Representing Decomposition with Number Bonds and Arrays
Representing Decomposition with Number Bonds and Arrays is a Grade 3 math skill from Eureka Math showing how breaking a factor into two addends can simplify multiplication. If c = a + b, then a larger array representing the multiplication can be split into two smaller arrays for a and b separately. This visual decomposition, shown through number bonds, connects the Distributive Property to array models. For example, 7 × 6 can be broken into (5 × 6) + (2 × 6) = 30 + 12 = 42. Third graders use this to multiply with facts they already know.
Key Concepts
A factor can be decomposed (broken apart) into two addends, represented by the equation $c = a + b$. This decomposition can be visually modeled by breaking a larger array, which represents the original multiplication, into two smaller arrays that represent the addends.
Common Questions
How does decomposing a factor help with multiplication?
Breaking a factor into two smaller addends splits the multiplication into two easier problems. You solve each part separately and add the products.
What is a number bond in the context of multiplication decomposition?
A number bond shows how a number (factor) is broken into two parts. In multiplication, it represents decomposing one factor into addends so the problem can be split into smaller arrays.
How does array decomposition demonstrate the Distributive Property?
A large array is split into two smaller arrays representing the addends. The total product equals the sum of the two smaller products, visually proving (a + b) × c = (a × c) + (b × c).
How would you use decomposition to find 8 × 7?
Break 8 into 5 + 3. Then: (5 × 7) + (3 × 7) = 35 + 21 = 56. The decomposed facts are easier to recall than 8 × 7 directly.
In which textbook is Representing Decomposition with Number Bonds and Arrays taught?
This skill is taught in Eureka Math, Grade 3.