Order of Operations Question Generator
Builds a sheet of order-of-operations questions where working left to right always gives the wrong answer — an expression that comes out the same either way tests nothing, and a surprising number of textbook examples are like that. Every question is computed and checked directly — not a fabricated or AI-guessed fact.
What this generator does
Every expression on the sheet is discriminating: bracket-free ones give a different result if you work strictly left to right, and bracketed ones give a different result if the brackets are deleted. A × B − C is deliberately never produced, because reading it left to right gets it right by accident and so it cannot tell you anything about whether the rule is understood.
How to use this tool
- Choose how many questions you want and how many operations each should involve.
- Press make questions, and work through the sheet.
- Show the answers to mark it, or show the working to see which operation goes first and why.
- Enter a seed word to rebuild the same sheet later.
Understanding the controls
- How many questions
- One to thirty. Ten is enough to tell whether someone has the rule or is guessing, because a guesser gets a predictable subset wrong.
- Level
- Gentle has three numbers and one operation that must jump the queue. Standard adds brackets and exact division. Stretch has four numbers and two operations out of reading order.
- Seed
- A word rebuilds the identical sheet, so two people can be given the same expressions with nothing shared but the word.
- Show the answers / show the working
- The working names which rule applies at each step rather than only showing the intermediate number.
Common use cases
- BODMAS, BIDMAS or PEMDAS practice
- Quick maths warm-ups
- Diagnosing whether someone is working left to right
- Self-testing before a maths quiz
How this generator works
One of a fixed set of expression shapes is drawn, then the numbers to fill it. Division only appears where the dividend is built as a multiple of the divisor, so it always comes out whole — a fraction here would be testing a different skill. The shapes were chosen so that every one of them fails when worked in the wrong order, and that property is checked automatically against every expression the tool can produce rather than assumed.
Randomness and fairness
The shape and the numbers are drawn separately, so the same shape recurs with different values across a sheet. Whether an expression contains brackets follows from the shape rather than being drawn on its own.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Indices and powers are not included, so the I or O of the acronym never actually appears.
- Nested brackets are not produced — there is at most one bracketed group per expression.
- A seeded sheet is reproducible and so is not cryptographically random — the seed determines every expression on it.
Common mistakes
- Doing division after multiplication because of the acronym
- Multiplication and division rank equally and are done left to right, as do addition and subtraction. BIDMAS lists them in pairs, not in strict order.
- Ignoring an implied bracket in a fraction
- A fraction bar groups everything above and below it. Written on one line, that grouping needs brackets.
Privacy and your data
Expressions are built in your browser and stay there. Your seed and level are never transmitted, never stored and never leave your device.
Related generators
- Algebra Substitution Question GeneratorSubstitution questions built to order — one letter, two letters, squares, brackets and division, all evaluating to whole numbers.
- Missing Operator Puzzle GeneratorThe numbers are given and the signs are blank: work out which combination of plus, minus and times reaches the target.
- Expression Notation GeneratorShows one arithmetic expression in infix, prefix and postfix, with all three evaluated separately and required to agree.
- Quadratic Equation GeneratorQuadratics built from their roots, so they always factorise, with the discriminant stated and the repeated-root case named.
- Simple Equation GeneratorLinear equations built to order — one step, two steps, unknowns on both sides and brackets — each with a whole-number solution.