Try to lower the bitrate, as that's the number of bits per second and that's what determines your size.
If it's a screencast directly saved from QT try to check for these settings there, else you have to import the file in any video editing software like Sony Vegas and export with new settings.
You can also set a variable bitrate (VBR), then set a range with a min and max bitrate.
I think you have to play around with these settings, because the size doesn't sound right. Sometimes I watch 2-hours long movies, with high-quality video, and the file is not even 2 GB.
Also, consider there is no point in having a bitrate or a resolution higher than the source (or raw) bitrate and resolution. When you export or render you should use the same or a lower one, but never higher. Setting it higher would be a waste of space.
In addition to this, consider breaking down videos longer than 7 minutes long. The ideal is from 4 to 7 minutes. Too long and students get bored, too short and students get upset.