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The Associative Property

What is the Associative Property?

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The addition or multiplication of a set of numbers is the same regardless of how the numbers are grouped. The associative property will involve 3 or more numbers. The parenthesis indicates the terms that are considered one unit. The groupings (Associative Property) are within the parenthesis. Hence, the numbers are 'associated' together. In multiplication, the product is always the same regardless of their grouping. The Associative Property is pretty basic to computational strategies. Remember, the groupings in the brackets are always done first, this is part of the order of operations.

Addition Example:

When we change the groupings of addends, the sum does not change:
(2 + 5) + 4 = 11 or 2 + (5 + 4) = 11
(9 + 3) + 4 = 16 or 9 + (3 + 4) = 16
Just remember that when the grouping of addends changes, the sum remains the same.

Multiplication Example

When we change the groupings of factors, the product does not change:
(3 x 2) x 4 = 24 or 3 x (2 x 4) = 24.
Just remember that when the grouping of factors changes, the product remains the same.

Think Grouping! Changing the grouping of addends does not change the sum, changing the groupings of factors, does not change the product.

Simply put, regardless of whether you show 3 x 4 or 4 x 3, the final result is the same. In addition, 4 + 3 or 3 + 4, you know that the outcome is the same, the answer remains the same. However, this is NOT the case in subtraction or division so when you think of the associative property, remember that the final result or answer remains the same or it's not the associative property.

The understanding of the concept of associative property is much more important that the actual term associative property. Titles often confuse students and you'll discover that you'll ask what the associative property is, only to be returned with a blank look. However, if you say to a child something like "If I change the numbers in my addition sentence, does it matter? In other words, can I say 5 + 3 and 3 + 5, the child that understands will say yes because it's the same. When you ask if you can do this with subtraction, they'll laugh or tell you that you can't do that. So in essence, a child knows about the associative property which is really all that matters even though you may stump them when you ask for a definition of the associative property. Do I care that the definition escapes them? Not at all, if they indeed know the concept. Let's not trip our students up with labels and definitions when concept understanding is the key ingredient in math.

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