Learning pack · IGCSE handout

Proportion

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Proportion problems scale quantities. Direct and inverse proportion equations let you find the constant $k$ from one pair of values.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 40_proportion_handout.pdf · 40_proportion_handout_answers.pdf

Full topic summary

Proportion problems scale quantities. Direct and inverse proportion equations let you find the constant $k$ from one pair of values.

Key learning points

Direct: $y=kx$ ; inverse: $y=\frac{k}{x}$ .
Find $k$ from given values, then predict new values.
Tables of values: check ratios $y/x$ (direct) or products $xy$ (inverse).

Worked example 1 — Direct proportion

$y\propto x$ . When $x=4$ , $y=10$ . Find $y$ when $x=6$ .

Working

y=15

$y=kx$ with $k=2.5$ .

Worked example 2 — Inverse proportion

$y\propto\tfrac{1}{x}$ . When $x=2$ , $y=12$ . Find $y$ when $x=8$ .

Working

y=3

$xy$ constant.

Worked example 3 — Recipe scaling

Recipe for 4 needs $300\,\mathrm{g}$ . For 10?

Working

750\,\mathrm{g}

Scale by $\tfrac{10}{4}$ .

🎬 Topic videos

Golden Ratio Song - Numberphile
Numberphile · 3 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Golden Ratio BURN (Internet Beef) - Numberphile
Numberphile · 11 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Math Antics - Proportions
Math Antics · 11 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
The golden ratio spiral: visual infinite descent
Mathologer · 22 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Introduction to Ratios
Eddie Woo · 4 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Setting up proportions to solve word problems | 7th grade | Khan Academy
Khan Academy · 6 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.

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Browse the hub Learning Packs & Summary, or open the compact Proportion summary.