One to one correspondence between 2 sets matches each element of each set with accurately one element of other. This common sense idea of size is basis for tallying and counting. Even the toddler can see if she got fair share of gum drops by matching them up with the brother's share. Though, when natural idea of "same size" is extended to infinite sets, strange things start to occur.
For example, n<-->2n defines one to one correspondence between set N of natural numbers and even natural numbers, implying that we can "throw away" half of N and have the set of same size left. Matching is one to one as 2a=2b implies a=b for any numbers a and b. Show this correspondence between N and set of even natural numbers by providing at least for instance of matchups between specific numbers.
Generalize argument to illustrate that we can throw away 99% of N and still have the set of same size left. Show the correspondence with some particular examples.
Generalize further to illustrate that, for any nonzero number k, set kN of all natural-number multiples of k is same size as N. Write some examples.