This video may be useful for teaching kids arithmetic intuition from non-traditional angles, including for negative numbers. E.g. the double-rack-pinion adder and especially the X-Y rack multiplier.<p>Multiplication is typically modeled using repeated addition, or surface areas. But when negative numbers are involved, it may be unclear. You can stick to areas if you have a Cartesian plane where the upper left and lower right quadrants are understood to contain negative area. But that may seem arbitrary, requiring explanations that seem like hand waving if you don't already have an intuition for it. The mechanical multiplier replaces hand-waving explanations of sign with a waving arm that clearly reverses slope under the right geometric conditions, to produce a positive or negative number.