I use the Addition and Subtraction slide rule to give students an experiential manipulative that represents what happens when we add and subtract integers.

I was trying to come up with something similar for multiplication and division. I had a conversation with my math field instructor, Rachel Snyder, and she suggested the idea of using number lines to count off multiples. I played around with the idea, and the result was this.

The bubble calculator reinforces the notion of multiplication as repeated addition, and makes factoring more obvious, while connecting it to division. I asked the students what it meant if a number (e.g. 37) doesn't appear in the calculator, and they were very quick to grasp that this meant the number was prime.

You can download the wall poster version, which can be printed on 11 sheets of 8.5 by 11, and is approximately 8.5 inches by 9 feet assembled.