Both Mac and Dell laptops have a great feature called Video Mirroring that lets the laptop use an attached projector as a second display. Effectively, you have two working surfaces for the one laptop.
To make this easier for the future, set up your display preferences by going to Apple menu/System Preferences/Displays . When you have a projector plugged in, you will see two windows open, one for the laptop and one for the projector. Click the box 'Show displays in menu bar.
Next look for the small monitor icon in your menu bar at the top. Select it and you can change the resolution for both the laptop and the projector. Near the top, you can 'Turn off mirroring' which will make the projector a second and independent display.
The Dell laptop also has video mirroring, but they call it 'Extended Desktop'. You can pull up these options by right-clicking on the desktop and selecting Graphic Properties. Select Extended Desktop. Make the Notebook Primary and Monitor (your projector) as secondary. Select the side menu, Display Settings. Select the tab for the Notebook and adjust resolution as needed. Do the same for the Monitor. (Some teachers find success with 1280x720.) (For more on the E6400, see these directions.)