' describes people or things that are the same age. Learners may confuse the words because both begin with 'gleich-'. The important question is: if it is about the point in time, use 'gleichzeitig'. If it is about age, use 'gleichaltrig'.

Mein Sohn spielt gern mit gleichaltrigen Kindern aus der Nachbarschaft.
My son likes playing with children his own age from the neighborhood.
Im Büro telefonierte Anna und schrieb gleichzeitig eine E-Mail.
At the office, Anna talked on the phone and wrote an email at the same time.