Multiplication as scaling, for integers

This applet demonstrates how multiplication of whole numbers can be thought of as stretching, giving a link between the scaling and the repeated addition ideas of multiplication.

Change the scale factor (multiplier) by dragging the small blue point on the horizontal axis. Change the number being stretched (multiplicand) by dragging the top green dot. The product is the number of red dots.

The multiplier and multiplicand can both be negative. The colors change when this happens. Note that the English description of the multiplication doesn't make as much sense. It's hard to explain why negatives multiply the way they do using counting.

Susan Addington, Created with GeoGebra