CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Cuisenaire rods - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"472c9950-0d37-4621-9101-d6f52950bf2a","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Cuisenaire_rods","wgTitle":"Cuisenaire rods","wgCurRevisionId":1258723404,"wgRevisionId":1258723404,"wgArticleId":1549329,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles with short description","Short description matches Wikidata","EngvarB from February 2024","Webarchive template wayback links","Commons category link is on Wikidata","Belgian inventions","Language education materials","Mathematical manipulatives","Lists of shapes"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Cuisenaire_rods","wgRelevantArticleId":1549329,"wgIsProbablyEditable":true, "wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":20000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q508933","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics": true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init", "ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.quicksurveys.init","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Cuisenaire_ten.JPG/1200px-Cuisenaire_ten.JPG"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="608"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Cuisenaire_ten.JPG/800px-Cuisenaire_ten.JPG"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="405"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Cuisenaire_ten.JPG/640px-Cuisenaire_ten.JPG"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="324"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Cuisenaire rods - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Cuisenaire_rods"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Cuisenaire_rods&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Cuisenaire_rods"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Cuisenaire_rods rootpage-Cuisenaire_rods skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Cuisenaire+rods" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Cuisenaire+rods" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Cuisenaire+rods" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Cuisenaire+rods" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rods" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rods"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Rods</span> </div> </a> <ul id="toc-Rods-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Use_in_mathematics_teaching" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Use_in_mathematics_teaching"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Use in mathematics teaching</span> </div> </a> <ul id="toc-Use_in_mathematics_teaching-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_Silent_Way" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#The_Silent_Way"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>The Silent Way</span> </div> </a> <ul id="toc-The_Silent_Way-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_coloured_rods" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_coloured_rods"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Other coloured rods</span> </div> </a> <ul id="toc-Other_coloured_rods-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Cuisenaire rods</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 14 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-14" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">14 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%B6%D8%A8%D8%A7%D9%86_%D9%83%D9%88%D9%8A%D8%B2%D9%86%D9%8A%D8%B1" title="قضبان كويزنير – Arabic" lang="ar" hreflang="ar" data-title="قضبان كويزنير" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Reglets_num%C3%A8rics" title="Reglets numèrics – Catalan" lang="ca" hreflang="ca" data-title="Reglets numèrics" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Cuisenaire-St%C3%A4bchen" title="Cuisenaire-Stäbchen – German" lang="de" hreflang="de" data-title="Cuisenaire-Stäbchen" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Regletas_de_Cuisenaire" title="Regletas de Cuisenaire – Spanish" lang="es" hreflang="es" data-title="Regletas de Cuisenaire" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Cuisenaire_zotzak" title="Cuisenaire zotzak – Basque" lang="eu" hreflang="eu" data-title="Cuisenaire zotzak" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/R%C3%A9glettes_Cuisenaire" title="Réglettes Cuisenaire – French" lang="fr" hreflang="fr" data-title="Réglettes Cuisenaire" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%80%B4%EC%A6%88%EB%84%A4%EC%96%B4_%EB%A7%89%EB%8C%80" title="퀴즈네어 막대 – Korean" lang="ko" hreflang="ko" data-title="퀴즈네어 막대" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Regoli_Cuisenaire" title="Regoli Cuisenaire – Italian" lang="it" hreflang="it" data-title="Regoli Cuisenaire" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%91%D7%93%D7%99%D7%93%D7%99%D7%9D" title="בדידים – Hebrew" lang="he" hreflang="he" data-title="בדידים" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Cuisenaire-rudak" title="Cuisenaire-rudak – Hungarian" lang="hu" hreflang="hu" data-title="Cuisenaire-rudak" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Klocki_Cuisenaire%E2%80%99a" title="Klocki Cuisenaire’a – Polish" lang="pl" hreflang="pl" data-title="Klocki Cuisenaire’a" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%81%E0%AE%9A%E0%AF%87%E0%AE%A9%E0%AF%88%E0%AE%B0%E0%AF%87_%E0%AE%95%E0%AF%8B%E0%AE%B2%E0%AF%8D%E0%AE%95%E0%AE%B3%E0%AF%8D" title="குசேனைரே கோல்கள் – Tamil" lang="ta" hreflang="ta" data-title="குசேனைரே கோல்கள்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%B0%D0%BB%D0%B8%D1%87%D0%BA%D0%B8_%D0%9A%D1%8E%D1%97%D0%B7%D0%B5%D0%BD%D0%B5%D1%80%D0%B0" title="Палички