---
title: "Real-World Mathematical Modelling"
description: "Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations"
canonical: https://lightmysky.com/learn/mathematics/real-world-mathematical-modelling-mt_yqZiX6vS7D
source: https://lightmysky.com/learn/mathematics/real-world-mathematical-modelling-mt_yqZiX6vS7D.md
retrieved: 2026-10-19
---

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# Real-World Mathematical Modelling

Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations

Subject: Mathematics · Area: Mathematical Thinking · Ages 10 to 11
Page: https://lightmysky.com/learn/mathematics/real-world-mathematical-modelling-mt_yqZiX6vS7D

## Ready when they can

- Choose a bar model or double number line to represent a ratio problem and solve it
- Model a volume problem with a labelled diagram, apply the formula, and interpret the result in context
- Determine whether a measurement answer should be rounded and to what degree of accuracy

## Lesson: Modelling real problems with ratio, volume, and scale

When you solve a real problem, you often have to choose how to picture it first. A bar model splits a ratio into equal parts. A double number line lines up two related amounts so you can see how they grow together. Pick whichever picture matches the problem, then solve it.

*(drawing: This bar model splits paint into 2 parts blue and 5 parts white. Each part stands for the same amount.)*

**Example.** A fish tank is 40 cm long, 20 cm wide, and 25 cm tall. To find its volume, multiply length by width by height: 40 x 20 x 25 = 20,000 cm cubed. Since 1000 cm cubed equals 1 litre, that tank holds 20 litres of water.

*(drawing: A double number line puts two lines side by side, one for cookies and one for eggs. Each jump of 2 eggs matches a jump of 3 cookies, so the ratio stays the same.)*

**Tip.** Not every answer should be rounded the same way. Money often rounds to the nearest cent, while a tank's volume might round to the nearest litre. Finish your calculation first, then round to match what you are measuring.

**Recap.** To model a real problem, pick a bar model, double number line, or formula, solve it, then round your answer to match what you are measuring.

## Practice

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

## Needs first

- [Scale and similar shapes](https://lightmysky.com/learn/mathematics/scale-and-similar-shapes-mt_2OtRUM_0zW)
- [Real-World Maths Modelling](https://lightmysky.com/learn/mathematics/real-world-maths-modelling-mt_8xVHooT4aI)
- [Volume of cuboids](https://lightmysky.com/learn/mathematics/volume-of-cuboids-mt_nTL-owFJTF)

## Opens up

- [Simple formulae](https://lightmysky.com/learn/mathematics/simple-formulae-mt_3qrCtdoVAU)
- [Choosing a Model and Naming What It Ignores](https://lightmysky.com/learn/mathematics/choosing-a-model-and-naming-what-it-ignores-mt_UtK9aauJ6e)