Break the sentence down.
The rate of cancer [incidentally, this phrase is meaningless, but that's not the point] is half of something.
What is that something?
PS - probably not a useful contribution to your lesson
A bit of history: it used to be the case that English was often rendered nearly incomprehensible by the aping of the Latin tendency to relate parts of sentences to each other. This was fine in Latin, with its case endings (which showed what related to what), but didn't work in English. Until recently, and still occasionally - in formal writing - it was possible to use 'that', but without a verb: 'The rate of cancer is half that in the United States.'