Кюїзенера – Ukrainian" lang="uk" hreflang="uk" data-title="Палички Кюїзенера" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8F%A4%E6%B0%8F%E7%A7%AF%E6%9C%A8" title="古氏积木 – Chinese" lang="zh" hreflang="zh" data-title="古氏积木" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q508933#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Cuisenaire_rods" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Cuisenaire_rods" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Cuisenaire_rods"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Cuisenaire_rods&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Cuisenaire_rods&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Cuisenaire_rods"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Cuisenaire_rods&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Cuisenaire_rods&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Cuisenaire_rods" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Cuisenaire_rods" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Cuisenaire_rods&oldid=1258723404" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Cuisenaire_rods&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Cuisenaire_rods&id=1258723404&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FCuisenaire_rods"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FCuisenaire_rods"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Cuisenaire_rods&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Cuisenaire_rods&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Cuisenaire_rods" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q508933" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Learning aids</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cuisenaire_ten.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Cuisenaire_ten.JPG/220px-Cuisenaire_ten.JPG" decoding="async" width="220" height="111" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Cuisenaire_ten.JPG/330px-Cuisenaire_ten.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Cuisenaire_ten.JPG/440px-Cuisenaire_ten.JPG 2x" data-file-width="3895" data-file-height="1974" /></a><figcaption>Cuisenaire rods illustrating the <a href="/wiki/Divisor" title="Divisor">factors</a> of ten</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Amicable_numbers_rods_220_and_284.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Amicable_numbers_rods_220_and_284.png/220px-Amicable_numbers_rods_220_and_284.png" decoding="async" width="220" height="282" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Amicable_numbers_rods_220_and_284.png/330px-Amicable_numbers_rods_220_and_284.png 1.5x, //upload.wikimedia.org/wikipedia/commons/e/e4/Amicable_numbers_rods_220_and_284.png 2x" data-file-width="393" data-file-height="504" /></a><figcaption>A demonstration the first pair of <a href="/wiki/Amicable_numbers" title="Amicable numbers">amicable numbers</a>, (220,284)</figcaption></figure><p><b>Cuisenaire rods</b> are mathematics learning aids for pupils that provide an interactive, hands-on<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> way to explore mathematics and learn mathematical concepts, such as the four basic <a href="/wiki/Arithmetic" title="Arithmetic">arithmetical</a> operations, working with fractions and finding <a href="/wiki/Divisors" class="mw-redirect" title="Divisors">divisors</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In the early 1950s, <a href="/wiki/Caleb_Gattegno" title="Caleb Gattegno">Caleb Gattegno</a> popularised this set of coloured number rods created by <a href="/wiki/Georges_Cuisenaire" title="Georges Cuisenaire">Georges Cuisenaire</a> (1891–1975), a <a href="/wiki/Belgium" title="Belgium">Belgian</a> <a href="/wiki/Primary_school" title="Primary school">primary school</a> teacher, who called the rods <i>réglettes</i>. </p><p>According to Gattegno, "Georges Cuisenaire showed in the early 1950s that pupils who had been taught traditionally, and were rated 'weak', took huge strides when they shifted to using the material. They became 'very good' at traditional arithmetic when they were allowed to manipulate the rods."<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cuisenaire_rods&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The educationalists <a href="/wiki/Maria_Montessori" title="Maria Montessori">Maria Montessori</a> and <a href="/wiki/Friedrich_Fr%C3%B6bel" title="Friedrich Fröbel">Friedrich Fröbel</a> had used rods to represent numbers,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> but it was Georges Cuisenaire who introduced the rods that were to be used across the world from the 1950s onwards. In 1952, he published <i>Les nombres en couleurs</i>, Numbers in Color, which outlined their use. Cuisenaire, a violin player, taught music as well as arithmetic in the primary school in <a href="/wiki/Thuin" title="Thuin">Thuin</a>. He wondered why children found it easy and enjoyable to pick up a tune and yet found mathematics neither easy nor enjoyable. These comparisons with music and its representation led Cuisenaire to experiment in 1931 with a set of ten rods sawn out of wood, with lengths from 1 cm (0.4 in) to 10 cm (4 in). He painted each length of rod a different colour and began to use these in his teaching of arithmetic. The invention remained almost unknown outside the village of Thuin for about 23 years until, in April 1953, British mathematician and mathematics education specialist <a href="/wiki/Caleb_Gattegno" title="Caleb Gattegno">Caleb Gattegno</a> was invited to see pupils using the rods in Thuin. At this point he had already founded the <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060515004941/http://www.irdp.ch/cieaem/">International Commission for the Study and Improvement of Mathematics Education (CIEAEM)</a> and the <a href="/wiki/Association_of_Teachers_of_Mathematics" title="Association of Teachers of Mathematics">Association of Teachers of Mathematics</a>, but this marked a turning point in his understanding: </p> <blockquote><p>Then, Cuisenaire took us to a table in one corner of the room where pupils were standing round a pile of colored sticks and doing sums which seemed to me to be unusually hard for children of that age. At this sight, all other impressions of the surrounding vanished, to be replaced by a growing excitement. After listening to Cuisenaire asking his first and second grade pupils questions and hearing their answers immediately and with complete self-assurance and accuracy, the excitement then turned into irrepressible enthusiasm and a sense of illumination.<sup id="cite_ref-FTTOM3_6-0" class="reference"><a href="#cite_note-FTTOM3-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>Gattegno named the rods "Cuisenaire rods" and began trialing and popularizing them. Seeing that the rods allowed pupils "to expand on their latent mathematical abilities in a creative and enjoyable fashion", Gattegno's pedagogy shifted radically as he began to stand back and allow pupils to take a leading role: </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cuisenaire_rod_experimentation.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Cuisenaire_rod_experimentation.jpg/220px-Cuisenaire_rod_experimentation.jpg" decoding="async" width="220" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Cuisenaire_rod_experimentation.jpg/330px-Cuisenaire_rod_experimentation.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Cuisenaire_rod_experimentation.jpg/440px-Cuisenaire_rod_experimentation.jpg 2x" data-file-width="4480" data-file-height="3032" /></a><figcaption>Example of Cuisenaire rods</figcaption></figure> <blockquote><p>Cuisenaire's gift of the rods led me to teach by non-interference making it necessary to watch and listen for the signs of truth that are made, but rarely recognized.<sup id="cite_ref-FTTOM3_6-1" class="reference"><a href="#cite_note-FTTOM3-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>While the material has found an important place in myriad teacher-centered lessons, Gattegno's <a href="/wiki/Student-centred_learning" class="mw-redirect" title="Student-centred learning">student-centered</a> practice also inspired a number of educators. The French-Canadian educator Madeleine Goutard in her 1963 <i>Mathematics and Children</i>, wrote: </p> <blockquote><p>The teacher is not the person who teaches him what he does not know. He is the one who reveals the child to himself by making him more conscious of, and more creative with his own mind. The parents of a little girl of six who was using the Cuisenaire rods at school marveled at her knowledge and asked her: 'Tell us how the teacher teaches you all this', to which the little girl replied: 'The teacher teaches us nothing. We find everything out for ourselves.'<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></p></blockquote> <p><a href="/wiki/John_Holt_(educator)" title="John Holt (educator)">John Holt</a>, in his 1964 <i><a href="/wiki/How_Children_Fail" title="How Children Fail">How Children Fail</a></i>, wrote: </p> <blockquote><p>This work has changed most of my ideas about the way to use Cuisenaire rods and other materials. It seemed to me at first that we could use them as devices for packing in recipes much faster than before, and many teachers seem to be using them this way. But this is a great mistake. What we ought to do is use these materials to enable children to make for themselves, out of their own experience and discoveries, a solid and growing understanding of the ways in which numbers and the operations of arithmetic work. Our aim must be to build soundly, and if this means that we must build more slowly, so be it. Some things we will be able to do much earlier than we used to, fractions for example.</p></blockquote> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:CBlock.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/CBlock.png/170px-CBlock.png" decoding="async" width="170" height="237" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/CBlock.png/255px-CBlock.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/CBlock.png/340px-CBlock.png 2x" data-file-width="1042" data-file-height="1450" /></a><figcaption>Michael Parekowhai's Cuisenaire rods inspired installation at the Queensland Art Gallery, 2015</figcaption></figure> <p>Gattegno formed the Cuisenaire Company in <a href="/wiki/Reading,_England" class="mw-redirect" title="Reading, England">Reading</a>, England, in 1954,<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and by the end of the 1950s, Cuisenaire rods had been adopted by teachers in 10,000 schools in more than a hundred countries.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The rods received wide use in the 1960s and 1970s. In 2000, the United States-based company Educational Teaching Aids (ETA) acquired the US Cuisenaire Company and formed ETA/Cuisenaire to sell Cuisenaire rods-related material. In 2004, Cuisenaire rods were featured in an exhibition of paintings and sculptures by <a href="/wiki/New_Zealand" title="New Zealand">New Zealand</a> artist <a href="/wiki/Michael_Parekowhai" class="mw-redirect" title="Michael Parekowhai">Michael Parekowhai</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Rods">Rods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cuisenaire_rods&action=edit&section=2" title="Edit section: Rods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cuisenaire_staircase.