BODMAS Order of Operations Generator

BODMAS worksheets with whole-number answers

Ask a class to work out 4 + 6 × 2 and roughly half will say 20. They can add. They can multiply. What has not landed yet is that the operations stand in a queue, and that the queue is a convention agreed on so that one written expression means one thing to everybody who reads it rather than whatever the reader's eye happens to reach first.

This generator produces pages of mixed expressions for practising that queue, with a BODMAS reminder bar printed across the top of the sheet. BODMAS, BIDMAS, PEMDAS — the acronyms differ by country, the precedence they describe does not, so the sheets work whichever one your classroom says.

What you can set

• Max number — the ceiling on the operands, between 3 and 20. This is your difficulty dial. At 5 the arithmetic disappears and only the ordering is being tested; at 20 a child who knows the rules can still get it wrong through a slip in the multiplication.
• Problems — 4 to 40, printed in two columns.
• Include brackets — adds forms like (a + b) × c and (a + b) ÷ c to the mix.
• Include exponents — sprinkles in squared and cubed terms, roughly one expression in three.
• Include answer key, a Name and Date pair, and A4 or US Letter.

Every answer is a whole number, and division is real

Expressions are generated, then evaluated, and anything landing on a fraction is thrown away before it reaches the page. Divisions are built so the dividend is a real multiple of the divisor. That matters. Plenty of order-of-operations worksheets quietly avoid division altogether, which leaves a child fluent in four of the six letters and unprepared for the two that were missing.

Answers are capped at 10,000. Without that, one cubed term would dwarf everything else on the page.

What the errors tell you

These mistakes are readable in a way that most arithmetic errors are not, because a wrong answer here names the rule that was skipped instead of just being wrong.

4 + 6 × 2 marked as 20 is strict left-to-right working. (5 + 3) × 2 marked as 11 means the brackets were ignored. 2 + 3² marked as 25 means the addition was done first. Each of those needs a different five-minute conversation, so it is worth reading the wrong answers rather than only counting them.

Notes

Turn brackets off and expressions stay flat. That is the right first lesson. Turn them on and the same page asks something harder, because a bracket overrules the precedence the child spent the previous week learning, and holding two rules in the right order is a bigger step than holding one.

The reminder bar spells out B O D M A S. A US class can cross it out and write PEMDAS. Same rule, different words, and explaining why the two countries landed on different acronyms is a fair thirty seconds of a lesson.