File this under “you probably knew this, Paul didn’t” – When last I checked (which may have been eons ago,) Google Messages worked on your phone, and it would also work from messages.google.com, but I don’t recall being able to connect a different device to the Messages app and have it work.
Install Google’s Messages on your tablet or other Android device, run it, going to the web address messaged.google.com should display a QR code that will allow you to pair with the app, open Messages on your carrier-connected phone and pair it per instructions. Bam, texting on your tablet.
*note* – I wrote the wrong instructions above, they were there for 8 months before it was pointed out to me. THis has been edited to have the correct ones. Sorry about that.
Your phone has to be on and working, have a data connection somehow to the network where the SMS/MMS fairies live, tablet has to be connected to the internet somehow, but it’s really useful for when you’re charging your phone or just too lazy to get to it and have the tablet in reach.
Now you can tablet and tub without needing a phone around as well.