Mathematics • Year 8 • Unit 1 • Lesson 4
Quantity as a Percentage — Real World
Use the (A ÷ B) × 100 formula from Lesson 4 in everyday contexts: test marks, profit margins, attendance, sports stats, and rainfall. Then explain your method in your own words.
1. Word problems
Each problem asks you to express one quantity as a percentage of another. Show your working — a single final answer with no working only earns half marks.
1.1 — Two unequal tests. You scored 34 out of 40 on a science test. Your friend scored 43 out of 50 on a longer one.
(a) Convert both scores to percentages.
(b) Who did better, and by how many percentage points? 3 marks
1.2 — Attendance. In Term 1 (40 school days), Lin was present on 36 days.
(a) Express her attendance as a percentage.
(b) What percentage of days was she absent? 3 marks
1.3 — Free throws. A school basketballer attempts 25 free throws in a season and makes 19 of them.
(a) Find her free-throw shooting percentage.
(b) Her teammate's percentage is 72%. Who has the better percentage? 3 marks
1.4 — School canteen. The canteen sells 240 lunches one day. Of these, 84 are vegetarian.
(a) Express the vegetarian lunches as a percentage of the total.
(b) Express the non-vegetarian lunches as a percentage of the total.
(c) Check that your two percentages add to 100%. 3 marks
1.5 — Rainfall. Sydney's average yearly rainfall is about 1200 mm. In April alone last year, Sydney recorded 90 mm of rain.
(a) What percentage of the average yearly rainfall fell in that single month? Round to 1 dp.
(b) Compare that with the "fair share" — one month is what fraction of a year, and what is that as a percentage? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 Asha argues "I got more questions right than Eli, so I scored better." Asha got 47 right out of 60; Eli got 74 right out of 95. In your own words, explain (i) why "more questions right" is NOT the same as "better percentage", (ii) how to convert each into a fair comparison, and (iii) who actually scored higher. Use the words "part" and "whole" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Two unequal tests
(a) You: 34/40 × 100 = 85%. Friend: 43/50 × 100 = 86%.
(b) Friend did better, by 1 percentage point.
1.2 — Attendance
(a) 36/40 × 100 = 90% attendance.
(b) Absent: 4 days out of 40 = 4/40 × 100 = 10%. (Or 100% − 90% = 10%. ✓)
1.3 — Free throws
(a) 19/25 × 100 = 0.76 × 100 = 76%.
(b) 76% > 72%, so the school basketballer has the better shooting percentage.
1.4 — School canteen
(a) Veg = 84/240 × 100 = 0.35 × 100 = 35%.
(b) Non-veg = 156/240 × 100 = 0.65 × 100 = 65%.
(c) 35% + 65% = 100%. ✓
1.5 — Rainfall
(a) 90/1200 × 100 = 7.5% of the yearly average fell in that single April.
(b) Fair share = 1/12 × 100 ≈ 8.3% per month. So April was just below average — about 0.8 percentage points under its "fair share".
2.1 — Explain your thinking (sample response)
Comparing "raw counts" isn't fair when the totals are different. The two tests have different wholes (60 questions vs 95 questions), so the same part means different things. To compare fairly, we express each score as a percentage by dividing the part by the whole and multiplying by 100. Asha: 47 ÷ 60 × 100 ≈ 78.3%. Eli: 74 ÷ 95 × 100 ≈ 77.9%. So even though Eli got more questions right in absolute terms, Asha scored higher — by about 0.4 percentage points. Percentages put both onto the same "out of 100" scale, which is what makes comparison meaningful.
Marking: 1 mark for explaining why raw counts mislead; 1 mark for naming the formula or steps; 1 mark for both percentages calculated correctly; 1 mark for the correct conclusion and clear writing using "part" / "whole".