Understanding who the poor represent under the Old Covenant, let's look at the beatitudes.
Remember, under the Old Covenant, people were blessed for their obedience to the law and cursed for their disobedience. If you kept the commandments, you got health, wealth and prosperity. Outward blessings for outward obedience I am assuming. And if you disobeyed the commandments you got the opposite: Sickness, poverty, famine. Get it? Under the law, if you do good, you get good. If you do bad, you get bad. Simple enough. A covenant based on performance.
Now, poor guys were considered poor because they were not as obedient. The rich were considered blessed because they were obedient.
Understanding this, Jesus' very first words before the sermon on the mount are this:
"Blessed are you who are poor, for yours is the kingdom of God."
"Blessed are you who are hungry now, for you shall be satisfied ."
"Blessed are you who weep now, for you shall laugh."
And for the rich He says,
"But woe to you who are rich, for you have received your consolation."
"Woe to you who are full now, for you shall be hungry."
"Woe to you, when all people speak well of you, for so their fathers did to the false prophets."