Decompose Multiplication Using an Array
Decompose Multiplication Using an Array is a Grade 3 math skill from Eureka Math applying the Distributive Property visually. A large array can be split into two smaller arrays, and the total product equals the sum of the two smaller products: (a + b) × c = (a × c) + (b × c). For example, 7 × 6 can be split into (5 × 6) + (2 × 6) = 30 + 12 = 42. This strategy lets students use known facts to derive unknown facts, providing a flexible tool for multiplication beyond immediate recall.
Key Concepts
You can break apart a multiplication problem into two smaller problems and add the products. This is shown by the distributive property: $$ (a + b) \times c = (a \times c) + (b \times c) $$.
Common Questions
How do you decompose multiplication using an array?
Split the large array into two smaller arrays by breaking one factor into two addends. Multiply each part, then add the products: (a + b) × c = (a × c) + (b × c).
Show how to decompose 8 × 7 using an array.
Break 8 into 5 + 3. Draw a 5 × 7 array and a 3 × 7 array. Products: 35 + 21 = 56. So 8 × 7 = 56.
Why is decomposing arrays useful for harder multiplication facts?
It reduces an unfamiliar fact to two familiar ones. If you know 5s and single-digit facts, you can decompose any larger factor and use those known facts.
What mathematical property does array decomposition illustrate?
The Distributive Property: (a + b) × c = (a × c) + (b × c). Breaking a factor into parts and multiplying each demonstrates this property visually.
In which textbook is Decompose Multiplication Using an Array taught?
This skill is taught in Eureka Math, Grade 3.