Parent guide · 6 min read
Order of operations: why PEMDAS trips kids up, and how to fix it
Most children can recite PEMDAS — parentheses, exponents, multiplication and division, addition and subtraction — within a week of meeting it. Getting the right answer from it consistently takes a lot longer, and the gap between the two surprises a lot of parents. This guide is about that gap: why a child who knows the rule by heart still gets problems wrong, and what actually closes it.
Try this tonight
4 things you can do at home
Watch one problem worked out loud
Ask your child to solve a mixed problem like 20 − 4 × 3 + 2 while saying each step. Listen for whether they multiply before subtracting, or just work left to right regardless of the symbols in between.
Test the "same rank" rule specifically
Give a problem with only multiplication and division, like 12 ÷ 3 × 2, and ask which they do first. Many children guess multiplication always wins; the real rule is left to right when the operations are the same rank.
Circle the operations before solving anything
Before your child calculates, have them circle every operation symbol in the problem and label each with its rank (parentheses, exponents, multiply/divide, add/subtract). This turns an invisible mental rule into something they can see and check.
Check the answer a second way
For a problem with parentheses, have your child solve it once with the parentheses and once pretending they are not there, and compare the two answers. Seeing how much the answer changes makes the rule concrete instead of abstract.
Why knowing PEMDAS is not the same as using it
PEMDAS is easy to memorise because it is just a list of letters. Applying it under pressure, in the middle of a longer problem, is a different skill: it means constantly checking "what operation is this, and what rank is it" before doing any arithmetic, rather than just working through the problem left to right the way earlier maths mostly allowed.
That is exactly why the mistakes often show up in children who are otherwise doing fine in maths. Nothing about order of operations is conceptually hard — the trouble is a new habit (check rank before you calculate) replacing an old one (just go left to right) that worked perfectly well until now.
The two mistakes that cause almost all the trouble
The first is ignoring rank altogether and working strictly left to right, so 20 − 4 × 3 becomes "20 minus 4, then times 3" instead of "4 times 3, then subtract from 20". The second, more subtle mistake is assuming multiplication always beats division, or addition always beats subtraction, when really same-rank operations are done left to right: in 12 ÷ 3 × 2, division comes first only because it is written first, not because division always outranks multiplication.
Both mistakes are really the same underlying gap: a rule that says "check rank, not position" partially learned as "some operations just come first". Naming which of the two is happening is what makes practice useful — drilling more mixed problems without knowing which mistake is being made just repeats the same error at a slightly larger scale.
A worked example: 6 + 2 × (5 − 3)²
Start inside the parentheses: 5 − 3 = 2. Next comes the exponent: 2² = 4. Now the expression is 6 + 2 × 4, with only multiplication and addition left. Multiplication outranks addition, so that goes next: 2 × 4 = 8. Finally, 6 + 8 = 14.
The step most children skip is re-scanning the whole expression after each simplification, rather than just continuing where they left off. After squaring, the problem is genuinely a new, simpler one (6 + 2 × 4), and treating it that way — check rank again from scratch — is what keeps a longer problem from going wrong halfway through.
Why this gap resurfaces in algebra
Order of operations is not just an arithmetic topic that gets left behind — it is the rule that makes an algebraic expression like 3x + 2(x − 1) mean one specific thing instead of several possible ones. A child who works left to right instead of by rank will simplify expressions incorrectly long before the algebra itself is the problem.
That is why this particular gap is worth closing properly rather than working around with a calculator: calculators apply order of operations correctly, which means they hide exactly the mistake this guide is about instead of catching it.
Signs it’s time for outside help
When home help has done what it can
- Can recite PEMDAS but still gets mixed problems wrong.
- Solves problems strictly left to right regardless of the operations involved.
- Assumes multiplication always comes before division, or addition always before subtraction.
- Gets the right digits but the wrong final answer on multi-step problems.
- Simplifies algebraic expressions inconsistently, getting a different answer each time.
- Relies on a calculator for anything with more than one operation.
Questions parents ask
FAQ
What age do children learn order of operations?
Most children meet it around ages 10–12 (US Grades 5–6, UK/AU Years 6–7), once they are comfortable with all four basic operations and are starting to see expressions with more than one operation in them.
Is PEMDAS the same everywhere?
The idea is universal; the acronym differs by country — PEMDAS (US), BODMAS or BIDMAS (UK/AU). All describe the same ranking: brackets first, then exponents/orders, then multiplication and division left to right, then addition and subtraction left to right.
Does multiplication always come before division?
No — that is one of the two most common mistakes. Multiplication and division share a rank and are done left to right, whichever is written first. The same is true for addition and subtraction.
Is it normal for a child who is good at maths to still get this wrong?
Yes. Order of operations replaces a "just go left to right" habit that worked fine for years, so the mistake is about habit, not understanding. Most children fix it within a couple of weeks of targeted practice.
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