---
title: "Modelling Situations with Formulae and Graphs"
description: "Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representati"
canonical: https://lightmysky.com/learn/mathematics/modelling-situations-with-formulae-and-graphs-mt_z5iwdZyeDr
source: https://lightmysky.com/learn/mathematics/modelling-situations-with-formulae-and-graphs-mt_z5iwdZyeDr.md
retrieved: 2026-09-12
---

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# Modelling Situations with Formulae and Graphs

Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations

Subject: Mathematics · Area: Algebra · Ages 11 to 13
Page: https://lightmysky.com/learn/mathematics/modelling-situations-with-formulae-and-graphs-mt_z5iwdZyeDr

## Ready when they can

- Translate a word problem or real-world situation into an algebraic expression or formula
- Construct a table of values from an algebraic rule
- Plot the corresponding graph and interpret it in the context of the problem

## Lesson: Turning situations into formulas and graphs

A formula is a short rule written with letters and numbers. It lets you turn a real situation into maths you can calculate. If one quantity depends on another, like cost depending on distance, you can write that link as a formula.

**Example.** A taxi charges £2 just to start the ride, plus £1.50 for every mile you travel. Let m stand for the number of miles. The total cost is c = 2 + 1.5m. Check it for 4 miles: c = 2 + 1.5 × 4 = 8, so the ride costs £8.

*(drawing: Each bar is a value from the table for c = 2 + 1.5m: put in a number of miles, get out a cost.)*

**Tip.** To draw the graph, plot each pair of numbers as a point: miles across, cost up. The points form a straight line because the cost rises by the same £1.50 each time. Where the line crosses the cost axis shows the starting fee, and how steep it is shows the price per mile.

**Recap.** A word problem becomes a formula, the formula becomes a table, and the table becomes a graph you can read.

## Practice

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

## Needs first

- [Coordinates (age 11+)](https://lightmysky.com/learn/mathematics/coordinates-age-11-mt_hVpGOEz2kG)
- [Algebraic Notation](https://lightmysky.com/learn/mathematics/algebraic-notation-mt_KwdjWEmMNo)

## Opens up

- [Algebraic Proof with Odd, Even and Consecutive Numbers](https://lightmysky.com/learn/mathematics/algebraic-proof-with-odd-even-and-consecutive-numbers-mt_p9bajOC17q)
- [Linear Function Graphs](https://lightmysky.com/learn/mathematics/linear-function-graphs-mt_WBdHkc2HTf)