Mathematics Ratio & Proportionusually ages 12–14

Proportion

Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations

How to tell they’ve got it

Tick these off as you see them — no test required.

Identify whether a real-world relationship is direct or inverse proportion and justify the choice
Set up and solve a direct-proportion equation (e.g. if 4 pens cost £6, find the cost of 10)
Sketch graphs showing direct proportion (straight line through origin) and inverse proportion (curve)

🖨 Print this page to keep the checklist — it prints beautifully.

Try this together

Does your child understand the difference between quantities that grow together at the same rate (direct proportion) and ones where one goes up as the other goes down — like more workers meaning fewer days to finish a job (inverse proportion)?

Where this sits on the map

Stuck here? Check the skills it builds on first. Confident? Here’s what it unlocks.

Builds on

Dividing Quantities by Ratioages 11–13Proportion problems require dividing quantities in given ratios

Proportion Graphsages 11–14Direct and inverse proportion with graphical representations requires reading and plotting proportion graphs (y = kx through origin)

Proportional Reasoning Vocabularyages 11–14Direct and inverse proportion require 'direct proportion' and 'inverse proportion' as precisely understood contrasting terms

Ratio Notation and Relationshipsages 12–14Direct/inverse proportion requires understanding multiplicative relationships

Linear Function Graphsages 12–14Graphical representations of proportion connect to linear graphs (y = kx through origin)

Proportionthis skill · ages 12–14

Unlocks

Compound Unitsages 11–14Speed, density, and unit pricing are applications of direct/inverse proportion

solid = must come firstdashed = helps

Curriculum alignment

Candidate matches to official curriculum codes — machine-suggested, unreviewed (v0.1).

This skill sits beyond Year 6 in the Australian Curriculum, so no F–6 code is matched. It also sits beyond the NSW K–6 syllabuses. It also sits beyond Level 6 in the Victorian Curriculum.

Nearby on the map

Percentages (age 12+)ages 12–14 Ratio Notation and Relationshipsages 12–14 Compound Unitsages 11–14 Dividing Quantities by Ratioages 11–13

All Ratio & Proportion skills →