Mathematics • Year 8 • Unit 1 • Lesson 18
Ratio in the Real World
Use ratio thinking on maps, recipes, model cars, hospital saline solutions and house plans. Then explain in your own words why "keeping the same ratio" is the rule that connects them all.
1. Word problems
Each problem uses the lesson's idea: when something is "in the same ratio", every part scales by the same multiplier. Show your working — a final answer with no working only earns half marks.
1.1 — Hiking map. Your hiking map has scale 1 : 25 000. You measure 8 cm between the campsite and the lookout.
(a) What does 1 cm on the map represent in real life (in metres)?
(b) How far is the real walk in kilometres? 3 marks
1.2 — Cordial party mix. A cordial recipe uses 1 part syrup to 6 parts water. For a party, you want to make 560 mL of cordial.
(a) How much syrup do you need?
(b) How much water? 3 marks
1.3 — Cookie recipe. A recipe for 12 cookies uses 300 g of flour. You want to bake 20 cookies for a stall, keeping the same ratio.
(a) Find the scale factor (20 ÷ 12, as a fraction or decimal).
(b) Find the amount of flour needed for 20 cookies. 3 marks
1.4 — Hospital saline. A nurse needs to prepare a saline solution in the ratio 9 parts water to 1 part salt by volume. She starts with 360 mL of distilled water.
(a) How much salt should she add to keep the ratio?
(b) What's the total volume of the finished solution? 3 marks
1.5 — House plan. A house plan has scale 1 : 100. The lounge room measures 5 cm by 7 cm on the plan.
(a) What are the real-life dimensions of the lounge room, in metres?
(b) What is the real-life floor area, in square metres? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate says "A recipe for 4 people uses 320 g of flour. To make it for 7 people I just add 3 lots of flour — so 320 + 3 × 320/4 = 560 g." Then they add "But I could also just add half-as-much-again because 7 is roughly double 4, so 320 + 160 = 480 g would also work."
In your own words, explain (i) which method gives the right answer, (ii) why the other method is wrong, and (iii) how the "scale factor" idea makes both of their methods unnecessary. Use the phrase "the same ratio" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Hiking map 1 : 25 000, 8 cm
(a) 1 cm = 25 000 cm = 250 m.
(b) 8 cm × 250 m/cm = 2000 m = 2 km.
1.2 — Cordial 1 : 6, total 560 mL
Total parts = 7. 1 part = 560 ÷ 7 = 80 mL.
(a) Syrup = 1 × 80 = 80 mL.
(b) Water = 6 × 80 = 480 mL. Check: 80 + 480 = 560 ✓.
1.3 — Cookie recipe (12 → 20)
(a) Scale factor = 20 ÷ 12 = 5/3 (≈ 1.667).
(b) Flour = 300 × 5/3 = 500 g.
1.4 — Saline 9 water : 1 salt, 360 mL water
Water (9 parts) = 360 mL, so 1 part = 40 mL.
(a) Salt = 1 × 40 = 40 mL.
(b) Total = 360 + 40 = 400 mL.
1.5 — House plan 1 : 100, 5 cm × 7 cm
(a) 1 cm on plan = 100 cm = 1 m in real life. Lounge = 5 m × 7 m.
(b) Floor area = 5 × 7 = 35 m².
2.1 — Explain your thinking (sample response)
The first method (560 g) is correct. The classmate started with 320 g for 4 people, worked out that each person needs 80 g (320 ÷ 4 = 80), then added an extra 3 × 80 = 240 g for the 3 extra people, giving 560 g. This keeps the same ratio of 80 g flour per person.
The second method (480 g) is wrong. They said "7 is roughly double 4", but doubling 4 gives 8, not 7. By only adding 160 g, they end up at 480 g / 7 people ≈ 68.6 g per person, which is LESS than the original 80 g per person — so the recipe is no longer "the same ratio".
The fastest "scale factor" method: 7 ÷ 4 = 1.75. Then 320 × 1.75 = 560 g. This skips both of the classmate's working methods and instantly keeps the same ratio.
Marking: 1 mark for naming the correct method (560 g); 1 mark for explaining why the other method is wrong; 1 mark for describing the scale-factor shortcut; 1 mark for using "the same ratio" in a full-sentence explanation.