6.EE.A.3 6th Grade Expressions & Equations

Distributive Property

Apply the properties of operations to generate equivalent expressions.

How to explain it

At this standard, students expand expressions by applying the distributive property.

The anchor students hold onto: Distribute the outside factor to EVERY term inside the parentheses — never skip a term.

The Solving One-Step Equations lesson connects directly — distribution simplifies expressions inside equations, preparing students for the inverse-operation solving strategy.

Worked examples

Example 1

Expand: 4(n + 3)

Step 1Outside factor: 4; terms inside: n and 3

Step 2Multiply: 4 × n = 4n

Step 34 × 3 = 12 → 4n + 12

Answer4n + 12

Example 2

Expand: 5(2n − 3)

Step 1Outside factor: 5; terms inside: 2n and −3

Step 2Multiply: 5 × 2n = 10n

Step 35 × (−3) = −15 → 10n − 15

Answer10n − 15

Common mistakes

What students write Student expands 4(n − 3) as 4n + 12 (loses the minus sign).

The fix The sign is part of the term: 4 × (−3) = −12. Correct result: 4n − 12.

Try this A student expands 4(n + 5) and writes 4n + 5. Identify the error and give the correct expanded form.

What students write Student only multiplies the first term: 3(n + 2) = 3n + 2.

The fix EVERY term inside gets multiplied: 3(n + 2) = 3n + 6. Never skip a term.

Try this A student expands 4(n − 3) and writes 4n + 12. Identify the sign error and give the correct expanded form.

Teacher tip

Head off the two predictable errors before they happen. First: The sign is part of the term: 4 × (−3) = −12. Correct result: 4n − 12. Second: EVERY term inside gets multiplied: 3(n + 2) = 3n + 6. Never skip a term.