Mathematics • Year 7 • Unit 1 • Lesson 5
Order of Operations, Mixed Challenge
Bring together everything from Unit 1 so far: place value, integers, +, −, ×, ÷, powers and brackets. Choose the right operation order, spot a common BIDMAS mistake, and tackle an open-ended puzzle about where to put brackets.
1. Mixed problems, choose the right rule
Each question mixes brackets, powers, ×, ÷, +, − . Decide the order of operations before you start writing. Show your working. 2 marks each
1.1 Evaluate 30 − 4 × 5.
1.2 Evaluate (7 − 3) × (2 + 5).
1.3 Evaluate 3² + 4² .
1.4 Evaluate 100 ÷ (5 × 4) + 2.
1.5 Evaluate (3 + 2)² − 10. (Recall: a power means "multiply by itself", so 5² = 25.)
1.6 Evaluate 24 ÷ (8 − 2) × 3 + 4. Show every step on a new line.
2. Find the mistake
Another Year 7 student has tried to evaluate 20 − 8 ÷ 4 × 2. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's working, evaluate 20 − 8 ÷ 4 × 2:
Line 1: BIDMAS says ÷ comes before ×, so do ÷ first.
Line 2: 8 ÷ 4 = 2. Expression: 20 − 2 × 2.
Line 3: Now subtraction comes next: 20 − 2 = 18. Expression: 18 × 2.
Line 4: Answer: 18 × 2 = 36.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected final answer.
3. Open-ended challenge, make 12 four different ways
This question has more than one correct answer. Show your work clearly. 4 marks
3.1 Using the digits 2, 3, 4 and 5 exactly once each, and any combination of +, −, ×, ÷ and brackets, find three genuinely different expressions whose value is exactly 12.
For each expression: (i) write it down; (ii) evaluate it step by step using BIDMAS to confirm it equals 12.
Bonus: Find one expression using all four digits 2, 3, 4 and 5 exactly once, with one of them used as a base and another as its exponent, that still gives 12.
How did this worksheet feel?
What I'll revisit before next class:
1.1-30 − 4 × 5
× before −: 4 × 5 = 20. Then 30 − 20 = 10.
1.2, (7 − 3) × (2 + 5)
Brackets first: 7 − 3 = 4, 2 + 5 = 7. Then 4 × 7 = 28.
1.3-3² + 4²
Indices first: 3² = 9, 4² = 16. Then 9 + 16 = 25.
1.4-100 ÷ (5 × 4) + 2
Brackets first: 5 × 4 = 20. Expression: 100 ÷ 20 + 2.
÷ before +: 100 ÷ 20 = 5. Then 5 + 2 = 7.
1.5, (3 + 2)² − 10
Brackets first: 3 + 2 = 5. Expression: 5² − 10.
Indices: 5² = 25. Then 25 − 10 = 15.
1.6-24 ÷ (8 − 2) × 3 + 4
Step 1, brackets: 8 − 2 = 6. Expression: 24 ÷ 6 × 3 + 4.
Step 2, ÷ and × left to right: 24 ÷ 6 = 4. Expression: 4 × 3 + 4.
Step 3, × next: 4 × 3 = 12. Expression: 12 + 4.
Step 4, addition last: 12 + 4 = 16.
2, Find the mistake
(a) The mistake is on Line 3.
(b) BIDMAS says ÷ and × have equal priority and both come BEFORE addition/subtraction. The student should have done the multiplication (2 × 2) before the subtraction. Instead they did 20 − 2 first, which is the same trap as "20 − 2 × 2 = 18 × 2 = 36", wrong.
(c) Corrected working:
Line 1: 8 ÷ 4 = 2. Expression: 20 − 2 × 2.
Line 2 (fixed): × before −, so 2 × 2 = 4. Expression: 20 − 4.
Line 3 (fixed): 20 − 4 = 16.
The fix: × and ÷ are higher priority than + and − . Always.
3, Open-ended challenge (sample solutions)
Each expression uses 2, 3, 4 and 5 exactly once and follows BIDMAS:
Expression 1: (5 − 3) × (2 + 4) = 2 × 6 = 12.
Expression 2: (5 + 4 − 3) × 2 = 6 × 2 = 12.
Expression 3: (5 + 3) × 2 − 4 = 8 × 2 − 4 = 12. These use different operation structures.
Bonus: 5 × 4 − 23 = 20 − 8 = 12. The four digits are 5, 4, 2 (the base) and 3 (the exponent), each used once.
Marking: 1 mark for each of three distinct verified expressions using each digit once; 1 mark for a verified power expression using all four digits once.