Rectangle Multiplication of Integers

This virtual manipulative allows the user to visualize the product of two integers.

The array shows the product of two integers, with height equal to one factor and the width equal to the other factor. The colored array may be considered as groups in two ways (horizontal or vertical), as displayed in the text at the right, and the result of the multiplication is also shown. To change either of the factors, use the vertical and horizontal sliders, located inside the array.

Since this manipulative allows either (or both) of the factors to be negative, the color of the product shows whether the product is positive or negative. If both factors are positive, then of course the product is positive (blue). If the factors have opposite signs (one positive and one negative), then the product appears as negative (red) in either the second or fourth quadrant, but if both factors are negative, then the product, in the third quadrant, is positive.