Mathematics • Year 7 • Unit 1 • Lesson 5
Order of Operations
Build fluency with BIDMAS / BODMAS: B rackets, I ndices (powers), D ivision & M ultiplication (left to right), A ddition & S ubtraction (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.