What is PEMDAS and when do fifth graders learn it?

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction, and describes the conventional order for evaluating mathematical expressions. Fifth graders formalize this system as they write and interpret numerical expressions involving multiple operations (CCSS 5.OA.A.1-2). Students learn that multiplication and division are performed left to right (not multiplication before division), and the same applies to addition and subtraction. This distinction prevents the common mistake of always doing multiplication before division. Worksheets that present multi-step expressions requiring all PEMDAS rules, with space for showing each step, build procedural accuracy. Practice with expressions that produce different answers depending on the order of evaluation helps students understand why these conventions exist.

How do you teach PEMDAS to fifth graders?

Begin by reviewing fourth-grade parentheses work, then introduce the complete hierarchy. Use the mnemonic PEMDAS but immediately clarify that M and D are equal (left to right) and A and S are equal (left to right). Practice with expressions that test each level of the hierarchy separately before combining them. Show common errors: in 8 minus 3 plus 2, the answer is 7 (left to right), not 3 (subtracting the sum). Use real-world contexts to explain why certain operations come first. Worksheets that ask students to evaluate the same expression using different orders and compare results demonstrate why a universal convention is necessary. Include problems where students insert parentheses to change the value of an expression to build deeper understanding.

What common PEMDAS mistakes do fifth graders make?

The most frequent error is treating PEMDAS as a strict left-to-right sequence: doing all multiplication before any division, or all addition before any subtraction. In reality, multiplication and division share the same level and are resolved left to right, as do addition and subtraction. Another common mistake is forgetting to evaluate expressions inside nested parentheses from the inside out. Some students also ignore exponents or misapply them (treating 2 to the third power as 2 times 3 instead of 2 times 2 times 2). Worksheets that present intentionally tricky expressions testing each of these misconceptions, paired with step-by-step solution guides, help students self-correct. Error analysis exercises where students find mistakes in worked examples are especially effective for building PEMDAS accuracy.

5th Grade · Math · 5.OA.A.1

Order of Operations (PEMDAS) Lesson Plan for 5th Grade

A ready-to-teach order of operations (pemdas) lesson for 5th Grade, built around pemdas order of operations, parentheses, exponents in expressions, evaluating multi-step expressions. Print the plan, print the practice pages, and you are set.

Approximately 45 minutes

Learning objective

Evaluate expressions with parentheses before other operations
Apply order of operations to expressions using all four operations
Solve multi-step expressions by following parenthesis rules first

Materials

4 operations & parenthesis
PEMDAS including exponents
PEMDAS with nested parenthesis
Pencils, and whiteboard space for the modeled examples

Lesson steps

1. Warm up together (5 min)
Open with a quick count-around or number talk that touches order of operations (pemdas). Ask students where they have seen order of operations (pemdas) outside of math class. You are listening for who already has the vocabulary and who does not, so keep it light and let several students answer.
2. Model it (I do) (10 min)
Work two examples of order of operations (pemdas) on the board, thinking out loud the whole way. Say the quiet parts: what you notice first, which step you do next, and why. Deliberately make one small error on the second example and let the class catch it.
3. Practice together (we do) (10 min)
Work three more problems as a class. Ask a different student to supply each step rather than the whole answer. If a step stalls, drop back to concrete objects or a drawing before moving on.
4. Independent practice (you do) (15 min)
Hand out "4 operations & parenthesis". Students work independently while you circulate. Note who is fluent, who is counting on fingers, and who has not started, because that grouping drives tomorrow's small group.
5. Close the loop (5 min)
Pull the class back. Ask one student to explain a problem they got right and one to name something that is still confusing. End on the confusion, not the success, so students learn that naming a gap is normal.

Check for understanding

Collect the practice pages and sort them into three piles: fluent, developing, and not yet. Any student in the third pile needs order of operations (pemdas) retaught in a small group before the class moves on.

Differentiation

Extra support. Students who stall: pull them into a small group and rebuild order of operations (pemdas) with concrete materials or a simpler text before asking for the written work again. Do not send the page home as homework, it will just rehearse the misunderstanding.

Extension. Students who finish early: ask them to write their own order of operations (pemdas) problem for a partner to solve, then check the partner's work. Creating a problem is harder than solving one and it surfaces whether they really understand order of operations (pemdas).

Skills covered in this lesson

4 Operations & parenthesis · PEMDAS including exponents · PEMDAS with nested parenthesis

Practice pages for this lesson

3 items, 3 printable pages that match the independent-practice step.

Questions teachers ask about teaching order of operations (pemdas)

What is PEMDAS and when do fifth graders learn it?: PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction, and describes the conventional order for evaluating mathematical expressions. Fifth graders formalize this system as they write and interpret numerical expressions involving multiple operations (CCSS 5.OA.A.1-2). Students learn that multiplication and division are performed left to right (not multiplication before division), and the same applies to addition and subtraction. This distinction prevents the common mistake of always doing multiplication before division. Worksheets that present multi-step expressions requiring all PEMDAS rules, with space for showing each step, build procedural accuracy. Practice with expressions that produce different answers depending on the order of evaluation helps students understand why these conventions exist.
How do you teach PEMDAS to fifth graders?: Begin by reviewing fourth-grade parentheses work, then introduce the complete hierarchy. Use the mnemonic PEMDAS but immediately clarify that M and D are equal (left to right) and A and S are equal (left to right). Practice with expressions that test each level of the hierarchy separately before combining them. Show common errors: in 8 minus 3 plus 2, the answer is 7 (left to right), not 3 (subtracting the sum). Use real-world contexts to explain why certain operations come first. Worksheets that ask students to evaluate the same expression using different orders and compare results demonstrate why a universal convention is necessary. Include problems where students insert parentheses to change the value of an expression to build deeper understanding.
What common PEMDAS mistakes do fifth graders make?: The most frequent error is treating PEMDAS as a strict left-to-right sequence: doing all multiplication before any division, or all addition before any subtraction. In reality, multiplication and division share the same level and are resolved left to right, as do addition and subtraction. Another common mistake is forgetting to evaluate expressions inside nested parentheses from the inside out. Some students also ignore exponents or misapply them (treating 2 to the third power as 2 times 3 instead of 2 times 2 times 2). Worksheets that present intentionally tricky expressions testing each of these misconceptions, paired with step-by-step solution guides, help students self-correct. Error analysis exercises where students find mistakes in worked examples are especially effective for building PEMDAS accuracy.

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