Mathematics • Year 7 • Unit 1 • Lesson 12
Ratios in the Real World
Use ratios to scale recipes, share prize money fairly, mix paint colours, and check map scales. Ratios are how the real world describes "for every X of this, there is Y of that".
1. Word problems
Each problem uses the ratio ideas from Lesson 12: simplifying, dividing in a ratio, or finding a missing value. Show your working — answers with no working only earn half marks.
1.1 — Pancake recipe. A pancake recipe for 4 people uses 2 cups of flour and 3 cups of milk.
(a) Write the ratio of flour to milk.
(b) How much flour and milk are needed to feed 10 people? 3 marks
1.2 — Sharing prize money. Three friends won $480 in a trivia competition. They agree to share in the ratio 1:2:3 based on how many questions each answered.
(a) Find the value of one part.
(b) How much does each friend receive? 3 marks
1.3 — Mixing paint. To make a particular shade of green, mix yellow and blue paint in the ratio 4:3. You have 8 L of yellow paint.
(a) How much blue paint do you need?
(b) How much green paint will you have in total? 3 marks
1.4 — School population. In a Year 7 class, the ratio of boys to girls is 2:3. There are 30 students in total.
(a) How many boys are there?
(b) How many girls?
(c) If 4 more boys join the class, what is the new ratio of boys to girls in simplest form? 3 marks
1.5 — Map scale. On a map of the local park, the scale ratio is 1:500 (1 cm on the map represents 500 cm in real life).
(a) If the pond is 4 cm across on the map, how wide is it in real life? Give your answer in metres.
(b) A path is 75 m long in real life. How long does it appear on the map (in cm)? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate says "If we share $40 in the ratio 2:3, then the first person gets $2 and the second person gets $3 — because that's what the ratio says." In your own words, explain (i) why this is wrong, (ii) what the correct method is using "total parts" and "one part", and (iii) the correct shares with a check. End by writing one sentence about why the total-parts method works for any total amount, not just for one that happens to equal the sum of the ratio numbers.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Pancake recipe
(a) Flour : milk = 2:3.
(b) 10 people is 10 ÷ 4 = 2.5 × the recipe. Flour = 2 × 2.5 = 5 cups. Milk = 3 × 2.5 = 7.5 cups. Check ratio: 5:7.5 = 2:3 (× 2.5 both sides) ✓.
1.2 — Sharing prize money
(a) Total parts = 1 + 2 + 3 = 6. One part = $480 ÷ 6 = $80.
(b) Friend 1 = 1 × $80 = $80. Friend 2 = 2 × $80 = $160. Friend 3 = 3 × $80 = $240. Check: $80 + $160 + $240 = $480 ✓.
1.3 — Mixing paint
(a) 4:3 = 8:x → 4x = 3 × 8 = 24 → x = 6 L of blue.
(b) Total green = 8 + 6 = 14 L.
1.4 — School population
Parts = 5; one part = 30 ÷ 5 = 6.
(a) Boys = 2 × 6 = 12.
(b) Girls = 3 × 6 = 18. Check: 12 + 18 = 30 ✓.
(c) After 4 more boys: 16 boys, 18 girls. New ratio = 16:18 = 8:9 (÷ 2).
1.5 — Map scale
(a) 4 cm × 500 = 2000 cm = 20 m.
(b) 75 m = 7500 cm. Map length = 7500 ÷ 500 = 15 cm.
2.1 — Explain your thinking (sample response)
The classmate is wrong because the ratio numbers tell you how the total is split into parts, not the dollar amount each person receives. You can't just hand over $2 and $3 — that's only $5, but the total is $40.
The correct method has three steps: (1) Add the ratio parts to get total parts (here 2 + 3 = 5 parts). (2) Divide the total amount by total parts to find the value of one part ($40 ÷ 5 = $8 per part). (3) Multiply each ratio number by the value of one part: first share = 2 × $8 = $16; second share = 3 × $8 = $24. Check: $16 + $24 = $40 ✓.
The total-parts method works for any total because we always scale the parts by the same factor — the value of one part absorbs whatever the total happens to be.
Marking: 1 for spotting that $2+$3 doesn't equal $40; 1 for naming the 3-step method; 1 for correct shares $16 and $24; 1 for explaining the scaling idea.