How to explain PEMDAS to a child (and why the letters can mislead)

By 15Q20M Editorial · Last updated October 4, 2026

Explain PEMDAS as an agreement: everyone works a math expression in the same order so it has only one answer. Then teach it as four levels, not six steps: parentheses, exponents, multiplication and division from left to right, then addition and subtraction from left to right. Start with a story where the order changes the total.

Why do we need PEMDAS at all?

Show your child 20 − 4 × 3 + 1 and ask for the answer. Working straight from left to right gives 16, then 48, then 49. Multiplying first gives 20 − 12 + 1 = 9. Two people with the same expression would get two different answers, so mathematicians agreed on one order. Under that agreement, the answer is 9.

This is Day 15, Question 7 of our Grade 5 workbook, and one of its wrong answer choices is 49, the left-to-right answer. A simple way to say it to a child: the order of operations works like a traffic rule. Drivers agree to stay on the same side of the road, and mathematicians agreed on one order, so everyone who follows it gets the same answer.

How do I explain PEMDAS step by step?

Start with parentheses, using a story. This one is adapted from Day 15, Question 8 of our Grade 5 workbook, which asks children to pick the matching expression: Each gift bag holds 4 red and 6 blue erasers. After filling 5 bags, the owner removes 10 erasers for a display. How many erasers are left in the bags? Read the left column out loud and let your child answer and write.

That last row is the point of the whole lesson. Parentheses are how the writer says "do this part first." The rest of PEMDAS is the order everyone uses when there are no parentheses to say otherwise.

Why is PEMDAS confusing?

The six letters look like six steps in a line, with M before D and A before S. The rule has four levels. Multiplication and division share a level, and so do addition and subtraction. For multiplication and division, work from left to right, and do the same for addition and subtraction.

Two examples show why the levels matter. In 12 − 4 + 3, going left to right gives 8 + 3 = 11. Adding first because A comes before S gives 12 − 7 = 5, which is wrong. In 24 ÷ 4 × 2, going left to right gives 6 × 2 = 12. Multiplying first because M comes before D gives 24 ÷ 8 = 3, which is also wrong.

If your child likes the mnemonic "Please Excuse My Dear Aunt Sally," keep it, and add that My and Dear hold hands, and so do Aunt and Sally. A useful clue: in the UK the same rule often goes by BODMAS or BIDMAS, which put D before M. Both orders of letters are right because division and multiplication tie.

Do schools still teach PEMDAS?

Yes, the order of operations is still in the standards. Common Core does not use the word PEMDAS, so the name and the way it is drawn can vary by curriculum and classroom. The rule builds over several grades: a 3rd grade footnote expects children to use the conventional order, 5th grade adds parentheses, brackets, and braces (and exponents for powers of 10), and 6th grade brings exponents into expressions and names the Order of Operations.

What PEMDAS mistakes do kids make?

Mistake 1: going straight from left to right. That is how 20 − 4 × 3 + 1 becomes 49 instead of 9 (Grade 5, Day 15, Question 7). The check: before calculating, have your child circle every × and ÷. Those get done before any + or − outside parentheses.

Mistake 2: doing the addition first because it looks like one step. Day 46, Question 5 of our Grade 6 workbook asks which operation comes first in 12 ÷ 3 + 6, and one wrong choice is 3 + 6. The check: ask which level the ÷ is on and which level the + is on. Division's level comes first (level 3, before addition on level 4), so 12 ÷ 3 = 4 comes first, then 4 + 6 = 10.

Mistake 3: treating an exponent as multiplication by 2. Day 46, Question 6 shows a student who says (9 − 5)² = 8. The parentheses were right, 9 − 5 = 4, but then the student did 4 × 2. The check: have your child say it out loud, "4 squared means 4 times 4," so the answer is 16.

Mistake 4: leaving out parentheses when turning words into math. Day 15, Question 13 says: Subtract 3 from 12, then multiply by 5. The right expression is (12 − 3) × 5 = 45. Written as 12 − 3 × 5, the multiplication would happen first. The check: read the expression back in words and see if it matches the sentence.

How can I help my child practice order of operations at home?

Do:

• Start with a two-step story where the order changes the total, like bags of erasers or boxes of cookies.
• Ask your child to circle × and ÷ before calculating anything.
• Compare pairs without calculating exactly. Day 15, Question 14 asks which is larger: (8 + 2) × 5 or 8 + 2 × 5. They come out to 50 and 18.
• Ask what name the class uses, such as PEMDAS or another memory aid, and use the same one.

Avoid:

• Teaching the six letters as six separate steps.
• Viral puzzles like 8 ÷ 2(2 + 2). Adults online disagree about them because of how they are written. If one comes home, rewrite it with extra parentheses so the grouping is clear.
• Taking over the pencil. Ask which level comes next and let your child do the step.

Short practice on several days, going over mistakes the same day, can help you see whether the trouble is the order itself or the arithmetic inside each step.

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