Mathematics • Year 8 • Unit 1 • Lesson 1
FDP in the Real World
Use fractions, decimals and percentages where they actually show up: shop sale signs, sports stats, recipes, classroom surveys and phone batteries. Then explain your thinking in your own words.
1. Word problems
Each problem uses the idea that a fraction, a decimal and a percentage can describe the same proportion. Show your working — a single final answer with no working only earns half marks.
1.1 — Sale-sign battle. Three shops advertise the same jacket:
Shop A — "1/3 off". Shop B — "33% off". Shop C — "save 0.33 of the price".
(a) Convert each discount to a decimal (round to two decimal places if needed).
(b) Which shop gives the biggest saving? 3 marks
1.2 — Phone battery. Your phone screen shows the battery at 0.45 of full charge. The settings menu shows it as a percentage instead.
(a) What percentage will it show?
(b) Write that percentage as a fraction over 100, then simplify. 3 marks
1.3 — Free-throw stats. A basketballer made 7 out of 10 free throws in the first half. Her teammate shoots 0.65 of her free throws successfully (long-term average).
(a) Write the basketballer's first-half success as a fraction, decimal and percentage.
(b) Whose success rate is higher? 3 marks
1.4 — Class survey. In a class of 25 students, 9 walk to school, 11 catch the bus and the rest are dropped off.
(a) Write each group as a fraction of the class.
(b) Write each group as a percentage. (Use 100 ÷ 25 = 4, so each student is 4%.)
(c) Check your three percentages add to 100%. 3 marks
1.5 — Pizza party. Maria orders a large pizza cut into 8 equal slices for 4 friends. Lucas writes "each friend gets 1/4" and Aiden writes "each friend gets 25%" on a napkin.
(a) Are Lucas and Aiden saying the same thing? Show that 1/4 = 0.25 = 25%.
(b) How many slices is that per friend? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate says "0.5% is the same as 0.5, which is the same as a half." In your own words, explain (i) what mistake they have made, (ii) what 0.5% actually equals as a decimal and as a fraction, and (iii) how you'd convince them with one quick check. Use the phrase "% means out of 100" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Sale-sign battle
(a) 1/3 ≈ 0.33 (actually 0.333...); 33% = 0.33; 0.33 stays 0.33.
(b) Shop A's 1/3 is very slightly biggest (0.333... > 0.33), but all three are essentially the same discount — about a third off. In real life, the difference is less than 1c on a $100 jacket.
Take-away: fractions, decimals and percentages can look different but describe the same value.
1.2 — Phone battery
(a) 0.45 × 100 = 45%.
(b) 45% = 45/100. HCF of 45 and 100 is 5: 45 ÷ 5 = 9, 100 ÷ 5 = 20. Simplified: 9/20.
1.3 — Free-throw stats
(a) 7 out of 10 = 7/10 = 0.7 = 70%.
(b) 70% > 65%, so the basketballer has the higher first-half success rate (by 5 percentage points).
1.4 — Class survey
Dropped off: 25 − 9 − 11 = 5 students.
(a) Walk 9/25, bus 11/25, dropped off 5/25 (= 1/5).
(b) Each student = 100 ÷ 25 = 4%. So walk = 9 × 4 = 36%, bus = 11 × 4 = 44%, dropped off = 5 × 4 = 20%.
(c) Check: 36 + 44 + 20 = 100%. ✓
1.5 — Pizza party
(a) 1/4 = 1 ÷ 4 = 0.25, and 0.25 × 100 = 25%. So 1/4 = 0.25 = 25% — Lucas and Aiden are saying exactly the same thing.
(b) 1/4 of 8 slices = 8 ÷ 4 = 2 slices per friend.
2.1 — Explain your thinking (sample response)
The classmate has confused 0.5 with 0.5%. The symbol "%" means "out of 100", so 0.5% means 0.5 ÷ 100, not 0.5 on its own. As a decimal, 0.5% = 0.005, and as a fraction it's 5/1000, which simplifies to 1/200 — a very small slice, not half. A quick check: 1/2 of $100 is $50, but 0.5% of $100 is only 50c. They clearly can't both be right, which shows that 0.5% and 1/2 are completely different sizes.
Marking: 1 mark for spotting the mix-up; 1 mark for the correct decimal (0.005) or fraction (1/200); 1 mark for the quick check or sanity comparison; 1 mark for a clear, full-sentence explanation that uses "% means out of 100".