I have been reading this thread since it was started, but I am not sure I can say this gracefully. Our church was planted 50+ years ago by a big church in a lower income neighborhood. Only a bit more recently than that, low income housing was constructed nearby. The people who live in our church's neighborhood are still among those in our town who have the lowest income, the smallest property, and drive the oldest cars.
Our church just completed our annual VBS. Monthly during the school year we have a Parents Night Out. Based on the participation we have from our neighbors who live in low income housing in these events, we have been asked by the local housing authority to participate in helping provide childcare for
their events.
So with all due respect, here are my comments about your activity:
Please don't go to the projects. Go to the people. They have the same needs, desires, goals, and emotions as you do. Create relationships with them, love them as they are, minister to them even if they have a mess, especially if they are in a mess. Some of the people who live in these neighborhoods are evil people, just like some of those who live in upper-class neighborhoods. Most of them are not. Give them a chance. Think long term relationships and ask what needs are there that you can continue to meet after this one week of VBS. Work with the children. Go out for coffee with the parents. Or invite parents in to help with crafts, games, and/or refreshments. Get to know the moms and dads. By name. Pay a utility bill for them before their service is disconnected. Give them a job - employment if you are in a position to do so, or meet physical needs such as groceries, school clothes, school supplies, as they need it.
Don't assume they need it. Some of these people are financially doing just fine; their lives are in order. However, working at Wal-Mart or McDonalds doesn't pay enough to purchase the house of their dreams in the suburbs. They're getting by, but they are not wealthy. They are not part of the social system and don't need to be. Please don't insult them by making assumptions.
Many of those to whom we minister are unbelievers. And not surprisingly, they act like it!

Some of the parents smoke and use foul language, the children misbehave, mothers don't pick up their child on time. Some parents do drugs and for a few weeks live at the detox center. The teenagers are so angry they act out in some way, and move a few blocks further away to the juvenile justice center. Back at home there are pieces that need loving care and attention, not judgment and condemnation.
Please evaluate why you are going there. Is it because you had a great event and you want to share it? Or is it because Jesus is calling you there and the Holy Spirit won't let go of you until you find a friend in that neighborhood? Is this a project or a passion?