To increase the number of paper clips the nail attracts in the given scenario, the students could take the following two actions:
B. Add another battery - Increasing the voltage by adding another battery would increase the electrical current flowing through the wire, thereby strengthening the magnetic field produced by the electromagnet.
D. Increase the number of coils - Adding more coils of wire around the nail would also increase the strength of the magnetic field, allowing the electromagnet to lift more paper clips.
Thus, the correct choices are B and D.