Mathematics • Year 7 • Unit 1 • Lesson 5

Order of Operations — Real World

Use BIDMAS to work out shopping totals, snack costs, prize money calculations, ticket discounts, and lawn-mowing earnings. Whoever writes the expression has to think about which operations should be done first — or use brackets to make their meaning clear.

Apply · Real-World Maths

1. Word problems

Each problem needs you to write an expression and then evaluate it using BIDMAS. Show your working — a single answer with no working only earns half marks.

1.1 — Snack run. Jay buys 3 chocolate bars at $2 each and 1 drink at $4.

(a) Write a single expression for the total cost using one multiplication and one addition.
(b) Evaluate it using BIDMAS. 2 marks

Stuck? "3 bars at $2 each" = 3 × 2. Then add the drink at $4.

1.2 — Prize money split. A maths trivia team wins $80 in prize money. They donate $20 to charity, then split the rest equally between the 4 team members.

(a) Write a single expression using brackets so the subtraction is done first.
(b) Evaluate it. How much does each team member get?
(c) What would each member get if the brackets were left out and BIDMAS was followed strictly? 3 marks

Stuck on (c)? Without brackets, 80 − 20 ÷ 4 means do the division before the subtraction.

1.3 — Movie tickets with a discount. A cinema sells tickets at $15 each, but if you buy 4 tickets together you get $10 off the total. Maya is buying 4 tickets.

(a) Write the total cost as an expression using one multiplication and one subtraction.
(b) Evaluate it. 2 marks

Stuck? Cost = (tickets × price) − discount. Multiplication is done before subtraction.

1.4 — Square garden bed. Liam is building a small square garden bed and a separate rectangular path. The garden is 4 m × 4 m. The path is 2 m × 3 m.

(a) Write a single expression for the total area using one power and one multiplication and one addition.
(b) Evaluate it using BIDMAS. 2 marks

Stuck? Area of a square with side 4 is 4². Area of the path is 2 × 3. Total area = 4² + 2 × 3.

1.5 — Mowing lawns. Aisha mowed 5 lawns on Saturday for $12 each, and 3 lawns on Sunday for $15 each. She paid $7 for petrol over the weekend.

(a) Write a single expression for her profit over the weekend using two multiplications and one subtraction.
(b) Evaluate it. 3 marks

Stuck? Profit = (Saturday earnings) + (Sunday earnings) − petrol. Each set of earnings is its own multiplication.

2. Explain your thinking

This question is about communication, not just answers. Use full sentences. 4 marks

2.1 A classmate looks at 6 + 4 × 2 and writes "6 plus 4 is 10, times 2 is 20 — the answer is 20." In your own words, explain (i) what mistake they have made about the order of operations, (ii) what 6 + 4 × 2 actually equals, and (iii) how brackets could have been used to make their interpretation correct. Use the letters of BIDMAS or BODMAS in your explanation.

Stuck? Revisit lesson § "Spot the Trap" — × is always done before + unless brackets force the addition to come first.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

1.1 — Snack run

(a) Total = 3 × 2 + 4.
(b) BIDMAS: 3 × 2 = 6 (multiplication first), then 6 + 4 = $10.

1.2 — Prize money split

(a) Each member's share = (80 − 20) ÷ 4.
(b) Brackets first: 80 − 20 = 60. Then 60 ÷ 4 = $15 each.
(c) Without brackets: 80 − 20 ÷ 4. BIDMAS does ÷ first: 20 ÷ 4 = 5. Then 80 − 5 = $75 (which is just one person's share, not what was meant). This is why brackets matter — they protect your intended meaning.

1.3 — Movie tickets

(a) Total = 4 × 15 − 10.
(b) BIDMAS does × first: 4 × 15 = 60. Then 60 − 10 = $50.

1.4 — Square garden + path

(a) Total area = 4² + 2 × 3.
(b) Indices first: 4² = 16. Multiplication next: 2 × 3 = 6. Addition last: 16 + 6 = 22 m².

1.5 — Mowing lawns

(a) Profit = 5 × 12 + 3 × 15 − 7.
(b) BIDMAS does the two × first: 5 × 12 = 60, 3 × 15 = 45. Expression becomes 60 + 45 − 7. Left to right: 60 + 45 = 105; 105 − 7 = $98.

2.1 — Explain your thinking (sample response)

My classmate ignored the order of operations and just worked left to right. The rule from Lesson 5 is BIDMAS (or BODMAS): Brackets first, then Indices, then Division/Multiplication (left to right), then Addition/Subtraction (left to right). For 6 + 4 × 2 the multiplication MUST be done before the addition, so 4 × 2 = 8 first, then 6 + 8 = 14. The classmate got 20 by adding before multiplying. To make their interpretation correct, they would have to add brackets to force the addition: (6 + 4) × 2 = 10 × 2 = 20. So the brackets change what is calculated first — without them, BIDMAS does the × first.

Marking: 1 for naming BIDMAS / BODMAS; 1 for the correct answer 14; 1 for showing how brackets give 20; 1 for clear full-sentence explanation.