Order of Operations
When Year 6 pupils tackle 3 + 4 × 2, many instinctively work left to right and arrive at 14. However, the correct answer using BIDMAS is 11, as multiplication comes before addition. This fundamental concept appears in Year 6 SATs and forms the foundation for algebraic thinking in secondary maths.
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Why it matters
Order of operations prevents mathematical chaos in real-world calculations. When a builder calculates material costs using 5 × £12 + £8 for delivery, BIDMAS ensures the correct total of £68, not £108. In Year 6 SATs, pupils typically encounter 3-4 questions testing BIDMAS understanding, worth approximately 4-5 marks. Financial calculations, scientific formulas, and engineering designs all rely on consistent operation order. A pharmacy calculating dosages using 250mg × 3 + 50mg must follow BIDMAS to avoid dangerous errors. Even simple scenarios like calculating football match tickets (£15 × 4 children + £20 × 2 adults) require proper operation sequence to reach the correct £140 total. This mathematical convention ensures universal understanding across cultures and professions.
How to solve order of operations
Order of Operations (PEMDAS)
- Parentheses first.
- Then exponents.
- Then multiplication and division (left to right).
- Then addition and subtraction (left to right).
Example: 3 + 4 × 2 = 3 + 8 = 11 (not 14).
Worked examples
2 + 1 × 3 = _______
Answer: 5
- Multiply first → 1 × 3 = 3 — Multiplication before addition (PEMDAS).
- Then add → 2 + 3 = 5 — Now add the remaining term.
- Verify → 2 + 1 × 3 = 5 ✓ — Check the answer.
Willow says 9 + 7 × 5 = 44. Muhammad says 9 + 7 × 5 = 80. Who is correct?
Answer: Willow (44)
- Multiply first → 7 × 5 = 35 — Multiplication before addition.
- Then add → 9 + 35 = 44 — Add the remaining.
- Verify → 9 + 7 × 5 = 44 ✓ — Check.
Add parentheses to make it true: 10 × 3 + 3 − 2 = 58
Answer: 10 × (3 + 3) − 2
- Without parentheses → 10 × 3 + 3 − 2 = 31 — Without parentheses we get 31, not 58.
- Try grouping addition → 10 × (3 + 3) − 2 — Parentheses around the addition changes the order.
- Verify → 10 × (3 + 3) − 2 = 58 ✓ — Check.
Common mistakes
- Working strictly left to right without considering operation priority. Students often calculate 6 + 3 × 2 as (6 + 3) × 2 = 18 instead of 6 + (3 × 2) = 12.
- Forgetting that division has equal priority with multiplication. Pupils might calculate 12 ÷ 3 × 4 as 12 ÷ (3 × 4) = 1 instead of working left to right: (12 ÷ 3) × 4 = 16.
- Misapplying BIDMAS when parentheses create different groupings. Students calculate 2 × (5 + 3) as 2 × 5 + 3 = 13 instead of 2 × 8 = 16.
- Treating subtraction and addition with different priorities. Pupils often compute 10 - 4 + 2 as 10 - (4 + 2) = 4 instead of (10 - 4) + 2 = 8.