B
oth the ave maria and pater noster have a twofold separation in them. The first half is a glorification, the second half supplication. There is spiritual insight here that we should heed.
Hail Mary, full of grace, the Lord is with thee. Blessed art thou among women, and blessed is the fruit of thy womb, Jesus.
Fully declarative, making known the glory of the virgin. This is how we address her, by naming her relationship with the cosmos.
Holy Mary, mother of God, pray for us sinners, now and at the hour of our death.
Then we name ourselves, as sinners. We ask for her prayers only after her name is well-said.
Our Father, who art in Heaven, hallowed be thy name. Thy kingdom come, thy will be done, on Earth as it is in Heaven.
We name the Father, we declare him holy, we submit to his will.
Give us this day our daily bread, and forgive us our trespasses, as we forgive those who trespass against us. And lead us not into temptation, but deliver us from evil.
Here the supplication, where we set ourselves into relationship with the Lord via humility. Once He is named our Father, we may beseech Him as His children.