When I was in college, Professor Spurgin always said, "Repetition is the mother of all learning. Repetition is the mother of all learning. Repetition..." Thankfully, he stopped there, but the point was clear. This is a good reminder for memory work. In an effort to get it "done," I see a lot of kids trying to say their memory work to themselves too early. They know the basic gist of it, but since they haven't spent the proper time studying what is actually there, they're not actually memorizing (or in turn, saying) exactly what the passage/chief part says.
A better way would be to spend the first block of time simply reading the passage word for word off the page. It can be done as a whole or be broken up phrase by phrase. But by repeating it exactly as it's written, it will not only be memorized more easily, but more exactly and for a longer time. It does take more time than plowing through it to be "done," but the investment is always worth it.
One handy way to practice is by playing the eraser game. After writing out the passage and starting to learn it, a word (or a couple words) are erased. Then the child can read it again, including the erased words. Then erase a few more and repeat. Eventually, the whole passage will be gone from the paper, but planted in the brain!