  This paper develops a framework for the design of scoring rules to optimally
incentivize an agent to exert a multi-dimensional effort. This framework is a
generalization to strategic agents of the classical knapsack problem (cf.
Briest, Krysta, and V\"ocking, 2005, Singer, 2010) and it is foundational to
applying algorithmic mechanism design to the classroom. The paper identifies
two simple families of scoring rules that guarantee constant approximations to
the optimal scoring rule. The truncated separate scoring rule is the sum of
single dimensional scoring rules that is truncated to the bounded range of
feasible scores. The threshold scoring rule gives the maximum score if reports
exceed a threshold and zero otherwise. Approximate optimality of one or the
other of these rules is similar to the bundling or selling separately result of
Babaioff, Immorlica, Lucier, and Weinberg (2014). Finally, we show that the
approximate optimality of the best of those two simple scoring rules is robust
when the agent's choice of effort is made sequentially.
