math class 678 4-in-1 skill sheets
6.EE.A.1 6th Grade Expressions & Equations

Order of Operations & Exponents

Write and evaluate numerical expressions involving whole-number exponents.

How to explain it

At this standard, students evaluate numerical expressions using the correct order of operations (PEMDAS).

The anchor students hold onto: Parentheses first, then Exponents, then Multiplication/Division (left to right), then Addition/Subtraction (left to right). Remember: PEMDAS. aⁿ means the BASE (a) is used as a factor n times. The EXPONENT counts the factors. NEVER multiply base × exponent.

Where this leads next: writing and evaluating expressions with variables (6.EE.A.2).

Worked examples

Example 1 Parentheses + Exponents
3 + 2² × (5 − 3)
Step 1P: (5 − 3) = 2 → 3 + 2² × 2
Step 2E: 2² = 4 → 3 + 4 × 2
Step 3M: 4 × 2 = 8 → 3 + 8
Step 4A: 3 + 8 = 11
Answer11
Example 2 Left-to-Right Rule
20 − 4 × 3 + 2
Step 1No parentheses or exponents.
Step 2M: 4 × 3 = 12 → 20 − 12 + 2
Step 3Left to right: 20 − 12 = 8 → 8 + 2
Step 4A: 8 + 2 = 10
Answer10
Example 3
4 × 4 × 4 = ?
Step 1Count how many times 4 appears: 3 times.
Step 2Write in exponential form: 4³
Step 34³
Answer4³

Common mistakes

What students write Adding or subtracting before multiplying or dividing when no parentheses are present.
The fix Apply ×/÷ left to right before +/− — multiply first, then add.
Try this A student evaluates 4² = 4 × 2 = 8. Identify the error and give the correct evaluation.
What students write Evaluating the exponent AFTER multiplying or using the base as a coefficient first.
The fix Exponents come before ×/÷ — resolve the power before multiplying.
Try this A student evaluates 2⁵ = 25 by writing the base and exponent digits side by side. Identify the error and give the correct evaluation.
What students write Student multiplies base × exponent: evaluates 4² as 4×2 = 8.
The fix The exponent counts repeated factors, not a multiplier. 4² = 4×4 = 16.
What students write Student assumes switching base and exponent never changes the value.
The fix 2³ = 8 but 3² = 9. Switching base and exponent usually changes the value.

Teacher tip

Head off the two predictable errors before they happen. First: Apply ×/÷ left to right before +/− — multiply first, then add. Second: Exponents come before ×/÷ — resolve the power before multiplying.