---
key: mechanic/education--family-18
type: mechanic
id: education--family-18
lang: en
title: Arithmetic transformations
summary: >-
  Numbers or object groups change according to an arithmetic rule. The learner
  predicts and checks the operation’s result.
updatedAt: '2026-10-22'
status: active
url: 'https://gamemechanics.pro/en/knowledge/mechanic/education--family-18/'
jsonUrl: >-
  https://gamemechanics.pro/api/v1/knowledge/en/mechanic/education--family-18.json
markdownUrl: >-
  https://gamemechanics.pro/content/knowledge/en/mechanic/education--family-18.md
aliases: []
tags:
  - Educational games
  - 'Quantity, investigation and systems'
sourceIds:
  - source-19446e425a9a00b3
  - source-5b737ba9e639da22
sources:
  - id: source-19446e425a9a00b3
    title: '2048'
    url: 'https://github.com/gabrielecirulli/2048'
    verifiedAt: null
  - id: source-5b737ba9e639da22
    title: '2048'
    url: 'https://play2048.co/'
    verifiedAt: null
relations: []
placements:
  - catalogId: education
    id: family-18
    title: Educational games
    url: 'https://gamemechanics.pro/en/mechanics/education/#family-18'
    categoryIds:
      - systems
supersededBy: []
attributes:
  preview:
    updatedAt: '2026-10-22'
    title: Arithmetic transformations
    description: >-
      Numbers or object groups change according to an arithmetic rule. The
      learner predicts and checks the operation’s result.
    image:
      src: images/mechanics/systems-2048-original.webp
      width: 500
      height: 694
      game: '2048'
      sourceUrl: 'https://github.com/gabrielecirulli/2048'
      originalUrl: 'https://github.com/gabrielecirulli/2048/blob/master/index.html'
      credit: >-
        Gabriele Cirulli; screenshot of the unmodified original game, captured
        2026-10-22
      rights: >-
        © 2014 Gabriele Cirulli, MIT License. Screenshot converted to WebP on
        2026-10-22. License copy: images/mechanics/2048-license.txt.
      caption: The original 2048 after a sequence of normal moves
      alt: The original 2048 after a sequence of normal moves
      markers:
        - x: 86
          'y': 55
          label: Adjacent twos can be merged into a four
    tips:
      - Show what an operation does rather than only its notation.
    examples:
      - title: '2048'
        url: 'https://play2048.co/'
      - title: Original source
        url: 'https://github.com/gabrielecirulli/2048'
endsAt: null
provenance: >-
  Educational reference expanded from all 64 families and 749 variants of the
  original children-education taxonomy, with original editorial additions dated
  2026-10-20. Sources support specific methods and examples, not the entire
  classification or its effectiveness.
license: CC-BY-4.0
codeLicense: MIT
attribution: gamemechanics.pro contributors
catalogKey: catalog/education
---
# Arithmetic transformations

id: education--family-18
type: mechanic
key: mechanic/education--family-18
lang: en
status: active
url: https://gamemechanics.pro/en/knowledge/mechanic/education--family-18/

Numbers or object groups change according to an arithmetic rule. The learner predicts and checks the operation’s result.

## At a glance

![The original 2048 after a sequence of normal moves](https://gamemechanics.pro/images/mechanics/systems-2048-original.webp)

[2048](https://github.com/gabrielecirulli/2048) · © 2014 Gabriele Cirulli, MIT License. Screenshot converted to WebP on 2026-10-22. License copy: images/mechanics/2048-license.txt.

1. Adjacent twos can be merged into a four

- Show what an operation does rather than only its notation.

- [2048](https://play2048.co/)
- [Original source](https://github.com/gabrielecirulli/2048)

## How it works

Add and remove objects

## Variants

### Variants

<a id="family-18-branch-1"></a>

- Add and remove objects <a id="family-18-variant-1"></a>
- Combine groups <a id="family-18-variant-2"></a>
- Find differences <a id="family-18-variant-3"></a>
- Form equal groups <a id="family-18-variant-4"></a>
- Divide equally <a id="family-18-variant-5"></a>
- Divide with a remainder <a id="family-18-variant-6"></a>
- Restore an unknown component <a id="family-18-variant-7"></a>
- Balance an equality <a id="family-18-variant-8"></a>
- Choose an operation for a problem <a id="family-18-variant-9"></a>
- Build an expression <a id="family-18-variant-10"></a>
- Find alternative calculations <a id="family-18-variant-11"></a>
- Check through inverse operations <a id="family-18-variant-12"></a>

## Design example

Balance scales by adding and removing number blocks.

## Context and limits

A mechanic map for games with explicit learning goals, from first encounters with a topic to professional practice. It covers children, teenagers and adults; choose subject, difficulty, context and controls for the learner. Player actions, subject content, instructional support and assessment are distinct layers. Scores and game completion alone do not establish mastery or skill transfer.

## Connected materials


## Sources and provenance

Educational reference expanded from all 64 families and 749 variants of the original children-education taxonomy, with original editorial additions dated 2026-10-20. Sources support specific methods and examples, not the entire classification or its effectiveness.

- [2048](https://github.com/gabrielecirulli/2048) (id: source-19446e425a9a00b3)
- [2048](https://play2048.co/) (id: source-5b737ba9e639da22)

CC-BY-4.0 · gamemechanics.pro contributors