Students in qualities 3+ can more readily construct an knowledge of multiplication as soon as they see it visually. Because that example, lock can picture a marching band arranged in same rows or chairs set up evenly in an auditorium. In both cases, they space visualizing rows and also columns. An setup of objects, pictures, or number in rows and also columns is called an array. Arrays are useful representations of multiplication concepts (among other principles in mathematics).

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This selection has 4 rows and also 3 columns. It can also be described as a 4 through 3 array. Words "by" is regularly represented v a multiplication cross: 4 × 3.


Arrays1

Arrays2
Notice that the rows in each array are equal in length. Think the the rows together equal groups. Your students should have already used equal groups to main point (2.OA.C.4).


Multiply Two teams Of Six

Multiply 2 Rows 5 Columns
When you present students the connection in between equal groups and arrays, students can visualize how to use arrays come multiply. Lock will use arrays again later on to divide.

Look in ~ the multiplication sentence that explains the range below. The numbers in multiplication sentences have special names.


Multipliaction v Arrays Rows Columns Update
The number that space multiplied are dubbed factors. The result of multiplying the components is referred to as the product.

Now look at what wake up to the factors and also product in the multiplication sentence once the variety is rotate on that side.


The bespeak of the factors changed, but the product stayed the same. This is in fact constantly the case and a attribute that has actually piqued the attention of mathematicians for centuries. You can change the stimulate of factors, yet the product continues to be the same, a mathematical property recognized as the Commutative building of Multiplication. Students need to be acquainted with the commutative property because they have already seen it used to enhancement (1.OA.B.3).

Help student realize the by applying the commutative property, they understand twice as numerous multiplication facts. Because that example, if they recognize 8 × 5 = 40, then they likewise know 5 × 8 = 40.

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