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Cuisenaire_staircase.JPG/220px-Cuisenaire_staircase.JPG" decoding="async" width="220" height="194" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Cuisenaire_staircase.JPG/330px-Cuisenaire_staircase.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Cuisenaire_staircase.JPG/440px-Cuisenaire_staircase.JPG 2x" data-file-width="2615" data-file-height="2303" /></a><figcaption>Cuisenaire rods in a staircase arrangement</figcaption></figure> <table class="wikitable" style="text-align:center;"> <caption> </caption> <tbody><tr style="background:lightgrey;"> <th>Colour </th> <th>Common<br />abbreviation </th> <th>Length<br />(in centimetres) </th></tr> <tr> <td>White </td> <td>w </td> <td>1 </td></tr> <tr> <td style="background-color:red;">Red </td> <td>r </td> <td>2 </td></tr> <tr> <td style="background-color:lightgreen;">Light green </td> <td>g </td> <td>3 </td></tr> <tr> <td style="background-color:deeppink;">Purple (or pink) </td> <td>p </td> <td>4 </td></tr> <tr> <td style="background-color:yellow;">Yellow </td> <td>y </td> <td>5 </td></tr> <tr> <td style="background-color:darkgreen; color:white;">Dark green </td> <td>d </td> <td>6 </td></tr> <tr> <td style="background-color:black; color:white;">Black </td> <td>b </td> <td>7 </td></tr> <tr> <td style="background-color:brown; color:white;">Brown (or "tan") </td> <td>t </td> <td>8 </td></tr> <tr> <td style="background-color:blue; color:white;">Blue </td> <td>B </td> <td>9 </td></tr> <tr> <td style="background-color:orangered; color:white">Orange </td> <td>O </td> <td>10 </td></tr></tbody></table> <p>Another arrangement, common in Eastern Europe, extended by two large (> 10 cm or 4 in) sizes of rods, is the following: </p> <table class="wikitable" style="text-align:center;"> <caption> </caption> <tbody><tr style="background:lightgrey;"> <th>Colour </th> <th>Length<br />(in centimetres) </th></tr> <tr> <td>White </td> <td>1 </td></tr> <tr> <td style="background-color:pink;">Pink </td> <td>2 </td></tr> <tr> <td style="background-color:lightblue;">Light blue </td> <td>3 </td></tr> <tr> <td style="background-color:red;">Red </td> <td>4 </td></tr> <tr> <td style="background-color:yellow;">Yellow </td> <td>5 </td></tr> <tr> <td style="background-color:purple; color:white;">Purple </td> <td>6 </td></tr> <tr> <td style="background-color:black; color:white;">Black </td> <td>7 </td></tr> <tr> <td style="background-color:brown; color:white;">Brown </td> <td>8 </td></tr> <tr> <td style="background-color:darkblue; color:white;">Dark blue </td> <td>9 </td></tr> <tr> <td style="background-color:orangered; color:white;">Orange </td> <td>10 </td></tr> <tr> <td style="background-color:green; color:white;">Green </td> <td>12 </td></tr> <tr> <td style="background-color:tan;">Tan </td> <td>16 </td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Staircase_of_red_and_green_rods.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Staircase_of_red_and_green_rods.jpg/220px-Staircase_of_red_and_green_rods.jpg" decoding="async" width="220" height="119" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Staircase_of_red_and_green_rods.jpg/330px-Staircase_of_red_and_green_rods.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Staircase_of_red_and_green_rods.jpg/440px-Staircase_of_red_and_green_rods.jpg 2x" data-file-width="3236" data-file-height="1751" /></a><figcaption>A young child using a 'staircase' of red and green rods to investigate ways of composing the counting numbers</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Use_in_mathematics_teaching">Use in mathematics teaching</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cuisenaire_rods&action=edit&section=3" title="Edit section: Use in mathematics teaching"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The rods are used in teaching a variety of mathematical concepts, and with a wide age range of learners.<sup id="cite_ref-EYAdult_10-0" class="reference"><a href="#cite_note-EYAdult-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Topics they are used for include:<sup id="cite_ref-EYAdult_10-1" class="reference"><a href="#cite_note-EYAdult-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <ul><li>counting, sequences, patterns and algebraic reasoning;</li> <li>addition and subtraction (additive reasoning);</li> <li>multiplication and division (multiplicative reasoning);</li> <li>fractions, ratio and proportion;</li> <li>modular arithmetic leading to group theory.</li></ul> <div class="mw-heading mw-heading2"><h2 id="The_Silent_Way">The Silent Way</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cuisenaire_rods&action=edit&section=4" title="Edit section: The Silent Way"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Though primarily used for mathematics, they have also become popular in <a href="/wiki/Foreign_language_teaching" class="mw-redirect" title="Foreign language teaching">language-teaching</a> classrooms, particularly <a href="/wiki/The_Silent_Way" class="mw-redirect" title="The Silent Way">The Silent Way</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> They can be used: </p> <ul><li>to demonstrate most grammatical structures such as <a href="/wiki/Preposition" class="mw-redirect" title="Preposition">prepositions</a> of place, comparatives and superlatives, determiners, tenses, adverbs of time, manner, etc.;</li> <li>to show sentence and <a href="/wiki/Word_stress" class="mw-redirect" title="Word stress">word stress</a>, rising and falling intonation and word groupings;</li> <li>to create a visual model of constructs, for example the English verb tense system;<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li> <li>to represent physical objects: clocks, floor-plans, maps, people, animals, fruit, tools, etc., which can and has lead to the creation of stories.