-SMALL(B2:G2,1) 
...
The formula in column H2 (Dick's mark) is:
=IF(COUNT(B2,C2,D2,E2,F2,G2)=6,SUM(B2,C2,D2,E2,F2,G2)-MIN(B2,C2,D2,E2,F2,G2),SUM(B2,C2,D2,E2,F2,G2))
A more simple markup would be: =IF(COUNT(B2:G2)=6,SUM(B2:G2)-MIN(B2:G2),SUM(B2:G2))
In prose instead of programming that is: If the total items recorded equals 6 then add them together and subtract the minimum, otherwise just add them together.
If you know that every cell will have a number (like zero where the example currently has a blank space) then you do not need the IF part, you can just have =SUM(B2:G2)-MIN(B2:G2) The formula can then be extended downwards to the other students.
The SMALL option mentioned during the session would work if you wanted to drop one item, or more importantly two items. It does still have the same limit that if one item is blank (without a zero) then students would "lose" a good mark.
Here's an example with SMALL of dropping one item.
=IF(COUNT(B2:G2)=6,SUM(B2:G2)-SMALL(B2:G2,1),SUM(B2:G2))
Here's an example with SMALL of dropping two items.
=IF(COUNT(B2:G2)=6,SUM(B2:G2)-SMALL(B2:G2,1)-SMALL(B2:G2,2),SUM(B2:G2))
The formula can then be extended downwards to the other students.
...