Decomposing Factors with the Distributive Property
Decomposing Factors with the Distributive Property teaches Grade 3 students to break a difficult multiplication fact into two easier ones. From Eureka Math Grade 3: to multiply 7 × 8, decompose 8 as 5 + 3, then distribute: 7 × 5 + 7 × 3 = 35 + 21 = 56. This strategy lets students leverage known facts (×5, ×2, ×10) to derive unknown ones. The Distributive Property states a × (b + c) = a×b + a×c, and this Grade 3 application builds the conceptual foundation for expanding expressions in later algebra.
Key Concepts
The distributive property states that you can multiply a number by a sum by multiplying the number by each addend separately and then adding the products. $$a \times (b + c) = (a \times b) + (a \times c)$$.
Common Questions
What is the Distributive Property in Grade 3?
A multiplication fact can be split into two smaller facts: a × (b + c) = a×b + a×c. This turns one hard multiplication into two easier ones.
How does the Distributive Property help compute 7 × 8?
Decompose 8 as 5 + 3: 7×8 = 7×5 + 7×3 = 35 + 21 = 56.
How would you use the Distributive Property to find 6 × 9?
Decompose 9 as 5 + 4: 6×9 = 6×5 + 6×4 = 30 + 24 = 54.
Why decompose the second factor instead of the first?
Either factor can be decomposed. Students typically decompose the factor they find harder to multiply.
What facts are easiest to use as decomposition targets?
Facts involving 5, 10, and 2 are easiest. Decomposing into those addends lets you use anchor facts.
What Eureka Math grade introduces this strategy?
Grade 3, as part of operations and algebraic thinking for multiplication.