I had such a thing in Greece when I was a kid. By pulling the i-th and j-th band on a plastic board their product was being revealed. That's how I had learned the multiplication table very quickly.
I wanted to buy something like this for my little one, but I couldn't find anything similar. All math tables work now with buttons. So I decided to construct one by myself.
- bottom carton
- temlate carton, where I wrote the numbers but after putting it inside
- horizontal bands
- vertical bands
- cover carton with 100 quadratic holes
- stickers (s. below)
I fixed the band sliding by attaching small white stickers on the boundary between the bands (width = 1.4mm). On the right hand side, I fixed paper pieces with paper glue on the front side and post-it glue on the back side, so that I can pull them off and change the number board inside the construction (e.g. this one is for addition, I can change the template inside for sutraction or multiplication). Here the board with all squares closed:
And here some operations: