"Please Excuse My Dear Aunt Sally." Every middle schooler knows the mnemonic. Far fewer actually understand what it means — and even fewer apply it correctly when the problems get complex. Order of operations errors are among the most common mistakes in middle school math, and they cascade: a student who evaluates 3 + 4 × 2 as 14 instead of 11 will get every multi-step problem wrong, not because they can't do the arithmetic, but because they're doing it in the wrong order.
The concept itself is straightforward — parentheses first, then exponents, then multiplication/division (left to right), then addition/subtraction (left to right). But applying it consistently under the pressure of more complex expressions requires practice until it becomes automatic. Games provide that practice in a format that's more engaging than rows of expressions on a worksheet.
Common Order of Operations Mistakes
Understanding the typical errors helps you choose games that target the right skills.
Left-to-Right Instead of PEMDAS
The most basic error: students evaluate expressions from left to right without regard to operation priority. 3 + 4 × 2 becomes (3 + 4) × 2 = 14 instead of 3 + (4 × 2) = 11. This error comes from students treating math like reading — left to right, one step at a time.
Multiplication Before Division Always
PEMDAS makes students think multiplication always comes before division. It doesn't — they have equal priority and are evaluated left to right. 12 ÷ 3 × 2 should be (12 ÷ 3) × 2 = 8, not 12 ÷ (3 × 2) = 2. The same error happens with addition and subtraction.
Ignoring Nested Parentheses
When expressions have parentheses inside parentheses, students often work from left to right instead of inside out. 2 × (3 + (4 - 1)) should start with the innermost parentheses: 4 - 1 = 3, then 3 + 3 = 6, then 2 × 6 = 12.
Forgetting That Fraction Bars Are Grouping Symbols
The expression (6 + 2)/(4 - 2) means evaluate the top first, then the bottom, then divide. Many students don't recognize that the fraction bar functions like parentheses.
Best Games for Order of Operations Practice
1. Infinilearn
Best for: Practicing order of operations within broader middle school math · Price: Free · Grades: 6-8
Infinilearn includes order of operations problems as part of its adaptive problem bank. What makes it particularly effective for this topic is the interleaving: order of operations problems appear alongside other expression and equation problems, which forces students to recognize when PEMDAS applies (multi-operation expressions) and when it doesn't (single-operation problems). This contextual practice builds the automatic recognition that isolated PEMDAS drills don't.
The adaptive system identifies whether a student's errors come from order of operations specifically or from the underlying arithmetic. The parent dashboard shows performance on expressions and equations, helping you see whether PEMDAS is the sticking point.
Price: Free.
2. Target Number Games
Best for: Building operational fluency and PEMDAS intuition · Price: Free (deck of cards) · Players: 2+
Deal four cards face up. The target number is 24 (or any number you choose). Using all four numbers and any operations, try to make exactly the target. Parentheses are allowed and encouraged. This game naturally teaches order of operations because students must think about which operations to do first to reach the target.
"I have 3, 5, 7, and 2. Can I make 24? (7 - 5) × (3 + 2) × ... no. 3 × (7 + 2) - 5 = 22... close. (5 - 3) × (7 + 2) × ... wait, that's four operations." The mental process of trying different groupings IS order of operations practice.
3. PEMDAS Relay
Best for: Classroom or group practice · Time: 15-20 minutes · Materials: Whiteboards
Teams line up. Each team member evaluates one step of a multi-step expression. Player 1 evaluates the parentheses and passes the simplified expression to Player 2. Player 2 handles exponents. Player 3 handles multiplication/division. Player 4 handles addition/subtraction and writes the final answer. This forces students to think about which step comes when — the relay structure makes PEMDAS physical and sequential.
4. "Whose Expression Is It?" Challenge
Best for: Deep understanding of how parentheses change meaning · Time: 10-15 minutes · Materials: Whiteboard or paper
Write four numbers and four operations on the board. Students must place parentheses to create expressions that equal specific target values. For example, using 2 + 3 × 4 - 1: without parentheses it's 13. Can you place parentheses to make it 19? (2 + 3) × 4 - 1 = 19. Can you make it 10? 2 + 3 × (4 - 1) = 11... not quite. 2 + (3 × 4 - 1) = 13... same thing. This is tricky — and the challenge is what makes it engaging.
This activity builds deep understanding because students see firsthand how parentheses change the value of an expression. It's more powerful than evaluating pre-written expressions because students are constructing, not just following.
5. Khan Academy Order of Operations
Best for: Students who need instruction before practice · Price: Free · Grades: 5-7
Khan Academy's order of operations unit includes video instruction explaining why the order matters (not just what it is) and practice exercises with step-by-step hints. The mastery system ensures students demonstrate consistent accuracy before moving to harder expressions.
Strengths: Instruction + practice, mastery-based, free.
Limitation: Drill format, not gamified.
Teaching PEMDAS Better
The standard PEMDAS mnemonic actually causes some of the errors it's meant to prevent. Here's how to teach it more effectively.
Use GEMS Instead of PEMDAS
Some math educators prefer GEMS: Grouping symbols (parentheses, brackets, fraction bars), Exponents, Multiplication and Division (left to right), Subtraction and Addition (left to right). This avoids the "multiplication before division" misconception because M and D are combined into one step, as are S and A.
Emphasize "Left to Right" for Equal-Priority Operations
The biggest PEMDAS misconception is that multiplication always comes before division. Spend extra time on this: "When you see multiplication AND division in the same expression, go left to right. Same for addition and subtraction." Have students practice expressions specifically designed to test this: 12 ÷ 3 × 2, 10 - 4 + 3, 8 ÷ 2 × 4.
Show Why It Matters
Give students a real-world expression where order of operations changes the answer meaningfully. "You buy 3 shirts at $15 each and get a $10 coupon. Is your total 3 × 15 - 10 = $35 or 3 × (15 - 10) = $15?" The real-world context makes the stakes concrete.
Tips for Parents
- Check for the common errors first. Before assuming your child "doesn't understand PEMDAS," check whether they're making one of the specific errors listed above. Targeted correction is much faster than re-teaching the whole concept.
- Use the calculator as a teaching tool. Type an expression into a calculator and have your child predict the answer before pressing equals. If their prediction is wrong, the calculator shows the correct order of operations. This gives immediate feedback.
- Practice with games, not worksheets. Target 24 with a deck of cards provides more order of operations practice in 15 minutes than most worksheets, and your child will actually want to play it. Use Infinilearn for daily adaptive practice that includes PEMDAS problems alongside other topics.
The Bottom Line
Order of operations is a foundational skill that affects every multi-step math problem from 6th grade through calculus. The concept is simple but applying it consistently requires practice until it becomes automatic. Games like Target 24, PEMDAS relays, and parentheses challenges build this automaticity through engaging practice. Infinilearn's adaptive system ensures order of operations problems appear regularly mixed with other topics, building the contextual fluency that transfers to tests and real math. And teaching PEMDAS with the "left to right" emphasis prevents the most common misconceptions before they take root.