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Other_coloured_rods">Other coloured rods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cuisenaire_rods&action=edit&section=5" title="Edit section: Other coloured rods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Six_year_olds_in_class_using_a_Cuisenaire_track_to_explore_multiplication.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Six_year_olds_in_class_using_a_Cuisenaire_track_to_explore_multiplication.jpg/220px-Six_year_olds_in_class_using_a_Cuisenaire_track_to_explore_multiplication.jpg" decoding="async" width="220" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Six_year_olds_in_class_using_a_Cuisenaire_track_to_explore_multiplication.jpg/330px-Six_year_olds_in_class_using_a_Cuisenaire_track_to_explore_multiplication.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Six_year_olds_in_class_using_a_Cuisenaire_track_to_explore_multiplication.jpg/440px-Six_year_olds_in_class_using_a_Cuisenaire_track_to_explore_multiplication.jpg 2x" data-file-width="1272" data-file-height="1396" /></a><figcaption>Six year olds in class using a Cuisenaire track to explore multiplication</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cuisenaire_trays.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Cuisenaire_trays.jpg/220px-Cuisenaire_trays.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Cuisenaire_trays.jpg/330px-Cuisenaire_trays.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/43/Cuisenaire_trays.jpg/440px-Cuisenaire_trays.jpg 2x" data-file-width="600" data-file-height="450" /></a><figcaption>Trays for use with Cuisenaire rods</figcaption></figure> <p>In her first school, and in schools since then, <a href="/wiki/Maria_Montessori" title="Maria Montessori">Maria Montessori</a> used coloured rods in the classroom to teach concepts of both mathematics and length. This is possibly the first instance of coloured rods being used in the classroom for this purpose. </p><p><a href="/wiki/Catherine_Stern" title="Catherine Stern">Catherine Stern</a> also devised a set of coloured rods produced by staining wood with aesthetically pleasing colours, and published books on their use at around the same time as Cuisenaire and Gattegno.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Her rods were different colours to Cuisenaire's, and also larger, with a 2 cm (0.8 in) unit cube rather than 1 cm (0.4 in). She produced various resources to complement the rods, such as trays to arrange the rods in, and tracks to arrange them on. Tony Wing, in producing resources for Numicon, built on many of Stern's ideas, also making trays and tracks available for use with Cuisenaire rods.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>In 1961, <a href="/w/index.php?title=Seton_Pollock&action=edit&redlink=1" class="new" title="Seton Pollock (page does not exist)">Seton Pollock</a> produced the Colour Factor system,<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> consisting of rods from lengths 1 to 12 cm (0.39 to 4.7 in). Based on the work of Cuisenaire and Gattegno, he had invented a unified system for logically assigning a color to any number. After white (1), the primary colors red, blue and yellow are assigned to the first three primes (2, 3 and 5). Higher primes (7, 11 etc.) are associated with darkening shades of grey. The colors of non-prime numbers are obtained by mixing the colors associated with their factors – this is the key concept. A patent is registered in Pollock's name for an "Apparatus for teaching or studying mathematics".<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> The aesthetic and numerically comprehensive Color Factor system was marketed for some years by Seton Pollock's family, before being conveyed to the educational publishing house <a href="/wiki/Edward_Arnold_(publisher)" title="Edward Arnold (publisher)">Edward Arnold</a>. The colors of Pollock's system were named distinctively using, for example, "scarlet" instead of "red", and "amber" instead of "orange". They are listed below.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable" style="text-align:center;"> <caption> </caption> <tbody><tr style="background:lightgrey;"> <th>Colour </th> <th>Length <p>(in centimetres) </p> </th></tr> <tr> <td>White </td> <td>1 </td></tr> <tr> <td>Pink </td> <td>2 </td></tr> <tr> <td>Light Blue </td> <td>3 </td></tr> <tr> <td>Scarlet </td> <td>4 </td></tr> <tr> <td>Yellow </td> <td>5 </td></tr> <tr> <td>Violet </td> <td>6 </td></tr> <tr> <td>Grey </td> <td>7 </td></tr> <tr> <td>Crimson </td> <td>8 </td></tr> <tr> <td>Royal Blue </td> <td>9 </td></tr> <tr> <td>Amber </td> <td>10 </td></tr> <tr> <td>Dark Grey </td> <td>11 </td></tr> <tr> <td>Mauve </td> <td>12 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cuisenaire_rods&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Number_line" title="Number line">Number line</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cuisenaire_rods&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://archive.today/20130123012506/http://www.etacuisenaire.com/cuisenairerods/75th/sellon.jsp">"Cuisenaire Rods Come To America"</a>. Etacuisenaire.com. Archived from <a rel="nofollow" class="external text" href="http://www.etacuisenaire.com/cuisenairerods/75th/sellon.jsp">the original</a> on 2013-01-23<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-10-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Cuisenaire+Rods+Come+To+America&rft.pub=Etacuisenaire.com&rft_id=http%3A%2F%2Fwww.etacuisenaire.com%2Fcuisenairerods%2F75th%2Fsellon.jsp&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGregg" class="citation web cs1">Gregg, Simon. