Mathematics • Year 7 • Unit 1 • Lesson 5
Order of Operations
Build fluency with BIDMAS / BODMAS: Brackets, Indices (powers), Division & Multiplication (left to right), Addition & Subtraction (left to right). Get the order right and the answer falls out.
1. I do — fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Evaluate (5 + 3)² − 4 × (10 − 6).
Step 1 — Brackets first (the B in BIDMAS).
(5 + 3) = 8 and (10 − 6) = 4
Expression becomes: 8² − 4 × 4
Reason: anything inside brackets is treated as one number — finish it before going further.
Step 2 — Indices (powers) next (the I in BIDMAS).
8² = 8 × 8 = 64
Expression becomes: 64 − 4 × 4
Reason: powers come before × and ÷ in the order of operations.
Step 3 — Multiplication (the M in BIDMAS).
4 × 4 = 16
Expression becomes: 64 − 16
Reason: × is done before − . If we did 64 − 4 first, we'd get the wrong answer.
Step 4 — Subtraction last (the S in BIDMAS).
64 − 16 = 48
Reason: only + and − are left, so we do them last.
Answer: (5 + 3)² − 4 × (10 − 6) = 48.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Evaluate 12 + 8 ÷ 2 × 3.
Step 1 — Brackets: there are no brackets in this expression, so skip.
Step 2 — Indices: no powers either, so skip.
Step 3 — Division and multiplication (left to right). The leftmost of × or ÷ is ____. Do it first:
8 ÷ 2 = _______
Expression becomes: 12 + _______ × 3
Step 4 — Next × in the expression:
_______ × 3 = _______
Expression becomes: 12 + _______
Step 5 — Addition (last):
12 + _______ = _______
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation — single step
3.1 Evaluate 6 + 4 × 2. 1 mark
3.2 Evaluate 20 − 6 ÷ 3. 1 mark
3.3 Evaluate (4 + 2) × 5. 1 mark
3.4 Evaluate 3 + 2². 1 mark
Standard — combine two ideas
3.5 Evaluate 18 − 2 × (3 + 4). 2 marks
3.6 Evaluate 5² − 4 × 3. 2 marks
Extension — push your thinking
3.7 Evaluate [18 − (4 + 2) × 2] ÷ 3 + 5². Show each step on a new line. 3 marks
3.8 Add brackets to the expression 6 + 2 × 3 so that the answer becomes 24 (instead of the BIDMAS answer of 12). 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (12 + 8 ÷ 2 × 3)
Step 3: leftmost is ÷. 8 ÷ 2 = 4. Expression: 12 + 4 × 3.
Step 4: 4 × 3 = 12. Expression: 12 + 12.
Step 5: 12 + 12 = 24.
3.1 — 6 + 4 × 2
× before +: 4 × 2 = 8. Then 6 + 8 = 14.
Common slip: doing 6 + 4 first to get 10 × 2 = 20. Wrong — × is done before +.
3.2 — 20 − 6 ÷ 3
÷ before −: 6 ÷ 3 = 2. Then 20 − 2 = 18.
3.3 — (4 + 2) × 5
Brackets first: 4 + 2 = 6. Then 6 × 5 = 30.
3.4 — 3 + 2²
Indices before +: 2² = 4. Then 3 + 4 = 7.
3.5 — 18 − 2 × (3 + 4)
Brackets: 3 + 4 = 7. Expression: 18 − 2 × 7.
× before −: 2 × 7 = 14. Then 18 − 14 = 4.
3.6 — 5² − 4 × 3
Indices: 5² = 25. Expression: 25 − 4 × 3.
× before −: 4 × 3 = 12. Then 25 − 12 = 13.
3.7 — [18 − (4 + 2) × 2] ÷ 3 + 5²
Step 1 — innermost brackets: (4 + 2) = 6. Expression: [18 − 6 × 2] ÷ 3 + 5².
Step 2 — multiplication inside brackets: 6 × 2 = 12. Expression: [18 − 12] ÷ 3 + 5².
Step 3 — finish brackets: 18 − 12 = 6. Expression: 6 ÷ 3 + 5².
Step 4 — indices: 5² = 25. Expression: 6 ÷ 3 + 25.
Step 5 — division before addition: 6 ÷ 3 = 2.
Step 6 — finally add: 2 + 25 = 27.
3.8 — Add brackets to 6 + 2 × 3 to get 24
Wrap the addition in brackets so it is done first: (6 + 2) × 3.
Check: (6 + 2) × 3 = 8 × 3 = 24 ✓. Without the brackets, BIDMAS gives 6 + 2 × 3 = 6 + 6 = 12.