Jennifer got this from a grandma in the grocery store — they are an excellent source of hacks!
As our kids got older, we started buying the economy-sized cheese blocks. One day, a grandmother shopping with her grandkids gave me this hack: take the cheese out of the plastic, and wrap it tightly in aluminum foil. The cheese would last longer, and wouldn't get dried out at the open end. To my surprise, it worked! Now I cut the blocks into two or three smaller chunks, and use one at a time. We buy two blocks (mozzarella and cheddar), and they both stay fresh for at least 2 weeks. I don't know how long they'll really last, as we use them up too quickly; perhaps someone else knows the shelf-life of foiled cheese?
I've written about freezing shredded cheese, which I swear by. Not sure how block cheese fares the freeze-n-thaw.