Mathematics • Year 8 • Unit 1 • Lesson 3
Percentage of a Quantity — Real World
Use the multiplier and unitary methods from Lesson 3 in everyday contexts: school enrolment, sale prices, road trips, tipping at a café, and screen time. Then explain your method in your own words.
1. Word problems
Each problem asks you to find a percentage of a quantity. Show your working and state which method you used (multiplier or unitary).
1.1 — Walking to school. 15% of the 120 Year 8 students walk to school.
(a) How many students walk?
(b) Show working using both methods — multiplier AND unitary — to check the answer matches. 3 marks
1.2 — Hoodie on sale. A $80 hoodie is marked "30% off".
(a) Find 30% of $80 — this is the discount amount.
(b) Subtract the discount from $80 to find the sale price. 3 marks
1.3 — Road trip. Dad drives 450 km of an 800 km road trip before lunch. The car's nav app reports progress as a percentage.
(a) Show that he has driven roughly 56% of the way (this part is a Lesson 4 idea — you'll formalise it next lesson).
(b) Use the multiplier method to find what 25% of the 800 km is — i.e. when he reaches the quarter-way mark, how many km has he covered? 3 marks
1.4 — Café tip. A family bill comes to $65. They want to leave a 10% tip.
(a) Find 10% of $65 (mental method — 10% is "divide by 10").
(b) What is the total amount they pay (bill + tip)?
(c) Use a similar mental approach to find a 5% tip on the same bill. 3 marks
1.5 — Screen time. A Year 8 student spends 35% of their 14-hour weekday awake-time on screens (school computer + phone + TV).
(a) How many hours of screen time is that per day?
(b) How many hours is that per week (Mon–Fri)? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 Your friend says: "I always use the unitary method because it's clearer. The multiplier method is just a trick." In your own words, write a reply that (i) describes when the multiplier method is faster, (ii) describes when the unitary method is more useful, and (iii) gives one example of a calculation where each method shines. Mention "1%" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Walking to school
(a) 18 students walk.
(b) Multiplier: 0.15 × 120 = 18. Unitary: 1% of 120 = 1.2, then 15 × 1.2 = 18. ✓ Both methods match.
1.2 — Hoodie on sale
(a) Discount = 30% of $80 = 0.30 × 80 = $24.
(b) Sale price = $80 − $24 = $56.
1.3 — Road trip
(a) 450/800 × 100 = 56.25% ≈ 56% of the way.
(b) 25% of 800 km = 0.25 × 800 = 200 km at the quarter-mark.
1.4 — Café tip
(a) 10% of $65 = $65 ÷ 10 = $6.50.
(b) Total = $65 + $6.50 = $71.50.
(c) 5% is half of 10%: $6.50 ÷ 2 = $3.25.
1.5 — Screen time
(a) 0.35 × 14 = 4.9 hours/day.
(b) 4.9 × 5 = 24.5 hours/week on screens just on weekdays.
2.1 — Explain your thinking (sample response)
Both methods are useful, just in different situations. The multiplier method is fastest when you have a calculator, because you turn the percent into a decimal and do one multiplication — for example, 23% of $185 is just 0.23 × 185 on the calculator. The unitary method is more useful for mental maths, especially when the percentage is built from easy blocks like 10%, 5% or 1%. For instance, finding 17% of $240 in your head is easier as 10% ($24) + 5% ($12) + 2 × 1% ($4.80) = $40.80 than trying to multiply 0.17 × 240 mentally. The unitary method is also nicer when the number splits cleanly: 1% of $400 is exactly $4, which makes any percentage of $400 quick. So "always use unitary" is a bit limiting — pick whichever method matches the tools and numbers you have.
Marking: 1 mark for naming when multiplier is faster; 1 mark for when unitary is better; 1 mark for a concrete example of each; 1 mark for clarity and using the phrase "1%" somewhere.