This cross-product multiplication is also known as Cartesian Product. This is the least known and naturally, least used approach. But I have found it very useful to develop understanding many aspects of multiplication.
There are several ways that might be used in introducing the cross-product definition. One of these is to describe a natural pairing situation. For example, if a girl had 3 tops and 2 skirts, how many different ways could she dress? See the figure to your left-hand side. You can see that the girl can dress in 6 different ways, which is the product of 3 and 2. See how this definition is different from that using set and array!
We can also think about 2 roads running horizontally and 3 running vertically, to solve 2 multiplied by 3. The points of intersection of these roads (where signal posts are required) represent the product! Take a look at the figure to your right-hand side.
The same experience can be given to the children easily by using 3 sticks of one color and 2 sticks of some different color. Children could be asked to lay 3 sticks horizontally and then can place two vertically on those laid earlier. Then, they could be asked to count the number of points where the differently colored sticks touch each other. As shown in the left-hand figure, children again discover that 3 x 2 is equal to 6.
The activity discussed above could be made more interesting by preparing tray of colored card paper. The four edges could be cut out to lay colored sticks made of colored pages of old magazines. The children would lay sticks of one color horizontally and the other color vertically on the edges of the tray, as shown in the figure here. They would then be asked to determine the number of cross-points. Because there are 6 cross-points, we say the product of 3 and 2 is 6.
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