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
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1858 concepts · 9 subjects
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Teaching approaches
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1 approach
Proportion means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Two colours of counters; Paper for ratio or percent notation. 1. Say the goal of Proportion in plain words once. 2. Adult shows 2 red : 3 blue and says the ratio (or 40% of 10). 3. Child builds three ratios or percentage amounts and records each notation. 4. Fresh check: one fresh ratio or percent reading. Record and stop. Done: three correct ratio/percent records. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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Practice this concept
Start practiceProportion practice
Practice key ideas from Proportion.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
PhET Interactive Simulations · Practice link — not the full lesson
Proportion Playground
Before you open · source notes
Proportion Playground supports hands-on exploration for Proportion. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Proportion Playground.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- 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)
“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)?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Ratio & Proportion
- Age range
- Ages 12–14
Standards