Regrouping Factors to Find New Side Lengths
Regrouping Factors to Find New Side Lengths is a Grade 3 math skill from Eureka Math applying the Associative Property of Multiplication to area problems. When three or more numbers are multiplied, regrouping the factors (changing which two are multiplied first) does not change the product: (a × b) × c = a × (b × c). Third graders use this to find side lengths of rectangles by regrouping factors, recognizing that the same product can come from different dimension pairs. This builds flexible numerical thinking and connects multiplication properties to geometry.
Key Concepts
The associative property of multiplication states that when you multiply three or more numbers, the way you group the factors does not change the final product. $$(a \times b) \times c = a \times (b \times c)$$.
Common Questions
What is the Associative Property of Multiplication?
The Associative Property states that when multiplying three or more numbers, the grouping of the factors does not change the product: (a × b) × c = a × (b × c).
How does regrouping factors help find different rectangle dimensions?
If a rectangle's area is 24 square units and one side is 4, you can regroup to find the other side: 24 = 4 × 6, so the other side is 6. Different groupings give different valid rectangles with the same area.
How is the Associative Property different from the Commutative Property?
The Commutative Property changes the order of two factors (a × b = b × a). The Associative Property changes which factors are grouped together in a product of three or more numbers.
Why does regrouping factors not change the product?
Multiplication is associative—the final result depends only on which numbers are multiplied, not on the order operations are performed. All groupings give the same total.
In which textbook is Regrouping Factors to Find New Side Lengths taught?
This skill is taught in Eureka Math, Grade 3.