Understanding The Distributive Property In Mathematics
How The Distributive Property Works and Why It Matters
The distributive property says that when you multiply a number by a sum, you can multiply each part of the sum first, and then add without changing the final answer. For example 9 x 12 can also be written as (9 x 2) + (9 x 10). This example highlights how the distributive property reinforces foundational skills like decomposing numbers and understanding place value.
Why Is The Distributive Property Important?
The Distributive Property Supports Mathematical Thinking
Understanding the distributive property gives students flexibility in their computations, and strengthens mental math skills. Breaking numbers apart into smaller, more manageable parts, helps students simplify complex calculations and approach problems with greater flexibility.
The distributive property also deepens students’ understanding of how operations like addition and multiplication, along with mathematical concepts like place value, and decomposing numbers, can work together. Recognizing patterns and relationships across these ideas, allows students to move beyond viewing them in isolation. Instead, they begin to see how these concepts connect and apply in meaningful ways across different contexts, reinforcing their ability to approach problems flexibly and strategically.
Strategies For Teaching The Distributive Property
Using Visual Representations
Area models provide a concrete, spatial representation of the distributive property. This helps support students in bridging conceptual and procedural understanding. For example:
- Draw a large rectangle to represent a multiplication problem like 4 x 8.
- Then break it into smaller rectangles to match the sum being used to represent one of the factors (in this case, 3 + 5 = 8).
- Divide the rectangle into two parts: 4×3 and 4×5.
- Label each part with its value and add the parts together to find the total area.
Arrays foster understanding of the distributive property by emphasizing its connection to grouping, an important concept in multiplication. Arrays help students visualize how numbers are grouped and how those groups can be split and recombined. For example:
Use objects like counters or tiles arranged in rows and columns. 4×8 can be represented with one array showing 4×3 and another array showing 4×5. Combine the two arrays to illustrate the total product.
Linking the Distributive Property to Place Value
The distributive property helps students break down numbers into their place value components, making complex calculations simpler and more intuitive. Using place value in this way reinforces students’ understanding of how numbers are composed and how they can be decomposed into smaller parts. For example:
Multiply 23 × 7 using the distributive property and place value.
- Break down 23 using place value: 23 = 20 + 3
- Apply the distributive property: 23 × 7 = (20 × 7) + (3 × 7)
- Simplify each part: 20 × 7 = 140 and 3 × 7 = 21
- Combine the results: 140 + 21 = 161
- Answer: 23 × 7 = 161