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140913052337/http://www.mathagogy.com/simon-gregg-how-i-teach-using-cuisenaire-rods/">"How I teach using Cuisenaire rods"</a>. mathagogy.com. Archived from <a rel="nofollow" class="external text" href="http://www.mathagogy.com/simon-gregg-how-i-teach-using-cuisenaire-rods/">the original</a> on 13 September 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">22 April</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=How+I+teach+using+Cuisenaire+rods&rft.pub=mathagogy.com&rft.aulast=Gregg&rft.aufirst=Simon&rft_id=http%3A%2F%2Fwww.mathagogy.com%2Fsimon-gregg-how-i-teach-using-cuisenaire-rods%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20131029222159/http://teachertech.rice.edu/Participants/silha/Lessons/exercise2.html">"Teaching fractions with Cuisenaire rods"</a>. Teachertech.rice.edu. Archived from <a rel="nofollow" class="external text" href="http://teachertech.rice.edu/Participants/silha/Lessons/exercise2.html">the original</a> on 2013-10-29<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-10-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Teaching+fractions+with+Cuisenaire+rods&rft.pub=Teachertech.rice.edu&rft_id=http%3A%2F%2Fteachertech.rice.edu%2FParticipants%2Fsilha%2FLessons%2Fexercise2.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGattegno" class="citation book cs1">Gattegno, Caleb. <i>The Science of Education Part 2B: the Awareness of Mathematization</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0878252084" title="Special:BookSources/978-0878252084"><bdi>978-0878252084</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Science+of+Education+Part+2B%3A+the+Awareness+of+Mathematization&rft.isbn=978-0878252084&rft.aulast=Gattegno&rft.aufirst=Caleb&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFroebel_Web" class="citation web cs1">Froebel Web. <a rel="nofollow" class="external text" href="http://www.froebelweb.org/web2026.html">"Georges Cuisenaire created numbers in color"</a>. Froebelweb.org<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-10-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Georges+Cuisenaire+created+numbers+in+color&rft.pub=Froebelweb.org&rft.au=Froebel+Web&rft_id=http%3A%2F%2Fwww.froebelweb.org%2Fweb2026.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-FTTOM3-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-FTTOM3_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FTTOM3_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGattegno2011" class="citation book cs1">Gattegno, Caleb (2011). <a rel="nofollow" class="external text" href="https://issuu.com/eswi/docs/fttomv3webbook"><i>For the Teaching of Mathematics Volume 3</i></a> (2nd ed.). Educational Solutions. pp. 173–178. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-87825-337-1" title="Special:BookSources/978-0-87825-337-1"><bdi>978-0-87825-337-1</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">28 October</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=For+the+Teaching+of+Mathematics+Volume+3&rft.pages=173-178&rft.edition=2nd&rft.pub=Educational+Solutions&rft.date=2011&rft.isbn=978-0-87825-337-1&rft.aulast=Gattegno&rft.aufirst=Caleb&rft_id=https%3A%2F%2Fissuu.com%2Feswi%2Fdocs%2Ffttomv3webbook&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoutard2015" class="citation book cs1">Goutard, Madeleine (2015). <a rel="nofollow" class="external text" href="http://shop.cuisenaire.co.uk/mathematics-and-children/"><i>Mathematics and Children</i></a> (2nd ed.). Reading: Educational Explorers Limited. p. 184. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-85225-602-2" title="Special:BookSources/978-0-85225-602-2"><bdi>978-0-85225-602-2</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">28 October</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+and+Children&rft.place=Reading&rft.pages=184&rft.edition=2nd&rft.pub=Educational+Explorers+Limited&rft.date=2015&rft.isbn=978-0-85225-602-2&rft.aulast=Goutard&rft.aufirst=Madeleine&rft_id=http%3A%2F%2Fshop.cuisenaire.co.uk%2Fmathematics-and-children%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.cuisenaire.co.uk/index.php/home/about-us">"About Us"</a>. <i>The Cuisenaire Company</i><span class="reference-accessdate">. Retrieved <span class="nowrap">28 October</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Cuisenaire+Company&rft.atitle=About+Us&rft_id=http%3A%2F%2Fwww.cuisenaire.co.uk%2Findex.php%2Fhome%2Fabout-us&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140610195412/http://www.highbeam.com/doc/1G1-255688425.html"><i>Association of Teachers of Mathematics Honours Dr. Caleb Gattegno at Annual Conference</i></a>, April 14, 2011, archived from <a rel="nofollow" class="external text" href="http://www.highbeam.com/doc/1G1-255688425.html">the original</a> on June 10, 2014<span class="reference-accessdate">, retrieved <span class="nowrap">January 2,</span> 2014</span> – via <a href="/wiki/Associated_Press" title="Associated Press">Associated Press</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Association+of+Teachers+of+Mathematics+Honours+Dr.+Caleb+Gattegno+at+Annual+Conference&rft.date=2011-04-14&rft_id=http%3A%2F%2Fwww.highbeam.com%2Fdoc%2F1G1-255688425.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-EYAdult-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-EYAdult_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-EYAdult_10-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreggOllertonWilliams2017" class="citation book cs1">Gregg, Simon; Ollerton, Mike; Williams, Helen (2017). <a rel="nofollow" class="external text" href="https://www.atm.org.uk/Shop/Cuisenaire---from-Early-Years-to-Adult/Cuisenaire---from-Early-Years-to-Adult-Book-and-Download/ACT103pk"><i>Cuisenaire – from Early Years to Adult</i></a>. Derby: Association of Teachers of Mathematics. