Order of operations worksheet generator

How it works

1. Choose two operations, three operations or a bracket pair, and whether division appears.
2. Set how many questions and whether an answer key is printed.
3. Download the PDF, print it, or copy a share link that restores these settings.

Using these worksheets in teaching

Order of operations is taught as a mnemonic and then quietly mis-taught as a queue: children learn PEMDAS as six steps in order and start multiplying before dividing because M comes before D in the word. It does not work that way. Multiplication and division share one level and are worked left to right across it, and so do addition and subtraction — which is why 12 − 4 + 3 is 11 and not 5, the single most common wrong answer on any precedence sheet. Say the rule as three tiers rather than six letters and that mistake mostly disappears. The second thing worth doing early is asking a child to predict the wrong answer as well as the right one: every question here has exactly two candidate answers, the left-to-right one and the correct one, and a child who can say what a careless reader would get has understood the rule rather than memorised a word. Parentheses deserve their own lesson rather than a harder row on the same sheet — their job is to override the tiers, so they only mean something to a child who already trusts the tiers.

Frequently asked questions

Is the mnemonic printed on the worksheet?

No, and that is a feature rather than an omission. The sheet prints the expressions, the working space and the answer key — no PEMDAS, no BODMAS, no BIDMAS. The rule is identical whichever of those a school says, so one PDF is usable in an American, an Australian and a British classroom without a word of it being wrong, and the mnemonic your class already uses is the one that gets said out loud.

Do the questions actually need the rule?

Yes — every single one. An expression is only printed when evaluating it left to right gives a different answer from evaluating it by precedence, so a child who works straight across the page gets it wrong and finds out. Questions like 2 + 3 × 4 where the two readings happen to agree are constructed away rather than filtered out afterwards, which is why the sheet is never short of questions.

Are the intermediate steps whole numbers?

Always. Each expression is built backwards from the answer, so every division lands exactly and no step along the way produces a fraction or a negative number. A child never has to decide whether an awkward part-way value means they have made a mistake — it means they have.

What do the three difficulties print?

Two operations prints a ± b × c, the shortest expression that can be got wrong by reading across. Three operations adds a third operator and still no parentheses. With brackets adds one parenthesis pair to a four-operand expression, which is where the rule stops being a habit and starts being a decision.

Can I turn division off?

Yes. Division is the harder half of the rule — it shares a precedence level with multiplication but is not commutative, so its position matters — and a class meeting precedence for the first time is usually better off with multiplication only for a week or two.

Why are the sheets capped at 40 questions?

Because a precedence question needs room for the working, and forty already runs to two dense columns. If you need more, print more class versions: each one has its own questions and its own answer key section.

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