An array represents multiplication as a rectangular arrangement of equal-sized units: one factor names the number of rows and the other the number in each row, while the product is the total number of units. The learner connects arrays with repeated addition, equations, and area models, understands that rotating an array exchanges the factors without changing the product, and can partition larger whole-number arrays to show partial products; fractional, negative, and algebraic arrays are outside this scope.
An array is a rectangular arrangement of equal-sized objects. One factor tells the number of rows, and the other tells how many objects are in each row.
Suppose there are 4 rows with 6 dots in each row:
There are 4 equal groups of 6, so repeated addition gives
The multiplication equation is
The product, , is the total number of dots. The same array can also represent the area of a rectangle that is 4 units long and 6 units wide:
If the array is turned, it has 6 rows of 4:
The factors switch places, but the total stays the same. You can also split the 6 dots in each row into 4 and 2:
So an array shows the rows, the equal number in each row, and the total product.
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