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-898611-97-4" title="Special:BookSources/978-1-898611-97-4"><bdi>978-1-898611-97-4</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">3 October</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cuisenaire+%E2%80%93+from+Early+Years+to+Adult&rft.place=Derby&rft.pub=Association+of+Teachers+of+Mathematics&rft.date=2017&rft.isbn=978-1-898611-97-4&rft.aulast=Gregg&rft.aufirst=Simon&rft.au=Ollerton%2C+Mike&rft.au=Williams%2C+Helen&rft_id=https%3A%2F%2Fwww.atm.org.uk%2FShop%2FCuisenaire---from-Early-Years-to-Adult%2FCuisenaire---from-Early-Years-to-Adult-Book-and-Download%2FACT103pk&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160304050227/http://www.glenys-hanson.info/pedagogical-articles/grammar-articles/beginner-silent-way-exercises-using-rods/">"Beginner Silent Way exercises using Cuisenaire rods"</a>. glenys-hanson.info. Archived from <a rel="nofollow" class="external text" href="http://www.glenys-hanson.info/pedagogical-articles/grammar-articles/beginner-silent-way-exercises-using-rods/">the original</a> on 2016-03-04<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-04-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Beginner+Silent+Way+exercises+using+Cuisenaire+rods&rft.pub=glenys-hanson.info&rft_id=http%3A%2F%2Fwww.glenys-hanson.info%2Fpedagogical-articles%2Fgrammar-articles%2Fbeginner-silent-way-exercises-using-rods%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160316223851/http://www.glenys-hanson.info/pedagogical-articles/grammar-articles/english-verb-tenses-a-dynamic-presentation/">"English Verb Tenses: a dynamic presentation using the Cuisenaire Rods"</a>. glenys-hanson.info. Archived from <a rel="nofollow" class="external text" href="http://www.glenys-hanson.info/pedagogical-articles/grammar-articles/english-verb-tenses-a-dynamic-presentation">the original</a> on 2016-03-16<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-04-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=English+Verb+Tenses%3A+a+dynamic+presentation+using+the+Cuisenaire+Rods&rft.pub=glenys-hanson.info&rft_id=http%3A%2F%2Fwww.glenys-hanson.info%2Fpedagogical-articles%2Fgrammar-articles%2Fenglish-verb-tenses-a-dynamic-presentation&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=Yvb2VFUKQv4">"Silent Way: rods, describing a scene (part 6 of 8)"</a>. YouTube. 2010-04-11. <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211212/Yvb2VFUKQv4">Archived</a> from the original on 2021-12-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-10-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Silent+Way%3A+rods%2C+describing+a+scene+%28part+6+of+8%29&rft.pub=YouTube&rft.date=2010-04-11&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DYvb2VFUKQv4&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.sternmath.com/">"Stern Math: A Multisensory, Manipulative-Based, Conceptual Approach"</a>. Sternmath.com<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-05-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Stern+Math%3A+A+Multisensory%2C+Manipulative-Based%2C+Conceptual+Approach&rft.pub=Sternmath.com&rft_id=http%3A%2F%2Fwww.sternmath.com%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20180406133248/http://www.sternmath.com/who-we-are.html">"Stern Math: About the Authors"</a>. Sternmath.com. Archived from <a rel="nofollow" class="external text" href="http://www.sternmath.com/who-we-are.html">the original</a> on 2018-04-06<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-05-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Stern+Math%3A+About+the+Authors&rft.pub=Sternmath.com&rft_id=http%3A%2F%2Fwww.sternmath.com%2Fwho-we-are.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWing1996" class="citation journal cs1">Wing, Tony (1 December 1996). "Working towards mental arithmetic... and (still) counting". <i>Mathematics Teaching</i> (157): 10–14.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematics+Teaching&rft.atitle=Working+towards+mental+arithmetic...+and+%28still%29+counting&rft.issue=157&rft.pages=10-14&rft.date=1996-12-01&rft.aulast=Wing&rft.aufirst=Tony&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160412072206/http://www.coloracademy.co.uk/ColorAcademy%202006/subjects/mathematics/mathematics.htm">"ColorAcademy 2005 - Mathematics & Measurement"</a>. ColorAcademy. 2004. Archived from <a rel="nofollow" class="external text" href="http://www.coloracademy.co.uk/ColorAcademy%202006/subjects/mathematics/mathematics.htm">the original</a> on 2016-04-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-05-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=ColorAcademy+2005+-+Mathematics+%26+Measurement&rft.pub=ColorAcademy&rft.date=2004&rft_id=http%3A%2F%2Fwww.coloracademy.co.uk%2FColorAcademy%25202006%2Fsubjects%2Fmathematics%2Fmathematics.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span>(brief overview of the history of Colour Factor)</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://patents.google.com/patent/US3204343">"Apparatus for teaching or studying mathematics"</a>. United States Patent Office. 1965<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-02-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Apparatus+for+teaching+or+studying+mathematics&rft.pub=United+States+Patent+Office&rft.date=1965&rft_id=https%3A%2F%2Fpatents.google.com%2Fpatent%2FUS3204343&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEwbank1978" class="citation journal cs1">Ewbank, William A. (1978). "The Use of Color for Teaching Mathematics". <i>The Arithmetic Teacher</i>. <b>26</b> (1). National Council of Teachers of Mathematics: 53–57. