---
title: "Bar Models for Ratios"
description: "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-who"
canonical: https://lightmysky.com/learn/mathematics/bar-models-for-ratios-mt_ePXg_XyCKU
source: https://lightmysky.com/learn/mathematics/bar-models-for-ratios-mt_ePXg_XyCKU.md
retrieved: 2026-10-19
---

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# 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

Subject: Mathematics · Area: Ratio & Proportion · Ages 9 to 12
Page: https://lightmysky.com/learn/mathematics/bar-models-for-ratios-mt_ePXg_XyCKU

## Ready when they can

- 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

## Lesson: Bar Models for Ratios

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.

*(drawing: Five equal boxes, each worth £4. Ana takes 3 boxes, Ben takes 2 boxes.)*

**Example.** 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.

**Tip.** 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.

**Recap.** Draw the ratio as equal boxes, find what one box is worth, then multiply to read off each share.

## Practice

17 questions on this page, each with its working shown.

## Needs first

- [Modelling with multiplication and fractions](https://lightmysky.com/learn/mathematics/modelling-with-multiplication-and-fractions-mt_K3R0yaHVcx)

## Opens up

- [Scale and similar shapes](https://lightmysky.com/learn/mathematics/scale-and-similar-shapes-mt_2OtRUM_0zW)
- [Unequal sharing and grouping](https://lightmysky.com/learn/mathematics/unequal-sharing-and-grouping-mt_FnUJMXPUZX)
- [Ratio Problems](https://lightmysky.com/learn/mathematics/ratio-problems-mt_h0gJcSuwdL)
- [Dividing Quantities by Ratio](https://lightmysky.com/learn/mathematics/dividing-quantities-by-ratio-mt_nOCPx5qw0Z)
- [Calculating percentages](https://lightmysky.com/learn/mathematics/calculating-percentages-mt_PNSyfH56eQ)