Bar Models for Ratios
Represent ratio and proportion problems using bar models (rectangular strips divided into equal parts labelled with quantities) and tape diagrams (segmented strips showing part-to-part and part-to-whole relationships); use these visual models to set up and solve unequal sharing, scaling, and percentage problems — drawing the diagram first, then reading off the answer
Typical age: 9–12 years
“If your child needs to share 30 stickers between two friends in a 2:3 ratio, can they draw a bar model — splitting a strip into 5 equal boxes — and use it to work out each share without just guessing?”
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Needs first
Nothing — this is a great starting point!
Unlocks next
- Scale and similar shapes
Scale factor problems for similar shapes can be represented as ratio bar models
- Understanding fractionsREQUIRED
Unequal sharing problems are the canonical use case for tape diagrams — the visual model makes the structure of the problem transparent
- Ratio ProblemsREQUIRED
Solving relative-sizes problems is most reliably scaffolded by drawing a bar model to set up the relationship
- Dividing Quantities by RatioREQUIRED
Dividing a quantity in a given ratio is the natural next step from the bar model representation
- Calculating Percentages
Percentage-of-amount problems can be set up as bar models showing 100% divided into parts