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
What a learner can do afterwards
- Draw a bar model to represent a ratio problem: e.g. sharing £20 in the ratio 3:2 by drawing 5 equal blocks
- Use a bar model to solve a proportion problem and explain each step
- Compare bar models with other representations (tables, double number lines) and explain when each is most useful
1 · Read
A bar model is a way to draw a ratio problem so you can see it before you solve it. You draw one long strip and split it into equal boxes, one box for each part of the ratio.
Grace and Tom share 18 sweets in the ratio 4:5. First, draw a strip with 4 + 5 = 9 equal boxes. Next, work out one box: 18 ÷ 9 = 2 sweets. Then read off each share: Grace gets 4 boxes, so 4 × 2 = 8 sweets. Tom gets 5 boxes, so 5 × 2 = 10 sweets.
Always add the numbers in the ratio first to find the total number of boxes. Draw every box the same size, since each one stands for an equal part.
Draw the ratio as equal boxes, find what one box is worth, then multiply to read off each share.
More to read
Bar Model for Problems on Ratio Rate Direct Proportion
A bar model turns a ratio into blocks. Sharing 20 pounds in the ratio 3:2 means drawing 5 equal blocks, since 3 + 2 = 5. Each block is worth 20 / 5 = 4 pounds. The larger share takes 3 blocks (12 pounds) and the smaller takes 2 (8 pounds). Counting blocks first stops the classic error of splitting 20 into 3 and 2 directly.
5.4 Ratios and Proportions
Proportions hide in recipes and mixtures. A bar with 2 blocks of juice to 3 blocks of water splits any total into fifths. For 10 litres, each block is 2 litres, giving 4 litres of juice and 6 of water. Labelling each block with its value connects the picture to the arithmetic. Every block must be equal or the model lies.
Key ideas: comparing ratio relationships
Trickier problems give a difference instead of a total. With flour and sugar in the ratio 5:3 and 40 g more flour, the gap is 2 blocks, so one block is 20 g. Flour takes 5 blocks (100 g) and sugar 3 blocks (60 g). Bar models, tables and double number lines all show the same proportion. Bars suit sharing, number lines suit journeys: pick the picture that fits.
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2 · Watch
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Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.