Ratio Notation and Relationships
Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios
Lesson
Set out your lesson
“Ratio Notation and Relationships means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Two colours of counters
- Paper for ratio or percent notation
Extra for the adult
Worked example. 2 red and 3 blue is the ratio 2:3.
Optional challenge. For Ratio Notation and Relationships, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Ratio Notation and Relationships, not mastery.
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Teaching approaches
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1 approach
Ratio Notation and Relationships 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 Ratio Notation and Relationships 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.
Family records and proof options
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Practice this concept
Start practiceRatio Notation and Relationships practice
Practice key ideas from Ratio Notation and Relationships.
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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 Ratio Notation and Relationships. 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
- Explain why 'for every 2 red beads there are 5 blue beads' can be written as 2:5 or as 2/5 of the blue count
- Identify the multiplicative relationship in a table of values (e.g. y is always 3 times x)
- Connect the ratio a:b to the fraction a/b and to the linear function y = (a/b)x
“Can your child explain why a ratio like 3:4 is really the same as the fraction ¾ — and show how that relationship connects to a straight-line graph through the origin?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Ratio & Proportion
- Age range
- Ages 12–14
Standards