Hello.. I Try to porting CWM for Samsung Galaxy Tab3 8.0 
This CWM already tested on my tablet T311 everything is normal
I hope you Like 
And I do not know working or No For T310&T315 because i'm can not tested.. You Can Try For Tested and report back me..
"Sorry for my bad English"
(Special Thanks To emwno For Guide and Help Me)
Downloads
CWM Touch
Non-Touch
"For Back To Stock Recovery"
Flash This File Via CWM/TWRP: Stock Recovery
How to Use:
1. Download and Extrack To Your PC
2. Flash File "recovery.tar.md5" Via Odin
How To Root Via CWM
1. Download the zip and place it in the root of your externalsd.
2. Turn off your tablet
3. Go to CWM Recovery. by pressing Power+Vol UP
4. Select instal zip from sdcard > chose zip from sdcard
5. Select the root.zip file.
6. Reboot and done..
For Root Zip File Download Here : http://d-h.st/mVr
This CWM already tested on my tablet T311 everything is normal
And I do not know working or No For T310&T315 because i'm can not tested.. You Can Try For Tested and report back me..
"Sorry for my bad English"
(Special Thanks To emwno For Guide and Help Me)
Downloads
CWM Touch
Non-Touch
"For Back To Stock Recovery"
Flash This File Via CWM/TWRP: Stock Recovery
How to Use:
1. Download and Extrack To Your PC
2. Flash File "recovery.tar.md5" Via Odin
How To Root Via CWM
1. Download the zip and place it in the root of your externalsd.
2. Turn off your tablet
3. Go to CWM Recovery. by pressing Power+Vol UP
4. Select instal zip from sdcard > chose zip from sdcard
5. Select the root.zip file.
6. Reboot and done..
For Root Zip File Download Here : http://d-h.st/mVr
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