Creating a Pool of Remote Dekstop Hosts To Appear As One to an End User

So basically I've been asked by my dad to help him figure out what his school can do with their new tablets. I know I can remote dekstop (RD) to the Windows PCs they have they but I was wondering if there was a way to pool all the RD hosts together so that when users attempt to RD to a host the load is distributed evenly? I just don't want them to be logging on and off RD hosts looking for one that has little users or so they all don't end up on the same host making it run really slow.
Any body have any solutions? Preferably without Windows Server but if necessary I could move a VM in.

Does the School have an RDS server or are you talking about using remote desktop to connect to individual PCs?

@JCat Yeah sadly they don't have a server so it's just windows 7 Pro PCs.

Do you have an equal amount of PCs and Tablets?

What you are trying to do is exactly what RDS servers were designed to do.

Did the school just get a bunch of tablets as a donation or did they purchase these?

I am assuming all of the PCs are running windows 7 or 8? If that is the case, no more than one user will be able to log in with remote desktop per PC any ways, so you don't have to worry about system resources. If you have the same number of tablets and the same number of PCs, why not set each individual tablet to connect to a specific PC. That way each PC would be paired with a tablet. I would just label these accordingly so you know "Tablet A" auto connects to "PC A".

If you have a DNS server, you could setup Round Robin DNS to do a sudo load balancing thing with the PCs. I have my doubts that this would work effectively, but that's about the closest you can get to what you are wanting to do without a RDS server. You could also do some research on You may be able to take one of the PCs and max out the RAM and use it for a Terminal Server.

My other question would be, why would you want to access a keyboard and mouse style desktop environment from a touch screen interface? I think you will end up with a lot of frustrated kids. Why not use the tablets for what they were designed for and find some educational apps or something? I don't mean to sound rude about this and I apologize if it comes off that way, but your school would probably be better served not using tables for RDS clients.

Then again, I have little information to go on so I could be completely wrong. Keep us posted and hopefully someone can come up with an innovative solution for the hardware you have to work with.

Wow! Really helpful! I didn't know you could only have one user per PC. All the Machines will be updated to Windows 10 so it will be more touch friendly. I was thinking of upgrading the RAM and CPU of one machine and have that as a RDS for all users but it looks like I'd need server 2012 R2 or server 2015 when it is out. The bought a load of refurbished Samsung tablets which aren't up-datable to a more recent version of android so I can't get Microsoft Office Apps on them. I was looking into the terminal server which is the same as a RDS Broker which I don't think will work because I need to install roles on the hosts but Windows 8.1 doesn't have it. If Windows 10 dosen't have it like I'm expecting, that would mean I'd have to put a server OS on loads of machines. I'll be going in to check out what they have this week.