---
title: "Moving between situations, diagrams and equations"
description: "Move fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents"
canonical: https://lightmysky.com/learn/mathematics/moving-between-situations-diagrams-and-equations-mt_dXq9VWm31W
source: https://lightmysky.com/learn/mathematics/moving-between-situations-diagrams-and-equations-mt_dXq9VWm31W.md
retrieved: 2026-09-02
---

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# Moving between situations, diagrams and equations

Move fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents

Subject: Mathematics · Area: Mathematical Thinking · Ages 7 to 8
Page: https://lightmysky.com/learn/mathematics/moving-between-situations-diagrams-and-equations-mt_dXq9VWm31W

## Ready when they can

- Write an equation with three-digit numbers to match a measurement or money word problem
- Draw a bar model to represent a fraction problem and use it to solve
- Explain how a number line diagram relates to the quantities in a word problem

## Lesson: Fractions: pictures, number lines, and equations

A story problem with numbers can be shown in more than one way. You can draw a picture, like a bar cut into equal parts. You can jump along a number line. Or you can write an equation with numbers and a fraction. All three show the same amounts, just in different forms.

*(drawing: Sam read 3 out of 4 equal parts of his book.)*

**Example.** A school trip costs $240. Parents have already paid 3/4 of that. Split $240 into 4 equal parts: 240 ÷ 4 = 60. Then take 3 of those parts: 3 × 60 = 180. Parents paid $180, and the bar model shows it as 3 shaded parts out of 4.

**Example.** The same $240 fits on a number line. Start at 0, and the whole cost sits at 240. Four equal hops of $60 reach it, and 3 hops land on $180. A number line also shows taking away: start at the amount you had and hop back by what you spend. Where you land is what is left.

When you switch between a picture, a number line, and an equation, check that they agree. If your bar is cut into 4 equal parts, your equation uses fourths and your number line hops in fourths too. Two pictures that cut the same amount into different-sized parts are not showing the same thing.

**Recap.** A diagram, a number line, and an equation can all show the same fraction problem, and when they match, you know your answer is right.

## Practice

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

## Needs first

- [Numbers on a number line](https://lightmysky.com/learn/mathematics/numbers-on-a-number-line-mt_19j_5AuuQI)
- [Connecting Representations](https://lightmysky.com/learn/mathematics/connecting-representations-mt_EBYGhd8X3x)
- [Fractions on a number line](https://lightmysky.com/learn/mathematics/fractions-on-a-number-line-mt_Kr3IyA6m-O)
- [Writing simple fractions](https://lightmysky.com/learn/mathematics/writing-simple-fractions-mt_MyGblah2yY)

## Opens up

- [Moving between diagrams and equations with fractions](https://lightmysky.com/learn/mathematics/moving-between-diagrams-and-equations-with-fractions-mt_3VmBdlAeOZ)