Relate Array Rotation to the Commutative Property
Relate Array Rotation to the Commutative Property is a Grade 3 math skill from Eureka Math using the physical rotation of arrays to demonstrate a × b = b × a. Turning an array 90 degrees converts a rows-by-columns arrangement into a columns-by-rows arrangement, showing identical totals with swapped factors. For example, rotating a 5 × 4 array gives a 4 × 5 array—both contain 20 objects. This visual-physical demonstration makes the Commutative Property tangible and justifies why switching factor order never changes the product.
Key Concepts
The commutative property of multiplication states that changing the order of the factors does not change the product. $$a \times b = b \times a$$.
Common Questions
How does rotating an array demonstrate the Commutative Property?
Rotating an array 90 degrees swaps rows and columns. A 5 × 4 array becomes 4 × 5. Both have 20 objects. This proves 5 × 4 = 4 × 5 visually.
What changes and what stays the same when an array is rotated?
The orientation changes (rows become columns). The total count stays the same. This is the definition of the Commutative Property.
Write two multiplication equations for an array with 6 rows and 9 columns.
6 × 9 = 54 and 9 × 6 = 54. Both equations come from the same array (or its rotation).
Why does array rotation provide convincing proof of the Commutative Property?
The physical act of rotating preserves every single object in the array. Since no objects appear or disappear, the total must remain the same regardless of which dimension is called rows or columns.
In which textbook is Relate Array Rotation to the Commutative Property taught?
This skill is taught in Eureka Math, Grade 3.