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

1. 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).
2. Teach multiplication/division as ONE level worked left to right, and addition/subtraction as one level , not four separate steps.
3. Show how brackets change meaning: (3 + 4) × 2 = 14 versus 3 + 4 × 2 = 11.
4. Work multi-step examples slowly, rewriting the whole line after each single step.
5. 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.