How to teach order of operations
Grade 5 to Grade 6
When a calculation mixes operations (3 + 4 × 2), everyone must agree on the order, or the same expression gives different answers. The convention: brackets first, then multiplication and division (left to right), then addition and subtraction (left to right). Known as BODMAS, BIDMAS or PEMDAS depending on where you teach.
How to teach it
- Motivate it with the ambiguity: ask the class to work out 3 + 4 × 2 and let both 14 and 11 appear, then explain why we need a rule (the answer is 11).
- Teach multiplication/division as ONE level worked left to right, and addition/subtraction as one level, not four separate steps.
- Show how brackets change meaning: (3 + 4) × 2 = 14 versus 3 + 4 × 2 = 11.
- Work multi-step examples slowly, rewriting the whole line after each single step.
- Let students invent expressions that trap a calculator-style left-to-right reader.
Common mistakes
- Doing all multiplication before any division (8 ÷ 2 × 4 is 16, not 1), same level, left to right.
- Treating the mnemonic's letter order as strict order (the A before S in BODMAS doesn't mean addition first).
- Ignoring brackets that 'look finished' inside a longer expression.
- Skipping the rewrite: doing two steps at once is where slips happen.
Frequently asked questions
What is the order of operations?
When a calculation mixes operations, the order of operations is the agreed rule for which to do first: brackets, then multiplication and division from left to right, then addition and subtraction from left to right. It is known as BODMAS, BIDMAS or PEMDAS depending on where you teach.
What age or grade is order of operations taught?
The order of operations is usually taught in Grade 5 and Grade 6, once the four operations are fluent. Students learn why a shared rule is needed, then apply it to multi-step calculations and expressions with brackets.
What is 3 plus 4 times 2?
The answer is 11, not 14. Under the order of operations you do the multiplication first, so 4 times 2 is 8, then add 3 to get 11. Working strictly left to right would wrongly give 14, which is exactly why the rule exists.
Do you always do multiplication before division?
No. Multiplication and division sit at the same level and are worked left to right, whichever comes first. So 8 divided by 2 times 4 is 16, not 1, because you divide first, then multiply. Treating the mnemonic's letter order as strict order is a common mistake.
How do brackets change a calculation?
Brackets are done first, so they can change the answer completely. Without brackets, 3 plus 4 times 2 is 11. With brackets, (3 plus 4) times 2 is 14, because you add inside the brackets first, then multiply. Brackets let you force a different order.
Why do we need an order of operations at all?
Without an agreed order, the same expression could give different answers. Ask a class to work out 3 plus 4 times 2 and both 11 and 14 appear. A shared rule means everyone reaches the same, correct result, which is 11, so calculations are unambiguous.
What is the difference between BODMAS and PEMDAS?
They are the same rule with different names. BODMAS uses Brackets, Orders; PEMDAS uses Parentheses, Exponents. Both then do multiplication and division together, then addition and subtraction together. The letters just reflect local wording, not a different order, so the result is always the same.
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