ChromeOS has quite a different partitioning scheme than other OS'es. It uses 2 ROOT & KERNEL partitions (2,3,4,& 5), one pair active, one pair inactive. When a ChromeOS update comes along, it's loaded on the inactive KERN/ROOT partitions and, after a reboot, it switches to the alternate pair. This way, the system can automagically switch back to the inactive pair if something goes awry.
The user's space is obtained from the STATE partition and is for all users files, settings, etc. which includes the Downloads folder for each user where everything is stored. This is what you're referring to as your / directory.
When ChrUbuntu was installed on your system (it uses partitions 6 & 7 for the KERN & ROOT partitions) and takes the needed/specified space from partition 1 / STATE. On your system, only 4GB of space was left in the STATE partition for all users, which in my opinion isn't enough - especially when you have 320GB to work with.
I wouldn't attempt to merge partitions 1, 6 & 7 or even partitons 1 & 7 - which would wipe out both ChrUbuntu & ALL of your ChromeOS users. I have tried merging/resizing these before and failed. ChromeOS is pretty picky about it's structure - you can try if you want but please backup up what you can first and have a usb restore stick handy.
I believe your best bet is to back up everything you can to an external usb stick or sd card and/or Google Drive and then do a full usb restore, a powerwash won't get it since it doesn't repartition anything. Then you can start over and install ChrUbuntu if you like but specify a (much) smaller partition size, you could even safely say 160GB or so and that would be plenty of space for both ChrUbuntu and ChromeOS users.
I have an Acer C710 also but I replaced the 320GB hard drive with a 128GB SSD and it's a very nice system. I use 'ChrUbuntu' on my system as well as 'crouton' in a special 'separate partiton' branch. This arrangement uses both partitons 7 & 13 so it's pretty unique. Below is my partition layout:
sudo parted -l /dev/sda
Model: ATA SanDisk SDSSDHP1 (scsi)
Disk /dev/sda: 128GB
Sector size (logical/physical): 512B/512B
Partition Table: gpt
| Number | Start | End | Size | File system | Name | Flags |
| 1 | 4440MB | 32.9GB | 28.4GB | ext4 | STATE | |
| 2 | 10.5MB | 27.3MB | 16.8MB | | KERN-A | |
| 3 | 2292MB | 4440MB | 2147MB | ext2 | ROOT-A | |
| 4 | 27.3MB | 44.0MB | 16.8MB | | KERN-B | |
| 5 | 145MB | 2292MB | 2147MB | ext2 | ROOT-B | |
| 6 | 95.8GB | 95.8GB | 16.8MB | | KERN-C | |
| 7 | 95.8GB | 128GB | 32.2GB | ext4 | ROOT-C | |
| 8 | 44.0MB | 60.8MB | 16.8MB | ext4 | OEM | |
| 9 | 8422kB | 8423kB | 512B | | reserved | |
| 10 | 8423kB | 8423kB | 512B | | reserved | |
| 11 | 32.8kB | 8421kB | 8389kB | | RWFW | |
| 12 | 128MB | 145MB | 16.8MB | fat16 | EFI-SYSTEM | boot |
| 13 | 32.9GB | 95.8GB | 62.9GB | ext4 | CROUTON | |
P.S. Sorry, I couldn't get the table thingy working right so the above is a little hard to read - my 'markdown' skills aren't polished as yet...
Hope this helps,