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.5951%2FAT.26.1.0053">10.5951/AT.26.1.0053</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/41190497">41190497</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Arithmetic+Teacher&rft.atitle=The+Use+of+Color+for+Teaching+Mathematics&rft.volume=26&rft.issue=1&rft.pages=53-57&rft.date=1978&rft_id=info%3Adoi%2F10.5951%2FAT.26.1.0053&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F41190497%23id-name%3DJSTOR&rft.aulast=Ewbank&rft.aufirst=William+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACuisenaire+rods" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cuisenaire_rods&action=edit&section=8" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.persee.fr/doc/apliu_0248-9430_1996_num_16_2_1038">Cuisenaire rods in the language classroom</a> – article by John Mullen</li> <li><a rel="nofollow" class="external text" href="http://issuu.com/jmcuenca/docs/maths_with_rods">Maths with Rods - 40 exercise tabs to play with parents</a> – downloadable book with Creative Commons License</li> <li><a rel="nofollow" class="external text" href="http://teachertech.rice.edu/Participants/silha/Lessons/cuisen2.html">Learn Fractions with Cuisenaire Rods. Introduction</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210422121130/http://teachertech.rice.edu/Participants/silha/Lessons/cuisen2.html">Archived</a> 2021-04-22 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cuisenaire_rods&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Cuisenaire_rods" class="extiw" title="commons:Category:Cuisenaire rods">Cuisenaire rods</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=ae0McT5WYa8&list=PLBB2E26B16B96E9F5&feature=plcp&context=C3fd2f22FDOEgsToPDskKzaTHehRGAu5V8EM6hajul">A 1961 film from the National Film Board of Canada. Caleb Gattegno conducting a demonstration lesson with Cuisenaire rods: In 3 parts on YouTube</a></li> <li><a rel="nofollow" class="external text" href="http://mathtoybox.com/numblox/NumBlox.html">Online Cuisenaire rods</a> (NumBlox Freeplay)</li> <li><a rel="nofollow" class="external text" href="https://cuisenaire-rods.surge.sh/">Online interactive Cuisenaire rods</a></li> <li><a rel="nofollow" class="external text" href="http://www.cuisenaire.co.uk">The Cuisenaire Company</a> – registered UK trademark holder, with background to Cuisenaire and Gattegno.</li> <li><a rel="nofollow" class="external text" href="http://cuisenaire.eu">La méthode Cuisenaire – Les nombres en Couleurs – site officiel (in French)</a></li> <li><a rel="nofollow" class="external text" href="http://goupil.eklablog.fr/les-noums-de-brissiaud-ancetres-et-enjeux-a175398670">History of the number rods from 1806 to 2020</a> (in French).</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Cuisenaire_rods&oldid=1258723404">https://en.wikipedia.org/w/index.php?title=Cuisenaire_rods&oldid=1258723404</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Belgian_inventions" title="Category:Belgian inventions">Belgian inventions</a></li><li><a href="/wiki/Category:Language_education_materials" title="Category:Language education materials">Language education materials</a></li><li><a href="/wiki/Category:Mathematical_manipulatives" title="Category:Mathematical manipulatives">Mathematical manipulatives</a></li><li><a href="/wiki/Category:Lists_of_shapes" title="Category:Lists of shapes">Lists of shapes</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:EngvarB_from_February_2024" title="Category:EngvarB from February 2024">EngvarB from February 2024</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li><li><a href="/wiki/Category:Commons_category_link_is_on_Wikidata" title="Category:Commons category link is on Wikidata">Commons category link is on Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 21 November 2024, at 07:04<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Cuisenaire_rods&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-697b7966c5-9mt8t","wgBackendResponseTime":174,"wgPageParseReport":{"limitreport":{"cputime":"0.383","walltime":"0.481","ppvisitednodes":{"value":1393,"limit":1000000},"postexpandincludesize":{"value":35394,"limit":2097152},"templateargumentsize":{"value":741,"limit":2097152},"expansiondepth":{"value":13,"limit":100},"expensivefunctioncount":{"value":2,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":67998,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 402.206 1 -total"," 54.01% 217.246 1 Template:Reflist"," 35.71% 143.629 12 Template:Cite_web"," 17.13% 68.896 1 Template:Short_description"," 11.16% 44.882 1 Template:Commons_category"," 10.62% 42.719 1 Template:Sister_project"," 10.25% 41.220 2 Template:Pagetype"," 10.18% 40.955 1 Template:Side_box"," 8.55% 34.383 6 Template:Cvt"," 5.03% 20.221 4 Template:Cite_book"]},"scribunto":{"limitreport-timeusage":{"value":"0.226","limit":"10.000"},"limitreport-memusage":{"value":7128821,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-f69cdc8f6-nv2q5","timestamp":"20241122145450","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Cuisenaire rods","url":"https:\/\/en.wikipedia.org\/wiki\/Cuisenaire_rods","sameAs":"http:\/\/www.wikidata.org\/entity\/Q508933","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q508933","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2005-02-27T03:38:37Z","dateModified":"2024-11-21T07:04:29Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/b\/b0\/Cuisenaire_ten.JPG","headline":"learning aids"}</script> </body> </html>