Every complete sentence consists of two parts: a subject and a predicate.
Both parts are important to understand what's going on in the sentence.
A basic principle here is the "subject-verb agreement": subjects and predicates must agree in number.
In other words, singular subjects require singular verbs and plural subjects require plural verbs.
Here, the compound subject is plural, it's Peter and I. Hence, the verb were is plural.
Note: When you conjugate the verb (or change its form), only the subject of the sentence counts.
Here, even though the noun necklaces is plural, the verb smiles is singular because the subject woman is singular.
Subjects and predicates are the most important part of a sentence. It is really important to identify them in a sentence.
Here are two good reasons:
No wonder, this will help you build a solid grammar foundation from a young age.
This is actually not a complete thought or sentence. There is no subject and predicate.
If we wanted to fix that sentence, we would say:
This is a complete thought or sentence. There are both subject and predicate in the sentence.
First, we can find the verb which is looked.
Then we ask, who was looking (or who is doing the action)? The answer is Mom and I.
So, the subject is Mom and I, and the predicate is looked at the paintings.