{"schemaVersion":1,"record":{"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}],"sections":[{"id":"principle","title":"How it works","body":"Add and remove objects"},{"id":"variants","title":"Variants","body":"### Variants\n\n<a id=\"family-18-branch-1\"></a>\n\n- Add and remove objects <a id=\"family-18-variant-1\"></a>\n- Combine groups <a id=\"family-18-variant-2\"></a>\n- Find differences <a id=\"family-18-variant-3\"></a>\n- Form equal groups <a id=\"family-18-variant-4\"></a>\n- Divide equally <a id=\"family-18-variant-5\"></a>\n- Divide with a remainder <a id=\"family-18-variant-6\"></a>\n- Restore an unknown component <a id=\"family-18-variant-7\"></a>\n- Balance an equality <a id=\"family-18-variant-8\"></a>\n- Choose an operation for a problem <a id=\"family-18-variant-9\"></a>\n- Build an expression <a id=\"family-18-variant-10\"></a>\n- Find alternative calculations <a id=\"family-18-variant-11\"></a>\n- Check through inverse operations <a id=\"family-18-variant-12\"></a>"},{"id":"example","title":"Design example","body":"Balance scales by adding and removing number blocks."},{"id":"context","title":"Context and limits","body":"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."}],"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"}}