When you partition a drive, you can make one partition or more. Depending on which FAT system you choose and what your drive size is, you MAY be able to make the one parition occupy all the space. For example, in a FAT32 system you can make one partition up to 32 GB. By the way, you choose the FAT system when running FDISK when it asks you whether you want to use "large dirves" or something like that.
If you choose to make a partition less than the whole drive size, then you can create a second (or more) partition(s) in the spare space. But ALWAYS one partition must the the Primary Partition (usually the first created). Then the others are Extended Partitions.
All partitions created show up in DOS as drives with letter names (C;, D:, etc). But at first each contains absolutely nothing and cannot be used or read. For each you must FORMAT the drive. This creates the root directory and the FAT table for that drive. Only then can you use it. Now, when you format a drive, one option in the command line is to add the switch "/s", as in:"format c: /s". When that is used, after the drive format is complete, DOS will copy onto the new drive two key files, IO.SYS and MSDOS.SYS. These are hidden Read-Only files containing the basic I/O drivers and DOS. The IO.SYS MUST be the very first file in the root directory. DOS will make those arrangements if you use the "format c: /s" command.
Unless you do this format WITH the /s switch, your partitioned drive will not have those files. In fact, without any format command, you won't even be able to read or write to the partition - DOS will simply tell you the drives are not accessible, and may ask whether you want to format them now.
Either you are not formatting the drive following the steps correctly, you have a bad drive, or your school has a poorly written lab. It would help if you mentioned how the lab specified what command to use to format the drive.
Having been a computer instructor before, you are probably not following the lab procedures correctly. Read it and type in exactly what they say to type. Asking the question here may get you the correct answer, but you probably won't learn anything from it.