Considering the nonmetals what is the relationship between the group number for an element (carbon, for example, belongs to group 4a; see the periodic table on the inside front cover) and the number of single covalent bonds that element needs to form to conform to the octet rule

The Octet rule is essential to obey nature's law of stability. Among all the elements in the periodic table, the noble gases in Group 8 are the most stable in. Hence, all the other elements aim to achieve their electronic configuration. So, all elements must bond with others to conform to be a part of group 8. 

Bonds for non metals = 8 - Group number
Ex:
Bonds for oxygen = 8 - 4 = 4
Bonds for nitrogen = 8 - 5 = 3