The CARDboard Illustrative Aid to Computation was a cardboard computer created by Bell Labs to teach students the basics of computers. More information is on Wikipedia.
I made my own version of it from the few pictures I could find on the internet on the computer. It is very easy to build and really only requires scissors and tape to assemble. Make sure to see how one actually works online for guidance on how this one should be assembed and operated.
Here are PDF files to print and assemble:
Here are the original assembly instructions, original scans of the device, and guidebook that I have come across recently. The guidebook is still very informative 30 years later for how a CPU generally works since computer architecture has yet to fundamentally change.
The computer doesn't actually do arithmetic for you but instead keeps track of the current state of the computer and leads you around a handy dandy flowchart. I've been thinking of how to automate the computer in paper. It would be really cool to have a compressed air or crank powered paper computer.