I started looking at the National Semiconductor MM5799 again. That's the 4-bitter used in Mattel's Basketball, Hockey and Soccer games, as well as National's own Quiz Kid Racer and Quiz Kid Speller. It's part of the COPS I family; the 1977 databook on BitSavers has a lot of info, but leaves some questions unanswered. The COP4 series was released soon after and took over.
I started with Quiz Kid Racer since the source and object code are in patent US4051605. The die is bonded directly to the PCB, covered with a protective platic shield. I took pics of the ROM array and mapped the bits to the ROM dump in the patent; it matches exactly. Interestingly, the patent is specifically about competing with linked calculators, but mine doesn't have a connector to plug the cable into. The code allows solo play if a cable isn't inserted, so the same code works fine. Rik's site has a pic of a Ward's catalog page that mentions buying 2 to compete, and sending 2 proofs of purchase to National to get a free cable, and I saw a pic on ebay that looked like there was a bump on the right side. I guess they removed the functionality in later versions.
I first wrote a disassembler to match the assembler output in the patent, then started a simple emulator. QKR does a RAM test before flashing the symbols +, -, X and / as a menu. I guess they were worried that a RAM error could potentially teach children incorrect math. My emulator runs through the RAM test and flashes the symbols, waiting for a keypress, but I haven't implemented inputs yet. The MM5799 doesn't have enough output lines, so they used a shift register LED driver (DS8874) to multiplex the digits and strobe the keyboard lines.
I picked up a second unit that looks identical, but it flashes the symbols in a different order: X, /, +, -. I opened it up and it has a COP420 instead. The COP420 has plenty of I/O, so it doesn't need the LED driver. The bottom of the case has a spot for a piezo sounder, but none is installed.
There is a "space theme" version that lacks the Amateur, Pro and Complex buttons. I'm not sure if they removed that functionality, or if it's implemented differently.