---
title: "Connecting Representations"
description: "Move between real-world situations, drawings, and number sentences, explaining how each representation connects to the others (quantitative reasoning)"
canonical: https://lightmysky.com/learn/mathematics/connecting-representations-mt_EBYGhd8X3x
source: https://lightmysky.com/learn/mathematics/connecting-representations-mt_EBYGhd8X3x.md
retrieved: 2026-10-19
---

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# Connecting Representations

Move between real-world situations, drawings, and number sentences, explaining how each representation connects to the others (quantitative reasoning)

Subject: Mathematics · Area: Mathematical Thinking · Ages 6 to 7
Page: https://lightmysky.com/learn/mathematics/connecting-representations-mt_EBYGhd8X3x

## Ready when they can

- Write a number sentence (e.g. 14 + 5 = 19) to match a word problem and explain the connection
- Draw a bar model or part-whole diagram to represent a problem, then solve using the diagram
- Translate between a concrete model and a symbolic equation, describing what each number represents

## Lesson: Stories, pictures, and number sentences

A math problem can be told three ways: as a real story, as a picture, and as a number sentence. All three tell the same story. Learning to move between them helps you check your thinking and explain your answer.

*(drawing: 3 stars and 4 more stars make 7 stars. That matches the number sentence 3 + 4 = 7.)*

**Example.** Ben has 5 blocks. His sister gives him 4 more blocks. Story: Ben starts with some blocks and gets more. Picture: draw 5 blocks, then 4 more blocks next to them. Number sentence: 5 + 4 = 9. All three show the same 9 blocks.

Check your work by matching the three tellings against each other. Look at each number in your sentence and point to it in the picture, then find it in the story. If a number in your sentence is nowhere in the picture, that is the number to fix. Taking away works the same way: things crossed out in a picture are the ones that went, so the sentence that matches uses a take-away, not an add.

**Recap.** A real story, a picture, and a number sentence can show the same math idea. Check that all three match.

## Practice

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

## Needs first

- [Reading +, −, and = symbols](https://lightmysky.com/learn/mathematics/reading-and-symbols-mt_8RmpkDxT9L)
- [Inverse: addition undoes subtraction](https://lightmysky.com/learn/mathematics/inverse-addition-undoes-subtraction-mt_ehGS_uVSJv)
- [Real-World to Maths Connections](https://lightmysky.com/learn/mathematics/real-world-to-maths-connections-mt_IM1G_7QzTa)

## Opens up

- [Moving between situations, diagrams and equations](https://lightmysky.com/learn/mathematics/moving-between-situations-diagrams-and-equations-mt_dXq9VWm31W)