When Jesus teaches prayer, he begins by having us to assume the same relationship with God that he has. He tells us to join him in praying to God, his Father. He easily could have taken his start from the Psalms. The Psalms often have us direct our words to God (Ps. 54,55) or to the Lord (Ps. 18, 104, 105). In fact, the disciples around Jesus probably knew many (all?) the Psalms by heart. Jewish people of the first century had a pretty clear pattern of prayer ("They devoted themselves....to.. the prayers" Acts 2:42). So when they asked Jesus how to pray, both he and they knew they were asking for something distinct. Jesus teaches us to adress and call upon God's attention by saying "Our Father,..."
OUR It is easy and correct to see that Jesus is teaching us, his disciples, to pray together. This is a wonderful encouragement--we are never praying by ourselves. Even when praying feels lonely or boring or futile, Jesus teaches a truth that is larger than the truth we feel at a particular moment. We are not alone. We do not pray alone. Other people are praying as well, and with us. But even more importantly we are praying with Jesus. Jesus is praying with us. We unite our voice with Jesus in address God. When his disciples pray, we are joining Jesus in prayer.