You realize that the definition of term frequency might be a little too harsh, as the length of the documents could vary too much. As such, you choose to define the TF score as

tf(f_ik) = 1/2 + 1/2 (f_ik/max D_i)

where f_ik denotes the frequency that term T_k appears in document D_i and max D_i denotes the frequency of the most common term in D_i.

Discuss why you might want to consider this score instead.