Rotating Arrays and the Commutative Property
Rotating Arrays and the Commutative Property is a Grade 3 math skill from Eureka Math (final instance) demonstrating a × b = b × a through array rotation. Physically rotating an array 90 degrees transforms it from a rows-by-columns orientation to columns-by-rows, preserving the total object count. A 7 × 3 array rotated becomes a 3 × 7 array—both contain 21 objects. This repeated demonstration across multiple lessons in Eureka Math Grade 3 solidifies the Commutative Property as a reliable, testable rule rather than a memorized statement.
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
What does rotating an array prove about multiplication?
Rotating an array preserves the total count while swapping the row and column factors. This proves that a × b = b × a—changing the order of factors does not change the product.
Rotate a 7 × 3 array. What multiplication equation describes the rotated array?
The rotated array has 3 rows and 7 columns: 3 × 7 = 21. Combined with the original 7 × 3 = 21, this confirms both equal 21.
How many multiplication facts does each array rotation cover?
Each array (and its rotation) covers two multiplication facts: a × b and b × a. Together, one array confirms both facts simultaneously.
Why is this concept taught multiple times in Grade 3?
Repeated exposure to the Commutative Property through arrays builds deep understanding. Each repetition reinforces that the property holds for all factor pairs, not just specific examples.
In which textbook is this version of Rotating Arrays and the Commutative Property taught?
This skill is taught in Eureka Math, Grade 3.